getting a stochastic process from a conservative lagrangian a first approach abstract the transition probability p v for a stochastic process generated by a conservative lagrangian l l 0 e v is obtained at first order from a perturbation series found using a path integral this p v corresponds to the transition probability for a random walk with a probability density given by the sum of a normal distribution and a perturbation which may be understood as the contribution of the interaction of the random walk with the external field it is also found that the moment generating function for p v can be expressed as the generating function of a normal distribution modified by a perturbation applications of these results to a linear potential a harmonic oscillator potential and an exponentially decaying potential are shown

optimization of sparse linear arrays using harmony search algorithms a sparse linear array composed of a uniformly spaced core subarray and an extended sparse subarray is synthesized using a harmony search hs and an exploratory harmony search ehs algorithms the optimal solution is searched by changing the amplitudes of all the elements and the positions of the extended elements under a set of practical constraints performance of the ehs the hs a genetic algorithm ga and a particle swarm optimization pso algorithm has also been compared in synthesizing these sparse linear arrays

a novel meta heuristic optimization algorithm inspired by group hunting of animals hunting search a novel optimization algorithm is presented inspired by group hunting of animals such as lions wolves and dolphins although these hunters have differences in the way of hunting they are common in that all of them look for a prey in a group the hunters encircle the prey and gradually tighten the ring of siege until they catch the prey in addition each member of the group corrects its position based on its own position and the position of other members if the prey escapes from the ring hunters reorganize the group to siege the prey again several benchmark numerical optimization problems constrained and unconstrained are presented here to demonstrate the effectiveness and robustness of the proposed hunting search hus algorithm the results indicate that the proposed method is a powerful search and optimization technique it yields better solutions compared to those obtained by some current algorithms when applied to continuous problems

decoherence of semiclassical wigner functions the lindblad master equation governs the general markovian evolution of a density operator for an open quantum system semiclassical wigner functions represent density operators in phase space in terms of chords on a classical manifold so that the amplitude and phase of each chord contribution is classically defined inserting such a wigner function into a phase space version of the master equation its explicit evolution is derived in the absence of dissipation there results a simple extension of the unitary evolution of the semiclassical wigner function which does not affect the phase of each chord contribution while dampening its amplitude exponentially projecting the wigner function on to an orthogonal position or momentum basis the dampening of long chords emerges as the exponential decay of off diagonal elements of the density matrix

statistical entropy of open quantum systems dissipative quantum systems are frequently described within the framework of the so called system plus reservoir approach in this work we assign their description to the maximum entropy formalism and compare the resulting thermodynamic properties with those of the well established approaches due to the non negligible coupling to the heat reservoir these systems are nonextensive by nature and the former task may require the use of nonextensive parameter dependent informational entropies in doing so we address the problem of choosing appropriate forms of those entropies in order to describe a consistent thermodynamics for dissipative quantum systems nevertheless even having chosen the most successful and popular forms of those entropies we have proven our model to be a counterexample where this sort of approach leads us to wrong results

stochastic quantum langevin equation the stochastic representation of quantum mechanics is used to give a purely stochastic treatment of the quantum langevin equation a general coupling involving positions and velocities of the particle and harmonic modes with arbitrary dependence on the particle s position is dealt with summing over the modes in the path integral and using stochastic integrals the author obtains explicitly the reduced measure that is the stochastic process representing the time evolution of the small system in the presence of noise contact is made with the operatorial representation and a relation is established between the correlations of the noise in both representations a general condition on the coupling constants is given for recovering time locality in the continuum limit and the effects of renormalisation are re analysed within this purely stochastic approach

functional integral treatment of some quantum nondemolition systems in the scheme of a quantum nondemolition qnd measurement an observable is measured without perturbing its evolution in the context of studies of decoherence in quantum computing we examine the open quantum system of a two level atom or equivalently a spin 1 2 system in interaction with quantum reservoirs of either oscillators or spins under the qnd condition of the hamiltonian of the system commuting with the system reservoir interaction for completeness we also examine the well known non qnd spin bose problem for all these many body systems we use the methods of functional integration to work out the propagators the propagators for the qnd hamiltonians are shown to be analogous to the squeezing and rotation operators respectively for the two kinds of baths considered squeezing and rotation being both phase space area preserving canonical transformations this brings out an interesting connection between the energy preserving qnd hamiltonians and the homogeneous linear canonical transformations

zero point energies the uncertainty principle and positivity of the quantum brownian density operator high temperature and white noise approximations are frequently invoked when deriving the quantum brownian equation for an oscillator even if this white noise approximation is avoided it is shown that if the zero point energies of the environment are neglected as they often are the resultant equation will violate not only the basic tenet of quantum mechanics that requires the density operator to be positive but also the uncertainty principle when the zero point energies are included asymptotic results describing the evolution of the oscillator are obtained that preserve positivity and therefore the uncertainty principle

an intelligent global harmony search approach to continuous optimization problems abstract harmony search algorithm is a meta heuristic optimization method imitating the music improvisation process where musicians improvise their instruments pitches searching for a perfect state of harmony to solve continuous optimization problems more efficiently this paper presents an improved harmony search algorithm using the swarm intelligence technique applying the proposed algorithm to several well known benchmark problems it is shown that it can find better solutions in comparison with both basic harmony search algorithms and improved harmony search algorithms such as the self adaptive global best harmony search as well as novel global harmony search furthermore a study on the effect of changing the parameters of the proposed algorithm on its performance is carried out finally the proper values of the algorithm parameters are suggested

a novel modified differential evolution algorithm for constrained optimization problems a novel modified differential evolution algorithm nmde is proposed to solve constrained optimization problems in this paper the nmde algorithm modifies scale factor and crossover rate using an adaptive strategy for any solution if it is at a standstill its own scale factor and crossover rate will be adjusted in terms of the information of all successful solutions we can obtain satisfactory feasible solutions for constrained optimization problems by combining the nmde algorithm and a common penalty function method experimental results show that the proposed algorithm can yield better solutions than those reported in the literature for most problems and it can be an efficient alternative to solving constrained optimization problems

randomness as source for inspiring solution search methods music based approaches abstract as the world progresses towards industrialization engineering problems become increasingly complex and it becomes even more difficult to optimize these problems the reason for this is the increasing complexity of variables dimensions space complexity and time complexity in order to be able to cope with such a situation randomized intelligent optimization and search algorithms are proposed to optimize numerical benchmarking problems multi objective problems and solve difficult problems including a large number of variables dimensions constraints and objectives metaheuristic random search and optimization methods are widely used to search and find the most appropriate solutions for large scale optimization problems in an acceptable time they are general purposed methods that can be efficiently applied to optimization and search problems without too much modification to accommodate a specific probing metaheuristic optimization algorithms are generally categorized as physics music sociology biology swarm mathematics plant chemistry sports water and hybrid based although most of the intelligent metaheuristic methods are inspired by physics and biology concepts activities rules and processes in music can be an inspiration source of new intelligent optimization and search techniques that is why novel and efficient music inspired intelligent optimization and search methods having effective exploitation and exploration capabilities have been proposed in this paper music based metaheuristic optimization algorithms were gathered and analyzed for the first time harmony search and its versions melody search algorithm and method of musical composition have been examined in detail furthermore their performances have been compared within both unconstrained numerical benchmark functions and constrained problems and the obtained results from music based algorithms have been comparatively studied

finite time thermodynamics of port hamiltonian systems abstract in this paper we identify a class of time varying port hamiltonian systems that is suitable for studying problems at the intersection of statistical mechanics and control of physical systems those port hamiltonian systems are able to modify their internal structure as well as their interconnection with the environment over time the framework allows us to prove the first and second laws of thermodynamics but also lets us apply results from optimal and stochastic control theory to physical systems in particular we show how to use linear control theory to optimally extract work from a single heat source over a finite time interval in the manner of maxwell s demon furthermore the optimal controller is a time varying port hamiltonian system which can be physically implemented as a variable linear capacitor and transformer we also use the theory to design a heat engine operating between two heat sources in finite time carnot like cycles of maximum power and we compare those two heat engines

solutions of generic bilinear master equations for a quantum oscillator positive and factorized conditions on stationary states abstract we obtain the solutions of the generic bilinear master equation for a quantum oscillator with constant coefficients in the gaussian form the well behavedness and positive semidefiniteness of the stationary states could be characterized by a three dimensional minkowski vector by requiring the stationary states to satisfy a factorized condition we obtain a generic class of master equations that includes the well known ones and their generalizations some of which are completely positive a further subset of the master equations with the gibbs states as stationary states is also obtained for master equations with not completely positive generators an analysis on the stationary states for a given initial state suggests conditions on the coefficients of the master equations that generate positive evolution

a note on teaching learning based optimization algorithm teaching learning based optimization tlbo seems to be a rising star from amongst a number of metaheuristics with relatively competitive performances it is reported that it outperforms some of the well known metaheuristics regarding constrained benchmark functions constrained mechanical design and continuous non linear numerical optimization problems such a breakthrough has steered us towards investigating the secrets of tlbo s dominance this paper reports our findings on tlbo qualitatively and quantitatively through code reviews and experiments respectively our findings have revealed three important mistakes regarding tlbo 1 at least one unreported but important step 2 incorrect formulae on a number of fitness function evaluations and 3 misconceptions about parameter less control additionally unfair experimental settings conditions were used to conduct experimental comparisons e g different stopping criteria the experimental results for constrained and unconstrained benchmark functions under fairly equal conditions failed to validate its performance supremacy the ultimate goal of this paper is to provide reminders for metaheuristics researchers and practitioners in order to avoid similar mistakes regarding both the qualitative and quantitative aspects and to allow fair comparisons of the tlbo algorithm to be made with other metaheuristic algorithms

on the quantum dissipative generator weak coupling approximation and stochastic approach for a quantum open system the so called schr dinger langevin picture has been revisited in a second order perturbation it is shown that a non markovian evolution for the stochastic state vector leads to a dissipative generator which has a kossakowski lindblad form in this context it is possible to analyse the completely positive condition the equivalence of this picture with the trace out technique in the weak coupling approximation has been proved

path integral semiclassical and stochastic propagators for markovian open quantum systems we develop the path integral theory for master equations of general lindblad form positive semigroups describing markovian open quantum systems first the hamiltonian path integral expression for the propagator is derived which exhibits nicely the decoherence of pairs of phase space histories a very appealing picture arises in the semiclassical limit where the degree of decoherence is expressible in terms of a phase space decoherence distance functional for the important class of effective hamiltonians quadratic in the momenta we derive the lagrangian version of the path integral propagator we then evaluate the path integral approximately in a stationary phase approximation leading to a van vleck type propagator valid under semiclassical conditions we also derive the propagator for the soluble damped harmonic oscillator in closed form from path integrals finally connections to the active field of stochastic pure state descriptions of open quantum systems are established here in particular to linear quantum state diffusion

the nirenberg problem and its generalizations a unified approach making use of integral representations we develop a unified approach to establish blow up profiles compactness and existence of positive solutions of the conformally invariant equations p sigma v kv frac n 2 sigma n 2 sigma on the standard unit sphere mathbb s n for all sigma in 0 n 2 where p sigma is the intertwining operator of order 2 sigma finding positive solutions of these equations is equivalent to seeking metrics in the conformal class of the standard metric on spheres with prescribed certain curvatures when sigma 1 it is the prescribing scalar curvature problem or the nirenberg problem and when sigma 2 it is the prescribing q curvature problem

on higher spin partition functions we observe that the partition function of the set of all free massless higher spins s 0 1 2 3 in flat space is equal to one the ghost determinants cancel against the physical ones or equivalently the regularized total number of degrees of freedom vanishes this reflects large underlying gauge symmetry and suggests analogy with supersymmetric or topological theory the z 1 property extends also to the ads background i e the 1 loop vacuum partition function of vasiliev theory is equal to 1 assuming a particular regularization of the sum over spins this was noticed earlier as a consistency requirement for the vectorial ads cft duality we find that z 1 is true also in the conformal higher spin theory with higher derivative kinetic terms expanded near flat or conformally flat s4 background we also consider the partition function of free conformal theory of symmetric traceless rank s tensor field which has 2 derivative kinetic term but only scalar gauge invariance in flat 4d space this non unitary theory has weyl invariant action in curved background and it corresponds to partially massless field in ads5 we discuss in detail the special case of s 2 or conformal graviton compute the corresponding conformal anomaly coefficients and compare them with previously found expressions for generic representations of conformal group in 4 dimensions

a tabu harmony search based approach to fuzzy linear regression we propose an unconstrained global continuous optimization method based on tabu search and harmony search to support the design of fuzzy linear regression flr models tabu and harmony search strategies are used for diversification and intensification of flr respectively the proposed approach offers the flexibility to use any kind of an objective function based on client s requirements or requests and the nature of the dataset and then attains its minimum error moreover we elaborate on the error produced by this method and compare it with the errors resulting from the other known estimation methods to study the performance of the method three categories of datasets are considered numeric inputs symmetric fuzzy outputs symmetric fuzzy inputs symmetric fuzzy outputs and numeric inputs asymmetric fuzzy outputs through a series of experiments we demonstrate that in terms of the produced error with different model fitting measurements the proposed method outperforms or is pareto equivalent to the existing methods reported in the literature

construction of coarse grained order parameters in nonequilibrium systems we develop a renormalization group rg procedure that includes important system specific features the key ingredient is to systematize the coarse graining procedure that generates the rg flow the coarse graining technology comes from the control and operator theoretic model reduction the resulting generalized rg is a consistent generalization of the wilsonian rg we apply the procedure to a deterministic nonlinear wave equation nlwe with probabilistic initial conditions we derive the form of the projection operator from the dynamics of the nlwe and then use it to generate the rg flow for the distribution of initial conditions the probability density of the initial conditions is chosen to be a boltzmann weight that is quartic in the field variables in our calculation we find that in contrast to conventional implementations of the rg naive power counting breaks down we also show that the resulting rg equations are different from those derived from the conventional rg

a square root method for the density matrix and its applications to lindblad operators abstract the evolution of open systems subject to both hamiltonian and dissipative forces is studied by writing the nm element of the time t dependent density matrix in the form nm t 1 a 1 a n t m t the so called square root factors the t s are non square matrices and are averaged over a systems of the ensemble this square root description is exact evolution equations are then postulated for the t factors such as to reduce to the lindblad type evolution equations for the diagonal terms in the density matrix for the off diagonal terms they differ from the lindblad equations the square root factors t are not unique and the equations for the t s depend on the specific representation chosen two criteria can be suggested for fixing the choice of t s one is simplicity of the resulting equations and the other has to do with the reduction of the difference between the t formalism and the lindblad equations when the method is tested on cases which have been previously treated by other methods our results agree with them examples chosen are i molecular systems such that are either periodically driven near level degeneracies for which we calculate the decoherence occurring in multiple landau zener transitions or else when undergoing descent around conical intersections in the potential surfaces ii formal dissipative systems with lindblad type operators representing either a non markovian process or a two state system coupled to bosons attractive features of the present factorization method are complete positivity the no higher than linear increase of the implementation effort with the number of states involved and the introduction of randomness only at the start of the process

novel meta heuristic algorithms for clustering web documents clustering the web documents is one of the most important approaches for mining and extracting knowledge from the web recently one of the most attractive trends in clustering the high dimensional web pages has been tilt toward the learning and optimization approaches in this paper we propose novel hybrid harmony search hs based algorithms for clustering the web documents that finds a globally optimal partition of them into a specified number of clusters by modeling clustering as an optimization problem first we propose a pure harmony search based clustering algorithm that finds near global optimal clusters within a reasonable time then we hybridize k means and harmony clustering in two ways to achieve better clustering experimental results reveal that the proposed algorithms can find better clusters when compared to similar methods and also illustrate the robustness of the hybrid clustering algorithms

propagator for narrow potential barriers the schrodinger equation in integral form is applied to the one dimensional scattering problem in the case of a narrow potential barrier since the kernel can be considered in a first approximation separable an explicit expression for the propagator is found by means of the complementary error function the problem of a particle confined in a half space and interacting with a narrow potential barrier is also considered and solved in an approximate way

semiclassical klein kramers and smoluchowski equations for the brownian motion of a particle in an external potential the quantum brownian motion of a particle in an external potential v x is treated using the master equation for the wigner distribution function w x p t in phase space x p a heuristic method of determination of diffusion coefficients in the master equation is proposed the time evolution equation so obtained contains explicit quantum correction terms up to o 4 and in the classical limit 0 reduces to the klein kramers equation for a quantum oscillator the method yields an evolution equation for w x p t coinciding with that of agarwal 1971 phys rev a 4 739 in the non inertial regime by applying the brinkman expansion of the momentum distribution in weber functions brinkman 1956 physica 22 29 the corresponding semiclassical smoluchowski equation is derived

chemical langevin equation a path integral view of gillespie s derivation in 2000 gillespie rehabilitated the chemical langevin equation cle by describing two conditions that must be satisfied for it to yield a valid approximation of the chemical master equation cme in this work we construct an original path integral description of the cme and show how applying gillespie s two conditions to it directly leads to a path integral equivalent to the cle we compare this approach to the path integral equivalent of a large system size derivation and show that they are qualitatively different in particular both approaches involve converting many sums into many integrals and the difference between the two methods is essentially the difference between using the euler maclaurin formula and using riemann sums our results shed light on how path integrals can be used to conceptualize coarse graining biochemical systems and are readily generalizable

an improved global best harmony search algorithm this paper introduces an improved global best harmony search ighs algorithm the proposed modifications effectively combines a novel improvisation scheme with a previously developed mechanism for updating the pitch adjustment rate par and the distance bandwidth bw the aim of this modification is to efficiently investigate the search space by going through the stages of exploration and exploitation the proposed algorithm is compared against seven previous modifications to hs using rigorous statistical tests when applied to the cec05 benchmark functions showing a superior performance on most of the tested functions

global best harmony search harmony search hs is a new meta heuristic optimization method imitating the music improvisation process where musicians improvise their instruments pitches searching for a perfect state of harmony a new variant of hs called global best harmony search ghs is proposed in this paper where concepts from swarm intelligence are borrowed to enhance the performance of hs the performance of the ghs is investigated and compared with hs and a recently developed variation of hs the experiments conducted show that the ghs generally outperformed the other approaches when applied to ten benchmark problems the effect of noise on the performance of the three hs variants is investigated and a scalability study is conducted the effect of the ghs parameters is analyzed finally the three hs variants are compared on several integer programming test problems the results show that the three approaches seem to be an efficient alternative for solving integer programming problems 2007 elsevier inc all rights reserved

a self adaptive global best harmony search algorithm for continuous optimization problems this paper presents a self adaptive global best harmony search sghs algorithm for solving continuous optimization problems in the proposed sghs algorithm a new improvisation scheme is developed so that the good information captured in the current global best solution can be well utilized to generate new harmonies the harmony memory consideration rate hmcr and pitch adjustment rate par are dynamically adapted by the learning mechanisms proposed the distance bandwidth bw is dynamically adjusted to favor exploration in the early stages and exploitation during the final stages of the search process extensive computational simulations and comparisons are carried out by employing a set of 16 benchmark problems from literature the computational results show that the proposed sghs algorithm is more effective in finding better solutions than the state of the art harmony search hs variants

hybridizing harmony search algorithm with different mutation operators for continuous problems abstract harmony search hs is a recent ea inspired by musical improvisation process to seek a pleasing harmony mutation is a vital component used in evolutionary algorithms ea where a value in the population is randomly selected to be altered to improve the evolution process the original hs algorithm applies an operation similar to mutation during the random consideration operator during random selection operator a value within the range of the decision variable is selected randomly to explore different areas in the search space this paper aims at experimentally evaluating the performance of hs algorithm after replacing the random consideration operator in the original hs with five different mutation methods the different variations of hs are experimented on standard benchmark functions in terms of final obtained solution and convergence speed the results show that using polynomial mutation improves the performance of the hs algorithm for most of the used functions

sobolev trace inequalities of order four we establish sharp trace sobolev inequalities of order four on euclidean d balls for d 4 when d 4 our inequality generalizes the classical second order lebedev milin inequality on euclidean 2 balls our method relies on the use of scattering theory on hyperbolic d balls as an application we characterize the extremal metric of the main term in the log determinant formula corresponding to the conformal laplacian coupled with the boundary robin operator on euclidean 4 balls which surprisingly is not the flat metric on the ball

global dynamic harmony search algorithm gdhs this paper presents a new modification of harmony search hs algorithm to improve its accuracy and convergence speed and eliminates setting parameters that have to be defined before optimization process and it is difficult to predict fixed values for all kinds of problems the proposed algorithm is named global dynamic harmony search gdhs in this modification all the key parameters are changed to dynamic mode and there is no need to predefine any parameters also the domain is changed to dynamic mode to help a faster convergence two experiments with large sets of benchmark functions are executed to compare the proposed algorithms with other ones in the first experiment 15 benchmark problems are used to compare the proposed algorithm with other similar algorithms based on the harmony search method and in the second experiment 47 benchmark problems are used to compare the performance of the gdhs with other algorithms from different families including ga pso de and abc algorithms results showed that the proposed algorithm outperforms the other algorithms considering the point that the gdhs does not require any predefined parameter

dressed coordinates the path integral approach the recently introduced dressed coordinates are studied in the path integral approach these coordinates are defined in the context of a harmonic oscillator linearly coupled to massless scalar field and it is shown that in this model the dressed coordinates appear as a coordinate transformation preserving the path integral functional measure the analysis also generalizes the sum rules established in a previous work

superoperator representation of nonlinear response unifying quantum field and mode coupling theories computing response functions by following the time evolution of superoperators in liouville space whose vectors are ordinary hilbert space operators offers an attractive alternative to the diagrammatic perturbative expansion of many body equilibrium and nonequilibrium green s functions the bookkeeping of time ordering is naturally maintained in real physical time allowing the formulation of wick s theorem for superoperators giving a factorization of higher order response functions in terms of two fundamental green s functions backward propagations and analytic continuations using artificial times keldysh loops and matsubara contours are avoided a generating functional for nonlinear response functions unifies quantum field theory and the classical mode coupling formalism of nonlinear hydrodynamics and may be used for semiclassical expansions classical response functions are obtained without the explicit computation of stability matrices

a hybrid pso ga algorithm for constrained optimization problems the main objective of this paper is to present a hybrid technique named as a pso ga for solving the constrained optimization problems in this algorithm particle swarm optimization pso operates in the direction of improving the vector while the genetic algorithm ga has been used for modifying the decision vectors using genetic operators the balance between the exploration and exploitation abilities have been further improved by incorporating the genetic operators namely crossover and mutation in pso algorithm the constraints defined in the problem are handled with the help of the parameter free penalty function the experimental results of constrained optimization problems are reported and compared with the typical approaches exist in the literature as shown the solutions obtained by the proposed approach are superior to those of existing best solutions reported in the literature furthermore experimental results indicate that the proposed approach may yield better solutions to engineering problems than those obtained by using current algorithms

heat kernel expansions ambient metrics and conformal invariants abstract the conformal powers of the laplacian of a riemannian metric which are known as the gjms operators admit a combinatorial description in terms of the taylor coefficients of a natural second order one parameter family h r g of self adjoint elliptic differential operators h r g is a non laplace type perturbation of the conformal laplacian p 2 g h 0 g it is defined in terms of the metric g and covariant derivatives of the curvature of g we study the heat kernel coefficients a 2 k r g of h r g on closed manifolds we prove general structural results for the heat kernel coefficients a 2 k r g and derive explicit formulas for a 0 r g and a 2 r g in terms of renormalized volume coefficients the taylor coefficients of a 2 k r g as functions of r interpolate between the renormalized volume coefficients of a metric g k 0 and the heat kernel coefficients of the conformal laplacian of g r 0 although h r g is not conformally covariant there is a beautiful formula for the conformal variation of the trace of its heat kernel its proof rests on the combinatorial relations between taylor coefficients of h r g and gjms operators as a consequence we give a heat equation proof of the conformal transformation law of the integrated renormalized volume coefficients by refining these arguments we also give a heat equation proof of the conformal transformation law of the renormalized volume coefficients itself the taylor coefficients of a 2 r define a sequence of higher order riemannian curvature functionals with extremal properties at einstein metrics which are analogous to those of integrated renormalized volume coefficients among the various additional results the reader finds a polyakov type formula for the renormalized volume of a poincare einstein metric in terms of q curvature of its conformal infinity and additional holographic terms the present study of relations between spectral theoretic heat kernel coefficients and geometric quantities like renormalized volume coefficients is stimulated by the holographic perspective of the ads cft duality proposing relations between functional determinants and renormalized volumes

hamilton jacobi and fokker planck equations for the harmonic oscillator abstract using feynman s path integral formalism applied to stochastic classical processes we show the equivalence between the hamilton jacobi hj and fokker planck fp equations associated with an overdamped brownian harmonic oscillator in this case the langevin equation leads to a gaussian lagrangian function and then the path integration which defines the conditional probability density can be replaced by the extremal path due to this fact and following the classical dynamics formalism we prove the strict equivalence between the hj and fp equations we do this first for an ordinary brownian harmonic oscillator and then the proof is extended to an electrically charged brownian particle under the action of force fields magnetic field and additional time dependent force fields we observe that this extremal action principle allows us to derive in a straightforward way not only the hj differential equation but also its solution the extremal action

anomalous continuous time random walk spectral diffusion in coherent third order optical response recursive relations are derived for nonlinear optical response functions of a two level chromophore with stochastic frequency fluctuations described by a continuous time random walk stationary ensembles are constructed and signatures of anomalous relaxation in the photon echo signal are discussed for a two state jump modulation with a power law waiting time density function psi t approximately t alpha 1 stretched exponential decay of the photon echo signal is predicted for 0 alpha 1 and power law asymptotics for 1 alpha 2

an efficient constraint handling method for genetic algorithms many real world search and optimization problems involve inequality and or equality constraints and are thus posed as constrained optimization problems in trying to solve constrained optimization problems using genetic algorithms gas or classical optimization methods penalty function methods have been the most popular approach because of their simplicity and ease of implementation however since the penalty function approach is generic and applicable to any type of constraint linear or nonlinear their performance is not always satisfactory thus researchers have developed sophisticated penalty functions specific to the problem at hand and the search algorithm used for optimization however the most difficult aspect of the penalty function approach is to find appropriate penalty parameters needed to guide the search towards the constrained optimum in this paper ga s population based approach and ability to make pair wise comparison in tournament selection operator are exploited to devise a penalty function approach that does not require any penalty parameter careful comparisons among feasible and infeasible solutions are made so as to provide a search direction towards the feasible region once sufficient feasible solutions are found a niching method along with a controlled mutation operator is used to maintain diversity among feasible solutions this allows a real parameter ga s crossover operator to continuously find better feasible solutions gradually leading the search near the true optimum solution gas with this constraint handling approach have been tested on nine problems commonly used in the literature including an engineering design problem in all cases the proposed approach has been able to repeatedly find solutions closer to the true optimum solution than that reported earlier

an improved adaptive binary harmony search algorithm harmony search hs inspired by the music improvisation process is a new meta heuristic optimization method and has been successfully used to tackle the optimization problems in discrete or continuous space although the standard hs algorithm is able to solve binary coded optimization problems the pitch adjustment operator of hs is degenerated in the binary space which spoils the performance of the algorithm based on the analysis of the drawback of the standard hs an improved adaptive binary harmony search abhs algorithm is proposed in this paper to solve the binary coded problems more effectively various adaptive mechanisms are examined and investigated and a scalable adaptive strategy is developed for abhs to enhance its search ability and robustness the experimental results on the benchmark functions and 0 1 knapsack problems demonstrate that the proposed abhs is efficient and effective which outperforms the binary harmony search the novel global harmony search algorithm and the discrete binary particle swarm optimization in terms of the search accuracy and convergence speed

phase space dynamical model of an open system of interacting q bits the path integral form of the propagator for a stochastic schrodinger equation is used to derive stochastic differential equations on the quantum phase space of interacting q bits in a random environment the equations can be considered as an approximate classical model of the quantum system predictions of the model are compared with that of the exact quantum equations for various examples of the environment operators

ghs lem global best harmony search using learnable evolution models abstract this paper presents a new optimization algorithm called ghs lem which is based on the global best harmony search algorithm ghs and techniques from the learnable evolution models lem to improve convergence and accuracy of the algorithm the performance of the algorithm is evaluated with fifteen optimization functions commonly used by the optimization community in addition the results obtained are compared against the original harmony search algorithm the improved harmony search algorithm and the global best harmony search algorithm the assessment shows that the proposed algorithm ghs lem improves the accuracy of the results obtained in relation to the other options producing better results in most situations but more specifically in problems with high dimensionality where it offers a faster convergence with fewer iterations

open systems with error bounds spin boson model with spectral density variations in the study of open quantum systems one of the most common ways to describe environmental effects on the reduced dynamics is through the spectral density however in many models this object cannot be computed from first principles and needs to be inferred on phenomenological grounds or fitted to experimental data consequently some uncertainty regarding its form and parameters is unavoidable this in turn calls into question the accuracy of any theoretical predictions based on a given spectral density here we focus on the spin boson model as a prototypical open quantum system find two error bounds on predicted expectation values in terms of the spectral density variation considered and state a sufficient condition for the strongest one to apply we further demonstrate an application of our result by bounding the error brought about by the approximations involved in the hierarchical equations of motion resolution method for spin boson dynamics

nonlinear schrodinger equation with a white noise potential phase space approach to spread and singularity we propose a phase space formulation for the nonlinear schr odinger equation with a white noise potential in order to shed light on two issues the rate of spread and the singularity formation in the average sense our main tools are the energy law and the variance identity the method is completely elementary for the problem of wave spread we show that the ensemble averaged dispersion in the critical or defocusing case follows the cubic in time law while in the supercritical and subcritical focusing cases the cubic law becomes an upper and lower bound respectively we have also found that in the critical and supercritical focusing cases the presence of a white noise random potential results in different conditions for singularity with positive probability from the homogeneous case but does not prevent singularity formation we show that in the supercritical focusing case the ensemble averaged self interaction energy and the momentum variance can exceed any fixed level in a finite time with positive probability c 2005 elsevier b v all rights reserved

two derivations of the master equation of quantum brownian motion central to many discussion of decoherence is a master equation for the reduced density matrix of a massive particle experiencing scattering from its surrounding environment such as that of joos and zeh such master equations enjoy a close relationship with spontaneous localization models like the grw model the aim of this paper is to present two derivations of the master equation the first derivation is a pedagogical model designed to illustrate the origins of the master equation as simply as possible focusing on physical principles and without the complications of s matrix theory this derivation may serve as a useful tutorial example for students attempting to learn this subject area the second is the opposite a very general derivation using non relativistic many body field theory it reduces to the equation of the type given by joos and zeh in the one particle sector but correcting certain numerical factors which have recently become significant in connection with experimental tests of decoherence this master equation also emphasizes the role of local number density as the preferred basis for decoherence in this model

entropic uncertainty bound for open pointer based simultaneous measurements of conjugate observables we discuss the information entropy for a general open pointer based simultaneous measurement and show how it is bound from below this entropic uncertainty bound is a direct consequence of the structure of the entropy and can be obtained from the formal solution of the measurement dynamics furthermore the structural properties of the entropy allow us to give an intuitive interpretation of the noisy influence of the pointers and the environmental heat bath on the measurement results

path integral for quantum operations in this paper we consider a phase space path integral for general time dependent quantum operations not necessarily unitary we obtain the path integral for a completely positive quantum operation satisfied lindblad equation quantum markovian master equation we consider the path integral for quantum operation with a simple infinitesimal generator

solving the sum of ratios problems by a harmony search algorithm the sum of ratios problems have numerous applications in economy and engineering the sum of ratios problems are considered to be difficult as these functions are highly nonconvex and multimodal in this study we propose a harmony search algorithm for solving a sum of ratios problem numerical examples are also presented to demonstrate the effectiveness and robustness of the proposed method in all cases the solutions obtained using this method are superior to those obtained from other methods

eigenvalues of the liouvillians of quantum master equation for a harmonic oscillator abstract the eigenvalues of the liouvillians of markovian master equation for a harmonic oscillator have a generic form the liouvillians considered are quadratic in the position coordinates or creation and annihilation operators as well as having positive renormalized frequencies we prove this by showing that a generic liouvillian of this form can be similarly related to the liouvillian of the kossakowski lindblad equation whose eigenvalues are already known the left and right eigenfunctions of the generic liouvillian also form a complete and biorthogonal set examples of similarly related right eigenfunctions are given

unified picture of strong coupling stochastic thermodynamics and time reversals strong coupling statistical thermodynamics is formulated as the hamiltonian dynamics of an observed system interacting with another unobserved system a bath it is shown that the entropy production functional of stochastic thermodynamics defined as the log ratio of forward and backward system path probabilities is in a one to one relation with the log ratios of the joint initial conditions of the system and the bath a version of strong coupling statistical thermodynamics where the system bath interaction vanishes at the beginning and at the end of a process is as is also weak coupling stochastic thermodynamics related to the bath initially in equilibrium by itself the heat is then the change of bath energy over the process and it is discussed when this heat is a functional of the system history alone the version of strong coupling statistical thermodynamics introduced by seifert and jarzynski is related to the bath initially in conditional equilibrium with respect to the system this leads to heat as another functional of the system history which needs to be determined by thermodynamic integration the log ratio of forward and backward system path probabilities in a stochastic process is finally related to log ratios of the initial conditions of a combined system and bath it is shown that the entropy production formulas of stochastic processes under a general class of time reversals are given by the differences of bath energies in a larger underlying hamiltonian system the paper highlights the centrality of time reversal in stochastic thermodynamics also in the case of strong coupling

calderia leggett master equation and medium temperatures abstract the markovian approximation of quantum dissipation has been reconsidered in the model of caldeira and leggett physica a 121 1983 587 their high temperature master equation has been generalized to medium temperatures two additional damping terms in the master equation have been derived and shown to assure the lindblad form of the equation a transient term in the density matrix has been found and expressed in a simple form

wigner distribution functions for complex dynamical systems the emergence of the wigner boltzmann equation the equation of motion for the reduced wigner function of a system coupled to an external quantum system is presented for the specific case when the external quantum system can be modeled as a set of harmonic oscillators the result is derived from the wigner function formulation of the feynman vernon influence functional theory it is shown how the true self energy for the equation of motion is connected with the influence functional for the path integral explicit expressions are derived in terms of the bare wigner propagator finally we show under which approximations the resulting equation of motion reduces to the wigner boltzmann equation

a new meta heuristic algorithm for continuous engineering optimization harmony search theory and practice most engineering optimization algorithms are based on numerical linear and nonlinear programming methods that require substantial gradient information and usually seek to improve the solution in the neighborhood of a starting point these algorithms however reveal a limited approach to complicated real world optimization problems if there is more than one local optimum in the problem the result may depend on the selection of an initial point and the obtained optimal solution may not necessarily be the global optimum this paper describes a new harmony search hs meta heuristic algorithm based approach for engineering optimization problems with continuous design variables this recently developed hs algorithm is conceptualized using the musical process of searching for a perfect state of harmony it uses a stochastic random search instead of a gradient search so that derivative information is unnecessary various engineering optimization problems including mathematical function minimization and structural engineering optimization problems are presented to demonstrate the effectiveness and robustness of the hs algorithm the results indicate that the proposed approach is a powerful search and optimization technique that may yield better solutions to engineering problems than those obtained using current algorithms 2004 elsevier b v all rights reserved

global l1 theory and regularity for the 3d nonlinear wigner poisson fokker planck system abstract a global existence uniqueness and regularity theorem is proved for the simplest markovian wigner poisson fokker planck model incorporating friction and dissipation mechanisms the proof relies on green function and energy estimates under mild formulation making essential use of the husimi function and the elliptic regularization of the fokker planck operator

two parameter tuned meta heuristics for a discounted inventory control problem in a fuzzy environment highlightsa nearly real world mp mp inventory control problem under discounts and budget constraints is investigated the required storages space is considered a fuzzy number the goal is to find the optimal ordered quantities of the products a hsa is developed to solve the complex problem in this paper a nearly real world multi product multi period inventory control problem under budget constraint is investigated where shortages in combination with backorders and lost sales are considered for each product the ordered quantities of products are delivered in batch sizes with a known number of boxes each containing a pre specified number of products some products are purchased under an all unit discount policy and others are purchased under an incremental quantity discount with fuzzy discount rates the goal is to find the optimal ordered quantities of products such that not only the total inventory cost but also the required storage space considered as a fuzzy number to store the products is minimized the weighted linear sum of objectives is applied to generate a single objective model for the bi objective problem at hand and a harmony search algorithm is developed to solve the complex inventory problem as no benchmarks are available to validate the obtained results a particle swarm optimization algorithm is employed to solve the problem in addition to validate the results given by the harmony search method the parameters of both algorithms are tuned using both taguchi and response surface methodology rsm finally to assess the performance of the proposed algorithms some numerical examples are generated and the results are compared statistically

the caldeira leggett quantum master equation in wigner phase space continued fraction solution and application to brownian motion in periodic potentials the continued fraction method of solving classical fokker planck equations has been adapted to tackle quantum master equations of the caldeira leggett type this was done taking advantage of the phase space wigner representation of the quantum density matrix the approach differs from those in which some continued fraction expression is found for a certain quantity in that the full solution of the master equation is obtained by continued fraction methods this allows us to study in detail the effects of the environment fluctuations and dissipation on several classes of nonlinear quantum systems we apply the method to the canonical problem of quantum brownian motion in periodic potentials both for cosine and ratchet potentials lacking inversion symmetry

quantum brownian motion and generalizations of hermite polynomials abstract we introduce new families of orthogonal polynomials h d n motivated by the non equilibrium evolution of a quantum brownian particle qbp the h d n s generalize non trivially the standard hermite polynomials employed for classical brownian motion we treat several models labelled by d for a non equilibrium qbp by means of the wigner function w in the presence of a heat bath at thermal equilibrium with and without ab initio friction for long times for a suitable class of initial conditions the non equilibrium wigner function w should approach in some sense the time independent equilibrium wigner function w e q d which describes the thermal equilibrium of the qbp with the heat bath and plays a central role w e q d is chosen to be the weight function which orthogonalizes the h d n s new results on w e q d and on the h d n s are reported we justify the key role of the h d n s as follows using the h d n s moments w e q d n and w n are introduced for w e q d and w respectively at equilibrium all moments w e q d n except the lowest one w e q d 0 vanish identically off equilibrium one expects that for long times for suitable initial conditions i all non equilibrium moments w n except the lowest moment w 0 will approach zero while ii the lowest non equilibrium moment w 0 will tend to w e q d 0 0 to complete the justification we outline how the approximate long time non equilibrium theories determined by w 0 for the different models d yield smoluchowski equations and irreversible evolutions of the qbp towards thermal equilibrium

quantum smoluchowski equation a systematic study the strong friction regime at low temperatures is analyzed systematically starting from the formally exact path integral expression for the reduced dynamics this quantum smoluchowski regime allows for a type of semiclassical treatment in the inverse friction strength so that higher order quantum corrections to the original quantum smoluchowski equation j ankerhold p pechukas and h grabert phys rev lett 87 086802 2001 j ankerhold and h grabert phys rev lett 101 119903 2008 can be derived drift and diffusion coefficients are determined by the equilibrium distribution in position and are directly related to the corresponding action of extremal paths and fluctuations around them it is shown that the inclusion of higher order corrections reproduces the quantum enhancement above crossover for the decay rate out of a metastable well exactly

the effect of interference of coloured additive and multiplicative white noises on escape rate in this paper we have calculated the escape rate from a meta stable state for coloured and correlated noise driven open systems based on the fokker planck description of the stochastic process we consider the effect of two correlation times due to the additive coloured noise and the correlation between additive coloured and multiplicative white noises the effect of the noise correlation strength on the rate has also been investigated

eigenfunctions of the liouville operator periodic orbits and the principle of uniformity we investigate the eigenvalue problem for the dynamical variables evolution equation in classical mechanics where is the liouville operator the generator of the unitary one parameter group we show that the non constant eigenfunctions are distributions on the energy shell and non vanishing on its elementary retracing invariant submanifolds rational tori for the integrable case or periodic orbits for the chaotic case the formalism unveils an equivalent statement concerning the definition of a measure on the hilbert space of dynamical variables for the principle of uniformity introducing this measure which is delta concentrated on the periodic orbits we are able to derive the classical sum rules obtained from the principle of uniformity from the way the periodic orbits proliferate for increasing periods

reduction of overdamped stochastic processes in the coherent state representation the adiabatic elimination of fast variables from overdamped stochastic processes by functional integration is demonstrated adiabatic elimination entails the evaluation of a reduced evolution operator from the full evolution equation for fokker planck processes the reduced evolution operator may be expressed as a ground state expectation and it is shown how this is represented as a coherent state path integral the elimination is then achieved by functionally integrating out all reference to the fast variables the end result is a decoupling of the full evolution equation into separate equations for the fast and slow variables the method is demonstrated for brownian motion and for a system with multiplicative colored noise

an improved harmony search algorithm for solving optimization problems this paper develops an improved harmony search ihs algorithm for solving optimization problems ihs employs a novel method for generating new solution vectors that enhances accuracy and convergence rate of harmony search hs algorithm in this paper the impacts of constant parameters on harmony search algorithm are discussed and a strategy for tuning these parameters is presented the ihs algorithm has been successfully applied to various benchmarking and standard engineering optimization problems numerical results reveal that the proposed algorithm can find better solutions when compared to hs and other heuristic or deterministic methods and is a powerful search algorithm for various engineering optimization problems

path integral approach to quantum brownian motion abstract we apply the influence functional method of feynman and vernon to the study of brownian motion at arbitrary temperature by choosing a specific model for the dissipative interaction of the system of interest with its environment we are able to evaluate the influence functional in closed form and express it in terms of a few parameters such as the phenomenological viscosity coefficient we show that in the limit h 0 the results obtained from the influence functional formalism reduce to the classical fokker planck equation in the case of a simple harmonic oscillator with arbitrarily strong damping and at arbitrary temperature we obtain an explicit expression for the time evolution of the complete density matrix x x t when the system starts in a particular kind of pure state we compare our results with those of other approaches to the problem of dissipation in quantum mechanics

harmony search algorithm with dynamic control parameters abstract harmony search hs is a population based meta heuristic imitating the music improvisation process which has been successfully applied to optimization problems in recent years this paper presents an effective harmony search algorithm for solving global continuous optimization problems the proposed method presents a novel improvisation process which is different from the classical hs in two aspects firstly the candidate harmony is chosen from the harmony memory by a tournament selection rule so that the harmonies with better fitness will have more opportunities to be used in generating new harmonies secondly two key control parameters pitch adjustment rate par and bandwidth distance bw are adjusted dynamically with respect to the evolution of the search process and the different search spaces of the optimization problems numerical results demonstrate that the proposed algorithm performs much better than the existing hs variants in terms of the solution quality and the stability

novel derivative of harmony search algorithm for discrete design variables calculus has widespread applications in science and engineering optimization is one of its major subjects where a problem can be mathematically formulated and its optimal solution is determined by using derivatives however this calculus based derivative technique can only be applied to real valued or continuous valued functions rather than discrete valued functions while there are many situations where design variables contain not continuous values but discrete values by nature in order to consider these realistic design situations this study proposes a novel derivative for discrete design variables based on a harmony search algorithm detailed analysis shows how this new stochastic derivative works in the bench mark function and fluid transport network design hopefully this new derivative as a fundamental technology will be utilized in various science and engineering problems

chaotic harmony search algorithms harmony search hs is one of the newest and the easiest to code music inspired heuristics for optimization problems like the use of chaos in adjusting note parameters such as pitch dynamic rhythm duration tempo instrument selection attack time etc in real music and in sound synthesis and timbre construction this paper proposes new hs algorithms that use chaotic maps for parameter adaptation in order to improve the convergence characteristics and to prevent the hs to get stuck on local solutions this has been done by using of chaotic number generators each time a random number is needed by the classical hs algorithm seven new chaotic hs algorithms have been proposed and different chaotic maps have been analyzed in the benchmark functions it has been detected that coupling emergent results in different areas like those of hs and complex dynamics can improve the quality of results in some optimization problems it has been also shown that some of the proposed methods have somewhat increased the solution quality that is in some cases they improved the global searching capability by escaping the local solutions

symmetry of bilinear master equations for a quantum oscillator abstract we study the most general continuous transformation on the generators of bilinear master equations of a quantum oscillator we find that transformation operators that preserve the hermiticity of density operators and conserve the probability of reduced dynamics should be adjoint symmetric and they are not limited to the pure product of unitary operators in the bra and ket space but could be a mixture of them we need to include the more general transformation operators to explore the full symmetry of generic reduced dynamics we discuss how the operators are related to those considered in previous works and illustrate how they leave the reduced dynamics form invariant or map one into the other the positive semidefinite requirement on the density operator can be imposed to give a valid range of transformation parameters

reaction rate theory weak to strong friction turnover in kramers fokker planck model abstract we present a unified treatment for both weak and strong friction including the turnover regime of kramers fokker planck model for activated rate processes no recourse to a specific microscopic model a la grabert et al or langevin dynamics a la graham will be made upon introducing some new theoretical concepts such as a constrained gaussian transformation cgt and a dynamical extension of phase space eps the analysis proceeds in terms of the unstable mode energy and is systematic in a small parameter we also introduce a nonlinear toy model for barrier recrossing for a simplified discussion of aspects like finite barrier corrections the boundary layer approximation and exact solution in the absence of potential conditions

geometric selective harmony search abstract this paper presents a new variant of the harmony search algorithm called geometric selective harmony search the main differences between the proposed variant and the original formulation of harmony search are the integration of a selection procedure in the improvisation phase a new memory consideration process that makes use of a recombination operator and the integration of a new mutation operator we compare geometric selective harmony search with the original harmony search with another existing variant called improved harmony search and with two existing selection based harmony search algorithms the experimental study was conducted on 20 benchmark problems belonging to the cec 2010 suite one of the most well known state of the art benchmark sets the results show that geometric selective harmony search outperforms the other studied methods with statistical significance in almost all the considered benchmark problems

linearly coupled quantum oscillators with levy stable noise abstract the influence of an external noise on two linearly coupled quantum oscillators is investigated the noise is described by the probability measure corresponding to a symmetric levy stable distribution in calculations the path integral technique is used this paper is a continuation of investigations started by bose datta and feinsilver

non markovian expansion in quantum brownian motion abstract we consider the non markovian langevin evolution of a dissipative dynamical system in quantum mechanics in the path integral formalism after discussing the role of the frequency cutoff for the interaction of the system with the heat bath and the kernel and noise correlator that follow from the most common choices we derive an analytic expansion for the exact non markovian dissipation kernel and the corresponding colored noise in the general case that is consistent with the fluctuation dissipation theorem and incorporates systematically non local corrections we illustrate the modifications to results obtained using the traditional markovian langevin approach in the case of the exponential kernel and analyze the case of the non markovian brownian motion we present detailed results for the free and the quadratic cases which can be compared to exact solutions to test the convergence of the method and discuss potentials of a general nonlinear form

hybridizing harmony search algorithm with sequential quadratic programming for engineering optimization problems this study presents a hybrid harmony search algorithm hhsa to solve engineering optimization problems with continuous design variables although the harmony search algorithm hsa has proven its ability of finding near global regions within a reasonable time it is comparatively inefficient in performing local search in this study sequential quadratic programming sqp is employed to speed up local search and improve precision of the hsa solutions moreover an empirical study is performed in order to determine the impact of various parameters of the hsa on convergence behavior various benchmark engineering optimization problems are used to illustrate the effectiveness and robustness of the proposed algorithm numerical results reveal that the proposed hybrid algorithm in most cases is more effective than the hsa and other meta heuristic or deterministic methods

integrable structure of conformal field theory ii q operator and ddv equation this paper is a direct continuation of 1 where we began the study of the integrable structures in conformal field theory we show here how to construct the operators bf q pm lambda which act in the highest weight virasoro module and commute for different values of the parameter these operators appear to be the cft analogs of the q matrix of baxter 2 in particular they satisfy baxter s famous t q equation we also show that under natural assumptions about analytic properties of the operators as the functions of the baxter s relation allows one to derive the nonlinear integral equations of destri de vega ddv 3 for the eigenvalues of the q operators we then use the ddv equation to obtain the asymptotic expansions of the q operators at large it is remarkable that unlike the expansions of the t operators of 1 the asymptotic series for q contains the dual nonlocal integrals of motion along with the local ones we also discuss an intriguing relation between the vacuum eigenvalues of the q operators and the stationary transport properties in the boundary sine gordon model on this basis we propose a number of new exact results about finite voltage charge transport through the point contact in the quantum hall system

quantum moment hydrodynamics and the entropy principle this paper presents how a non commutative version of the entropy extremalization principle allows to construct new quantum hydrodynamic models our starting point is the moment method which consists in integrating the quantum liouville equation with respect to momentum p against a given vector of monomials of p like in the classical case the so obtained moment system is not closed inspired from levermore s procedure in the classical case 26 we propose to close the moment system by a quantum wigner distribution function which minimizes the entropy subject to the constraint that its moments are given in contrast to the classical case the quantum entropy is defined globally and not locally as the trace of an operator therefore the relation between the moments and the lagrange multipliers of the constrained entropy minimization problem becomes nonlocal and the resulting moment system involves nonlocal operators instead of purely local ones in the classical case in the present paper we discuss some practical aspects and consequences of this nonlocal feature

brownian motion quantum corrections and a generalization of the hermite polynomials the nonequilibrium evolution of a brownian particle in the presence of a heat bath at thermal equilibrium without imposing any friction mechanism from the outset is considered using a suitable family of orthogonal polynomials moments of the nonequilibrium probability distribution for the brownian particle are introduced which fulfill a recurrence relation we review the case of classical brownian motion in which the orthogonal polynomials are the hermite ones and the recurrence relation is a three term one after having performed a long time approximation in the recurrence relation the approximate nonequilibrium theory yields irreversible evolution of the brownian particle towards thermal equilibrium with the heat bath for quantum brownian motion which is the main subject of the present work we restrict ourselves to include the first quantum correction this leads us to introduce a new family of orthogonal polynomials which generalize the hermite ones some general properties of the new family are established the recurrence relation for the new moments of the nonequilibrium distribution including the first quantum correction turns out to be also a three term one which justifies the new family of polynomials a long time approximation on the new three term recurrence relation describes irreversible evolution towards equilibrium for the new moment of lowest order the standard smoluchowski equations for the lowest order moments are recovered consistently both classically and quantum mechanically

how to calculate decoherence matrices numerically abstract a central object in the interpretation of quantum mechanics of closed systems is the decoherence matrix but only for a very small number of models one is able to give explicit expressions for its elements so numerical methods are required unfortunately the dimensions of these matrices are usually very high which makes also a direct numerical calculation impossible in this paper i will develop an algorithm that combines the numerical calculation of the elements of the decoherence matrix with a permanent estimation if the chosen histories are almost decoherent the algorithm will provide the diagonal and maybe some near to diagonal elements only in this case within numerical errors we can assume that all not calculated elements are smaller than a given threshold if the histories are coherent the algorithm has to calculate too much data there exist too much non vanishing elements and the success depends mainly on the available computer time as an example i apply this procedure to the caldeira leggett model

quantum dynamical semigroups for diffusion models with hartree interaction we consider a class of evolution equations in lindblad form which model the dynamics of dissipative quantum mechanical systems with mean field interaction particularly this class includes the so called quantum fokker planck poisson model the existence and uniqueness of global in time mass preserving solutions is proved thus establishing the existence of a nonlinear conservative quantum dynamical semigroup the mathematical difficulties stem from combining an unbounded lindblad generator with the hartree nonlinearity

a heuristic approach to find the global optimum of function this paper presents the modified ant colony optimization maco based algorithm to find global optimum algorithm is based on that solution space of problem is restricted by the best solution of the previous iteration furthermore the proposed algorithm is that variables of problem are optimized concurrently this algorithm was tested on some standard test functions and successful results were obtained its performance was compared with the other algorithms and observed to be better

global best harmony search algorithm with control parameters co evolution based on pso and its application to constrained optimal problems a global best harmony search algorithm with control parameters co evolution based on particle swarm optimization pso ce ghs is proposed in pso ce ghs two control parameters i e harmony memory considering rate and pitch adjusting rate are encoded to be a symbiotic individual of original individual i e harmony vector harmony search operators are applied to evolve the original population and pso is applied to co evolve the symbiotic population thus with the evolution of the original population in pso ce ghs the symbiotic population is dynamically and self adaptively adjusted and the real time optimum control parameters are obtained the proposed pso ce ghs algorithm has been applied to various benchmark functions and constrained optimal problems the results show that the proposed algorithm can find better solutions when compared to hs and its variants

on fractional gjms operators we describe a new interpretation of the fractional gjms operators as generalized dirichlet to neumann operators associated to weighted gjms operators on naturally associated smooth metric measure spaces this gives a geometric interpretation of the caffarelli silvestre extension for when 0 1 and both a geometric interpretation and a curved analogue of the higher order extension found by r yang for when 1 we give three applications of this correspondence first we exhibit some energy identities for the fractional gjms operators in terms of energies in the compactified poincare einstein manifold including an interpretation as a renormalized energy second for 1 2 we show that if the scalar curvature and the fractional q curvature q2 of the boundary are nonnegative then the fractional gjms operator p2 is nonnegative third by assuming additionally that q2 is not identically zero we show that p2 satisfies a strong maximum principle 2014 wiley periodicals inc