exact solution of a 1d asymmetric exclusion model using a matrix formulation several recent works have shown that the one dimensional fully asymmetric exclusion model which describes a system of particles hopping in a preferred direction with hard core interactions can be solved exactly in the case of open boundaries here the authors present a new approach based on representing the weights of each configuration in the steady state as a product of noncommuting matrices with this approach the whole solution of the problem is reduced to finding two matrices and two vectors which satisfy very simple algebraic rules they obtain several explicit forms for these non commuting matrices which are in the general case infinite dimensional their approach allows exact expressions to be derived for the current and density profiles finally they discuss briefly two possible generalizations of their results the problem of partially asymmetric exclusion and the case of a mixture of two kinds of particles

phase separation and coarsening in one dimensional driven diffusive systems local dynamics leading to long range hamiltonians a driven system of three species of particles diffusing on a ring is studied in detail the dynamics is local and conserves the three densities a simple argument suggesting that the model should phase separate and break the translational symmetry is given we show that for the special case where the three densities are equal the model obeys detailed balance and the steady state distribution is governed by a hamiltonian with asymmetric long range interactions this provides an explicit demonstration of a simple mechanism for breaking of ergodicity in one dimension the steady state of finite size systems is studied using a generalized matrix product ansatz the coarsening process leading to phase separation is studied numerically and in a mean field model the system exhibits slow dynamics due to trapping in metastable states whose number is exponentially large in the system size the typical domain size is shown to grow logarithmically in time generalizations to a larger number of species are discussed

shift equivalence of measures and the intrinsic structure of shocks in the asymmetric simple exclusion process we investigate the properties of non translation invariant measures describing particle systems on mathbb z which are asymptotic to different translation invariant measures on the left and on the right often the structure of the transition region can only be observed from a point of view which is random in particular configuration dependent two such measures will be called shift equivalent if they differ only by the choice of such a viewpoint we introduce certain quantities called translation sums which under some auxiliary conditions characterize the equivalence classes our prime example is the asymmetric simple exclusion process for which the measures in question describe the microscopic structure of shocks in this case we compute explicitly the translation sums and find that shocks generated in different ways in particular via initial conditions in an infinite system or by boundary conditions in a finite system are described by shift equivalent measures we show also that when the shock in the infinite system is observed from the location of a second class particle treating this particle either as a first class particle or as an empty site leads to shift equivalent shock measures

oscillation for difference equations with continuous variable consider the delay difference equation y t y t p t h y t t t 0 where 0 0 and p c r r f c r r h c r r some oscillation criteria for this equation are obtained

universality classes in two component driven diffusive systems we study time dependent density fluctuations in the stationary state of driven diffusive systems with two conserved densities rho lambda using monte carlo simulations of two coupled single lane asymmetric simple exclusion processes we present numerical evidence for universality classes with dynamical exponents z 1 sqrt 5 2 and z 3 2 but different from the kardar parisi zhang kpz universality class which have not been reported yet for driven diffusive systems the numerical asymmetry of the dynamical structure functions converges slowly for some of the non kpz superdiffusive modes for which mode coupling theory predicts maximally asymmetric z stable levy scaling functions we show that all universality classes predicted by mode coupling theory for two conservation laws are generic they occur in two component systems with nonlinearities in the associated currents already of the minimal order rho lambda 2 rho mu the macroscopic stationary current density relation and the compressibility matrix determine completely all permissible universality classes through the mode coupling coefficients which we compute explicitly for general two component systems

exact results for one dimensional cellular automata with different types of updates we study two common types of time noncontinuous updates for one dimensional stochastic cellular automata with arbitrary nearest neighbor interactions and arbitrary open boundary conditions we first construct the stationary states using the matrix product formalism this construction then allows to prove a general connection between the stationary states which are produced by the two different types of updates using this connection we derive explicit relations between the densities and correlation functions for these different stationary states

exact results for 2d directed animals on a strip of finite width proves a conjecture giving the exact number of directed animals of s sites with any root on a strip of finite width of a square lattice the authors also rederive more simply some previous results concerning the connective constant and particular eigenvectors of the transfer matrix

phase transitions in an exactly soluble one dimensional exclusion process we consider an exclusion process with particles injected with rate at the origin and removed with rate at the right boundary of a one dimensional chain of sites the particles are allowed to hop onto unoccupied sites to the right only for the special case of 1 the model was solved previously by derridaet al here we extend the solution to general the phase diagram obtained from our exact solution differs from the one predicted by the mean field approximation

exact steady states of disordered hopping particle models with parallel and ordered sequential dynamics a one dimensional driven lattice gas with disorder in the particle hopping probabilities is considered it has previously been shown that in the version of the model with random sequential updating a phase transition occurs from a low density inhomogeneous phase to a high density congested phase here the steady states for both parallel fully synchronous updating and ordered sequential updating are solved exactly the phase transition is shown to persist in both cases with the critical densities being higher than that for random sequential dynamics the steady state velocities are related to the fugacity of a bose system suggesting a principle of minimization of velocity a generalization of the dynamics to the case where the hopping probabilities depend on the number of empty sites in front of the particles is also solved exactly in the case of parallel updating the models have natural interpretations as simplistic descriptions of traffic flow the relation to more sophisticated traffic flow models is discussed

phase diagram of a generalized abc model on the interval we study the equilibrium phase diagram of a generalized abc model on an interval of the one dimensional lattice each site i 1 n is occupied by a particle of type a b c with the average density of each particle species n n r fixed these particles interact via a mean field nonreflection symmetric pair interaction the interaction need not be invariant under cyclic permutation of the particle species as in the standard abc model studied earlier we prove in some cases and conjecture in others that the scaled infinite system n i n x 0 1 has a unique density profile x except for some special values of the r for which the system undergoes a second order phase transition from a uniform to a nonuniform periodic profile at a critical temperature t c 3 sqrt r a r b r c 2 pi

twenty five years after kls a celebration of non equilibrium statistical mechanics when lenz proposed a simple model for phase transitions in magnetism he couldn t have imagined that the ising model was to become a jewel in field of equilibrium statistical mechanics its role spans the spectrum from a good pedagogical example to a universality class in critical phenomena a quarter century ago katz lebowitz and spohn found a similar treasure by introducing a seemingly trivial modification to the ising lattice gas they took it into the vast realms of non equilibrium statistical mechanics an abundant variety of unexpected behavior emerged and caught many of us by surprise we present a brief review of some of the new insights garnered and some of the outstanding puzzles as well as speculate on the model s role in the future of non equilibrium statistical physics

oscillation of second order nonlinear difference equation with continuous variable in this paper we are mainly concerned with the second order nonlinear difference equation with continuous variable here by using the iterated integral transformations generalized riccati transformations and integrating factors we give some oscillatory criteria for this equation

n species stochastic models with boundaries and quadratic algebras stationary probability distributions for stochastic processes on linear chains with closed or open ends are obtained using the matrix product ansatz the matrices are representations of some quadratic algebras the algebras and the types of representations considered depend on the boundary conditions in the language of quantum chains we obtain the ground state of n state quantum chains with free boundary conditions or with non diagonal boundary terms at one or both ends in contrast to problems involving the bethe ansatz we do not have a general framework for arbitrary n which when specialized gives the known results for n 2 in fact the n 2 and n 2 cases appear to be very different

exact solution of a cellular automaton for traffic we present an exact solution of a probabilistic cellular automaton for traffic with open boundary conditions e g cars can enter and leave a part of a highway with certain probabilities the model studied is the asymmetric exclusion process asep with simultaneous updating of all sites it is equivalent to a special case vmax 1 of the nagel schreckenberg model for highway traffic which has found many applications in real time traffic simulations the simultaneous updating induces additional strong short range correlations compared to other updating schemes the stationary state is written in terms of a matrix product solution the corresponding algebra which expresses a system size recursion relation for the weights of the configurations is quartic in contrast to previous cases in which the algebra is quadratic we derive the phase diagram and compute various properties such as density profiles two point functions and the fluctuations in the number of particles cars in the system the current and the density profiles can be mapped onto the asep with other time discrete updating procedures through use of this mapping our results also give new results for these models

multiple shocks in a driven diffusive system with two species of particles abstract a one dimensional driven diffusive system with two types of particles and nearest neighbors interactions has been considered on a finite lattice with open boundaries the particles can enter and leave the system from both ends of the lattice and there is also a probability for converting the particle type at the boundaries we will show that on a special manifold in the parameters space multiple shocks evolve in the system for both species of particles which perform continuous time random walks on the lattice

a note on oscillation of second order nonlinear difference equation with continuous variable abstract in this paper by improving the proofs of some theorems in j math anal appl 255 2001 349 357 we obtain some new oscillation criteria for the second order nonlinear difference equation with continuous variable

one dimensional partially asymmetric simple exclusion process with open boundaries orthogonal polynomials approach the stationary state of the partially asymmetric simple exclusion process with open boundaries is reconsidered the so called matrix product ansatz is employed this enables us to construct the stationary state in the form of the product of the matrices d and e noticing the fact that the matrix c d e for the model is related to certain q orthogonal polynomials the model is analysed for a wide range of parameters the current and the correlation length are evaluated in the thermodynamic limit it turns out that the phase diagram for the correlation length is richer than that for the totally asymmetric case

efficient least squares fir system identification if finite impulse response fir system identification is performed by minimizing the squared error between the measured system output and an estimate from an fir system output a set of least squares normal equations to be solved for the fir system coefficients is obtained if the assumed fir system is of duration m samples the usual solution for the m least squares simultaneous equations requires a number of computational operations proportional to m3and storage of normal equation coefficients proportional to m2 the set of normal equations has an underlying structure however that can be exploited to yield a solution with computational operations proportional to m2and storage proportional to m such an efficient algorithmic solution is presented here

representations of the quadratic algebra and partially asymmetric diffusion with open boundaries we consider the one dimensional partially asymmetric exclusion model with open boundaries the model describes a system of hard core particles that hop stochastically in both directions with different rates at both boundaries particles are injected and extracted by means of the method of derrida et al the stationary probability measure can be expressed as a matrix product state involving two matrices forming a fock like representation of a general quadratic algebra we obtain the representations of this algebra which were unknown in the mathematical literature and use the two dimensional one to derive exact expressions for the density profile and correlation functions using the correspondence between the stochastic model and a quantum spin chain we obtain exact correlation functions for a spin heisenberg xxz chain with non diagonal boundary terms generalizations to other reaction diffusion models are discussed

q deformed poisson random variables on q fock space the q deformed poisson distribution has been introduced as the orthogonalizing probability measure for a certain q deformation of charlier polynomials which is reduced to the usual poisson distribution in the limit q 1 and takes the free poisson distribution in case of q 0 we give the operator on the q fock space which has the q deformed poisson distribution with respect to the vacuum state it is a linear combination of a q number operator a q gaussian random variable and a scalar operator this representation is of the same form as of hudson and parthasarathy on the symmetric fock space

an exclusion process on a tree with constant aggregate hopping rate we introduce a model of a totally asymmetric simple exclusion process tasep on a tree network where the aggregate hopping rate is constant from level to level with this choice for hopping rates the model shows the same phase diagram as the one dimensional case the potential applications of our model are in the area of distribution networks where a single large source supplies material to a large number of small sinks via a hierarchical network we show that mean field theory mft for our model is identical to that of the one dimensional tasep and that this mft is exact for the tasep on a tree in the limit of large branching ratio b or equivalently large coordination number we then present an exact solution for the two level tree or star network that allows the computation of any correlation function and confirm how mean field results are recovered as b as an example we compute the steady state current as a function of branching ratio we present simulation results that confirm these results and indicate that the convergence to mft with large branching ratio is quite rapid

stochastic models on a ring and quadratic algebras the three species diffusion problem the stationary state of a stochastic process on a ring can be expressed using traces of monomials of an associative algebra defined by quadratic relations we consider only exclusion processes and restrict the type of algebras such that one has recurrence relations for traces of words of different lengths this is possible only if the rates satisfy certain compatibility conditions these conditions are derived and explicit representations of the generators of the quadratic algebras are given

two way traffic flow exactly solvable model of traffic jam we study completely asymmetric two channel exclusion processes in one dimension it describes a two way traffic flow with cars moving in opposite directions the interchannel interaction makes cars slow down in the vicinity of approaching cars in the other lane particularly we consider in detail the system with a finite density of cars on one lane and a single car on the other when the interchannel interaction reaches a critical value a traffic jam occurs which turns out to be of first order phase transition we derive exact expressions for the average velocities the current the density profile and the k point density correlation functions we also obtain the exact probability of two cars being in one lane of distance r apart provided there is a finite density of cars on the other lane and show that the two cars form a weakly bound state in the jammed phase

the quantum group suq 2 and a q analogue of the boson operators a new realisation of the quantum group suq 2 is constructed by means of a q analogue to the jordan schwinger mapping determining thereby both the complete representation structure and q analogues to the wigner and racah operators to achieve this realisation a new elementary object is defined a q analogue to the harmonic oscillator the uncertainty relation for position and momentum in a q harmonic oscillator is quite unusual

exact results for one dimensional totally asymmetric diffusion models several types of totally asymmetric diffusion models with and without exclusion are considered for some models conditional probabilities of finding n particles on lattice sites at time t with initial occupation at time t 0 are expressed in a determinant form on the other hand the q boson totally asymmetric diffusion model is introduced which interpolates the free boson model and the model with exclusion like interaction the effects of the interaction are compared for the case of two particle diffusion

matrix product ground states for exclusion processes with parallel dynamics we show in the example of a one dimensional asymmetric exclusion process that stationary states of models with parallel dynamics may be written in a matrix product form the corresponding algebra is quadratic and involves three different matrices using this formalism we prove previous conjectures for the equal time correlation functions of the model

a comparative analysis of several transformations for enhancement and segmentation of magnetic resonance image scene sequences the performance of the eigenimage filter is compared with those of several other filters as applied to magnetic resonance image mri scene sequences for image enhancement and segmentation comparisons are made with principal component analysis matched modified matched maximum contrast target point ratio log ratio and angle image filters signal to noise ratio snr contrast to noise ratio cnr segmentation of a desired feature sdf and correction for partial volume averaging effects cpv are used as performance measures for comparison analytical expressions for snrs and cnrs of filtered images are derived and cpv by a linear filter is studied properties of filters are illustrated through their applications to simulated and acquired mri sequences of a phantom study and a clinical case advantages and weaknesses are discussed the conclusion is that the eigenimage filter is the optimal linear filter that achieves sdf and cpv simultaneously

partially asymmetric exclusion process with open boundaries exclusive diffusion on a one dimensional lattice is studied in the model particles hop stochastically in both directions but with different rates at the ends of the lattice particles are injected and removed the exact stationary probability measure is represented in the form of a matrix product as a generalization of the solution given by derrida et al j phys a 26 1493 1993 for the fully asymmetric process the phase diagram of the current on the infinite lattice is obtained analytic expressions for the current in the different phases are derived the model is equivalent to an xxz heisenberg chain with a certain type of boundary terms the ground state of which corresponds to the stationary solution of the master equation

an exact formula for the statistics of the current in the tasep with open boundaries we study the totally asymmetric exclusion process on a finite one dimensional lattice with open boundaries i e in contact with two reservoirs at different potentials the total time integrated current through the system is a random variable that scales linearly with time in the long time limit we conjecture a parametric representation for the generating function of the cumulants of the current which is related to the large deviation function by laplace transform this formula is valid for all system sizes and for all values of the boundary coupling parameters

surface pattern formation and scaling described by conserved lattice gases we extend our 2 1 dimensional discrete growth model odor et al phys rev e 79 021125 2009 with conserved local exchange dynamics of octahedra describing surface diffusion a roughening process was realized by uphill diffusion and curvature dependence by mapping the slopes onto particles two dimensional nonequilibrium binary lattice model emerges in which the smoothing or roughening surface diffusion can be described by attracting or repelling motion of oriented dimers the binary representation allows simulations on very large size and time scales we provide numerical evidence for mullins herring or molecular beam epitaxy class scaling of the surface width the competition of inverse mullins herring diffusion with a smoothing deposition which corresponds to a kardar parisi zhang kpz process generates different patterns dots or ripples we analyze numerically the scaling and wavelength growth behavior in these models in particular we confirm by large size simulations that the kpz type of scaling is stable against the addition of this surface diffusion hence this is the asymptotic behavior of the kuramoto sivashinsky equation as conjectured by field theory in two dimensions but has been debated numerically if very strong normal surface diffusion is added to a kpz process we observe smooth surfaces with logarithmic growth which can describe the mean field behavior of the strong coupling kpz class we show that ripple coarsening occurs if parallel surface currents are present otherwise logarithmic behavior emerges

exact diffusion constant for the one dimensional partially asymmetric exclusion model we calculate exactly the diffusion constant associated with the fluctuations of the current for the partial asymmetric exclusion model on a ring with an arbitrary number of particles and holes we also give the diffusion constant of a tagged particle on that ring our approach extends using the deformed harmonic oscillator algebra a result already known for the fully asymmetric case in the limit of weak asymmetry we extract from our exact expression the crossover between the edwards wilkinson and the kardar parisi zhang equations in 1 1 dimensions

phase diagram of the abc model on an interval the three species asymmetric abc model was initially defined on a ring by evans kafri koduvely and mukamel and the weakly asymmetric version was later studied by clincy derrida and evans here the latter model is studied on a one dimensional lattice of n sites with closed zero flux boundaries in this geometry the local particle conserving dynamics satisfies detailed balance with respect to a canonical gibbs measure with long range asymmetric pair interactions this generalizes results for the ring case where detailed balance holds and in fact the steady state measure is known only for the case of equal densities of the different species in the latter case the stationary states of the system on a ring and on an interval are the same we prove that in the limit n the scaled density profiles are given by pieces of the periodic trajectory of a particle moving in a quartic confining potential we further prove uniqueness of the profiles i e the existence of a single phase in all regions of the parameter space of average densities and temperature except at low temperature with all densities equal in this case a continuum of phases differing by translation coexist the results for the equal density case apply also to the system on the ring and there extend results of clincy et al

an iterative method for the identification of ma systems an iterative method for the identification of an nth order moving average ma system is proposed which is based on a matrix splitting because of the special structures of the matrices involved only o n storage is needed one iteration is accomplished in o n sup 2 operations and the algorithm may be executed on a pipeline multiprocessor few iterations are required to yield sufficient results so the algorithm is fast a simple error estimate can be obtained

the asymmetric exclusion process comparison of update procedures the asymmetric exclusion process asep has attracted a lot of interest not only because of its many applications e g in the context of the kinetics of biopolymerization and traffic flow theory but also because it is a paradigmatic model for nonequilibrium systems here we study the asep for different types of updates namely random sequential sequential sublattice parallel and parallel in order to compare the effects of the different update procedures on the properties of the stationary state we use large scale monte carlo simulations and analytical methods especially the so called matrix product ansatz mpa we present in detail the exact solution for the model with sublattice parallel and sequential updates using the mpa for the case of parallel update which is important for applications like traffic flow theory we determine the phase diagram the current and density profiles based on monte carlo simulations we furthermore suggest an mpa for that case and derive the corresponding matrix algebra

exact solution of the totally asymmetric simple exclusion process shock profiles the microscopic structure of macroscopic shocks in the one dimensional totally asymmetric simple exclusion process is obtained exactly from the complete solution of the stationary state of a model system containing two types of particles first and second class this nonequilibrium steady state factorizes about any second class particle which implies factorization in the one component system about the random shock position it also exhibits several other interesting features including long range correlations in the limit of zero density of the second class particles the solution also shows that a finite number of second class particles in a uniform background of first class particles form a weakly bound state

bounded continuous nonoscillatory solutions of second order nonlinear difference equations with continuous variable in this paper by using the fixed point theory under quite general condition on the nonlinear term we obtain an existence result concerning bounded continuous nonoscillatory solutions of a second order nonlinear difference equation with continuous variable

finite dimensional representations of a shock algebra the algebra describing a shock measure in the asymmetric simple exclusion model seen from a second class particle has finite dimensional representations if and only if the asymmetry parameterp of the model and the left and right asymptotic densitiesp of the shock satisfy 1 p p r p 1 p p 1 p for some integerr 1 the minimal dimension of the representation is then 2r these representations can be used to calculate correlation functions in the model

exact diffusion constant for one dimensional asymmetric exclusion models the one dimensional fully asymmetric exclusion model which describes a system of particles hopping in a preferred direction with hard core interactions is considered on a ring of size n the steady state of this system is known all configurations have equal weight which allows for easy computation of the average velocity of a particle in the steady state here an exact expression for the diffusion constant of a particle is obtained for arbitrary number of particles and system size by using a matrix formulation two limits of infinite system size n are discussed firstly when the number of particles remains finite as n to infinity the diffusion constant remains dependent on the exact number of particles due to correlations between successive collisions secondly when the density p of particles is non zero i e when the number of particles is equal to n rho as n to infinity the diffusion constant scales as n 12 the exponent 1 2 is related to the dynamic exponent z 3 2 of the kpz equation in 1 1 dimensions

on matrix product states for periodic boundary conditions the possibility of a matrix product representation for eigenstates with energy and momentum zero of a general m state quantum spin hamiltonian with nearest neighbour interaction and periodic boundary condition is considered for this representation we use the quadratic algebra defined in krebs and sandow 1997 j phys a math gen 30 3165 which is generated by 2m operators which fulfil m 2 quadratic relations endowed with a trace like function reflecting periodic boundary conditions it is shown that not every eigenstate with energy and momentum zero can be written in this way an explicit counter example is given this is in contrast to the case of open boundary conditions where every zero energy eigenstate can be written as a matrix product state using a fock like representation of the same quadratic algebra

the matrix product solution of the multispecies partially asymmetric exclusion process we find the exact solution for the stationary state measure of the partially asymmetric exclusion process on a ring with multiple species of particles the solution is in the form of a matrix product representation where the matrices for a system of n species are defined recursively in terms of the matrices for a system of n 1 species a complete proof is given based on the quadratic relations verified by these matrices this matrix product construction is interpreted in terms of the action of a transfer matrix

nonequilibrium steady states of matrix product form a solver s guide we consider the general problem of determining the steady state of stochastic nonequilibrium systems such as those that have been used to model among other things biological transport and traffic flow we begin with a broad overview of this class of driven diffusive systems which includes exclusion processes focusing on interesting physical properties such as shocks and phase transitions we then turn our attention specifically to those models for which the exact distribution of microstates in the steady state can be expressed in a matrix product form in addition to a gentle introduction to this matrix product approach how it works and how it relates to similar constructions that arise in other physical contexts we present a unified pedagogical account of the various means by which the statistical mechanical calculations of macroscopic physical quantities are actually performed we also review a number of more advanced topics including nonequilibrium free energy functionals the classification of exclusion processes involving multiple particle species existence proofs of a matrix product state for a given model and more complicated variants of the matrix product state that allow various types of parallel dynamics to be handled we conclude with a brief discussion of open problems for future research

recursive structures in the multispecies tasep we consider a multispecies generalization of the totally asymmetric simple exclusion process tasep with the simple hopping rule for the and th class particles the transition occurs with a rate independent from the values and ferrari and martin 2007 ann prob 35 807 obtained the stationary state of this model thanks to a combinatorial algorithm which was subsequently interpreted as a matrix product representation by evans et al 2009 j stat phys 135 217 this matrix ansatz shows that the stationary state of the multispecies tasep with n classes of particles n tasep can be constructed algebraically by the action of an operator on the n 1 tasep stationary state besides arita et al 2009 j phys a math theor 45 345002 analyzed the spectral structure of the markov matrix they showed that the set of eigenvalues of the n tasep contains those of the n 1 tasep and that the various spectral inclusions can be encoded in a hierarchical set theoretic structure known as the hasse diagram inspired by these works we define nontrivial operators that allow us to construct eigenvectors of the n tasep by lifting the eigenvectors of the n 1 tasep this goal is achieved by generalizing the matrix product representation and the ferrari martin algorithm in particular we show that the matrix ansatz is not only a convenient tool to write the stationary state but in fact intertwines markov matrices of different values of n

finite dimensional representations of the quadratic algebra applications to the exclusion process we study the one dimensional partially asymmetric simple exclusion process asep with open boundaries that describes a system of hard core particles hopping stochastically on a chain coupled to reservoirs at both ends derrida and coworkers showed in 1993 that the stationary probability distribution of this model can be represented as a trace on a quadratic algebra closely related to the deformed oscillator algebra we construct all finite dimensional irreducible representations of this algebra this enables us to compute the stationary bulk density as well as all correlation lengths for the asep on a set of special curves of the phase diagram

on position and momentum operators in the q oscillator algebra the aim of this paper is to study the position and momentum operators in q deformed oscillator algebras the natural form of the position operator is xp qpn a a qpn where p is a real number this operator is an operator representable by a jacobi matrix using the theory of jacobi matrices the theory of classical moment problem and the theory of basic hypergeometric functions it is shown that depending on values of q and p xp can be unbounded symmetric operator which has the deficiency indices 1 1 and hence is not self adjoint but has self adjoint extensions bounded self adjoint operator with continuous simple spectrum or self adjoint operator of trace class therefore with discrete spectrum with zero as the point of accumulation of eigenvalues the connection of the q deformed heisenberg relation px qxp 1 for the position and momentum operators with a q deformation of the quantum harmonic oscillator is also considered

an exact solution of a one dimensional asymmetric exclusion model with open boundaries a simple asymmetric exclusion model with open boundaries is solved exactly in one dimension the exact solution is obtained by deriving a recursion relation for the steady state if the steady state is known for all system sizes less thann then our equation 8 gives the steady state for sizen using this recursion we obtain closed expressions 48 for the average occupations of all sites the results are compared to the predictions of a mean field theory in particular for infinitely large systems the effect of the boundary decays as the distance to the power 1 2 instead of the inverse of the distance as predicted by the mean field theory

stochastic dynamics of discrete curves and multi type exclusion processes this study deals with continuous limits of interacting one dimensional diffusive systems arising from stochastic distortions of discrete curves with various kinds of coding representations these systems are essentially of a reaction diffusion nature in the non reversible case the invariant measure has in general a non gibbs form the corresponding steady state regime is analyzed in detail by using a tagged particle together with a state graph cycle expansion of the probability currents as a consequence the constants appearing in lotka volterra equations which describe the fluid limits of stationary states can be traced back directly at the discrete level to tagged particle cycles coefficients current fluctuations are also studied and the lagrangian is obtained via an iterative scheme the related hamilton jacobi equation which leads to the large deviation functional is investigated and solved in the reversible case just for the sake of checking

multi species asymmetric exclusion process in ordered sequential update a multi species generalization of the asymmetric simple exclusion process is studied with ordered sequential and sub lattice parallel updating schemes in this model particles hop with their own specific probabilities to their rightmost empty site and fast particles overtake slow ones with a definite probability using the matrix product ansatz technique we obtain the relevant algebra and study the uncorrelated stationary state of the model both for an open system and on a ring a complete comparison between the physical results in these updates and those of random sequential introduced in karimipour v 1999 a multi species asep and its relation to traffic flow phys rev e 59 205 and karimipour v 1998 a multi species asep steady state and correlation functions on a periodic lattice preprint cond mat 9809193 is made

the asymmetric exclusion model with sequential update we present a solution for the stationary state of an asymmetric exclusion model with sequential update and open boundary conditions we solve the model exactly for random hopping in both directions by applying a matrix product formalism which was recently used to solve the model with sublattice parallel update hinrichsen h 1995 weizmann inst preprint cond mat 9512172 it is shown that the matrix algebra describing the sequential update and sublattice parallel update are identical and can be mapped onto the random sequential case treated by derrida et al derrida b evans m r hakim v and pasquier v 1993 j phys a math gen 26 1493

phase transition in the abc model recent studies have shown that one dimensional driven systems can exhibit phase separation even if the dynamics is governed by local rules the mathrm abc model which comprises three particle species that diffuse asymmetrically around a ring shows anomalous coarsening into a phase separated steady state in the limiting case in which the dynamics is symmetric and the parameter q describing the asymmetry tends to one no phase separation occurs and the steady state of the system is disordered in the present work we consider the weak asymmetry regime q mathrm exp ensuremath ensuremath beta n where n is the system size and study how the disordered state is approached in the case of equal densities we find that the system exhibits a second order phase transition at some nonzero ensuremath beta c the value of ensuremath beta c 2 ensuremath pi sqrt 3 and the optimal profiles can be obtained by writing the exact large deviation functional for nonequal densities we write down mean field equations and analyze some of their predictions

the grand canonical abc model a reflection asymmetric mean field potts model we investigate the phase diagram of a three component system of particles on a one dimensional filled lattice or equivalently of a one dimensional three state potts model with reflection asymmetric mean field interactions the three types of particles are designated as a b and c the system is described by a grand canonical ensemble with temperature t and chemical potentials t a t b and t c we find that for a b c the system undergoes a phase transition from a uniform density to a continuum of phases at a critical temperature for other values of the chemical potentials the system has a unique equilibrium state as is the case for the canonical ensemble for this abc model the grand canonical ensemble is the stationary measure satisfying detailed balance for a natural dynamics we note that where tc is the critical temperature for a similar transition in the canonical ensemble at fixed equal densities ra rb rc 1 3

the noncommutative space of stochastic diffusion systems in the matrix product ground states approach to n species diffusion processes the stationary probability distribution is expressed as a matrix product state with respect to a quadratic algebra determined by the dynamics of the process we show that the quadratic algebra defines a noncommutative space with a glq n quantum group action as its symmetry boundary processes account for the appearance of parameter dependent linear terms in the algebraic relations we argue that for systems with boundary conditions the diffusion algebras are also obtained either by a shift of basis in the n dimensional quantum plane or by an appropriate change of basis in a lower dimensional one which leads to a reduction of the glq n symmetry

combinatorics of the two species asep and koornwinder moments abstract in previous work 12 13 14 the first and third authors introduced staircase tableaux which they used to give combinatorial formulas for the stationary distribution of the asymmetric simple exclusion process asep and for the moments of the askey wilson weight function the fact that the asep and askey wilson moments are related at all is unexpected and is due to 45 the asep is a model of particles hopping on a one dimensional lattice of n sites with open boundaries particles can enter and exit at both left and right borders it was introduced around 1970 34 43 and is cited as a model for both traffic flow and translation in protein synthesis meanwhile the askey wilson polynomials are a family of orthogonal polynomials in one variable which sit at the top of the hierarchy of classical orthogonal polynomials so from this previous work we have the relationship asep staircase tableaux askey wilson moments the askey wilson polynomials can be viewed as the one variable case of the multivariate koornwinder polynomials which are also known as the macdonald polynomials attached to the non reduced affine root system c n c n it is natural then to ask whether one can generalize the relationships among the asep askey wilson moments and staircase tableaux in such a way that koornwinder moments replace askey wilson moments in 15 we made a precise link between koornwinder moments and the two species asep a generalization of the asep which has two species of particles with different weights in this article we introduce rhombic staircase tableaux and show that we have the relationship 2 species asep rhombic staircase tableaux koornwinder moments in particular we give formulas for the stationary distribution of the two species asep and for koornwinder moments in terms of rhombic staircase tableaux download download high res image 75kb download download full size image

on matrix product ground states for reaction diffusion models we discuss a new mechanism leading to a matrix product form for the stationary state of one dimensional stochastic models the corresponding algebra is quadratic and involves four different matrices for the example of a coagulation decoagulation model explicit four dimensional representations are given and exact expressions for various physical quantities are recovered we also find the general structure of n point correlation functions at the phase transition

weighted averaging of a set of noisy images for maximum signal to noise ratio the problem of estimating a signal from a weighted average of n registered noisy observations is considered a set of optimal weighting coefficients is determined by maximizing a signal to noise ratio criterion this solution can be computed by first standardizing each observation with respect to its first and second moments and then evaluating the first eigenvector of the corresponding n n inner product matrix the resulting average is shown to be proportional to the first basis vector of the karhunen loeve transform provided that the data has been standardized in an appropriate fashion the low sensitivity of this approach to the presence of outliers is illustrated by using real electron micrographs of ostensibly identical virus particles

shock profiles for the asymmetric simple exclusion process in one dimension the asymmetric simple exclusion process asep on a one dimensional lattice is a system of particles which jump at rates p and 1 p here p 1 2 to adjacent empty sites on their right and left respectively the system is described on suitable macroscopic spatial and temporal scales by the inviscid burgers equation the latter has shock solutions with a discontinuous jump from left density rho to right density rho rho sqrt rho 1 rho rho 1 rho for a special value of the asymmetry given by p 1 p rho 1 rho rho 1 rho the measure is bernoulli with density rho on the left and rho on the right in the weakly asymmetric limit 2p 1 to0 the microscopic width of the shock diverges as 2p 1 1 the stationary measure is then essentially a superposition of bernoulli measures corresponding to a convolution of a density profile described by the viscous burgers equation with a well defined distribution for the location of the second class particle