an algebraic construction of generalized coherent states for shape invariant potentials generalized coherent states for shape invariant potentials are constructed using an algebraic approach based on supersymmetric quantum mechanics we show that this generalized formalism is able to a supply the essential requirements necessary to establish a connection between classical and quantum formulations of a given system continuity of labelling resolution of unity temporal stability and action identity b reproduce results already known for shape invariant systems such as harmonic oscillator double anharmonic poschl teller and self similar potentials and c point to a formalism that provides a unified description of the different kind of coherent states for quantum systems

equivalence of q bosons using the exponential phase operator various forms of the q boson are explained and their hidden symmetry revealed by transformations using the exponential phase operator both the one component and the multicomponent q bosons are discussed as a byproduct we obtain a new boson algebra having a shifted vacuum structure and define a global operator u 1 gauge transformation

a two level atom coupled to a two dimensional supersymmetric and shape invariant system models a class of bound state problems which represents the coupling of a two level atom with a two dimensional supersymmetric system involving two shape invariant potentials is introduced we study two models with different coupling hamiltonians

new q deformed coherent states with an explicitly known resolution of unity we construct a new family of q deformed coherent states zq where 0 q 1 these states are normalizable on the whole complex plane and continuous in their label z they allow the resolution of unity in the form of an ordinary integral with a positive weight function obtained through the analytic solution of the associated stieltjes power moment problem and expressed in terms of one of the two jacksons s q exponentials they also permit exact evaluation of matrix elements of physically relevant operators we use this to show that the photon number statistics for the states is sub poissonian and that they exhibit quadrature squeezing as well as an enhanced signal to quantum noise ratio over the conventional coherent state value finally we establish that they are the eigenstates of some deformed boson annihilation operator and study some of their characteristics in deformed quantum optics

stochastic averaging of strongly non linear oscillators under combined harmonic and white noise excitations abstract a stochastic averaging procedure of strongly non linear oscillators subject to external and or parametric excitations of both harmonic and white noise forces is developed by using the so called generalized harmonic functions the procedure is applied to a duffing oscillator with hardening stiffness under both external harmonic excitation and external and parametric excitations of white noises the averaged fokker planck kolmogrov equation is solved by using the path integration method based on the stationary joint probability density of amplitude and phase obtained by using the stochastic averaging and the path integration the stochastic jump of the duffing oscillator under combined harmonic and white noise excitations and its bifurcation as the system parameters frequency ratio strength of the non linearity amplitude of harmonic excitation and intensity of white noise change are examined for the first time

complementarity of suq 3 and uq 2 and q boson realization of the suq 3 irreducible representations the complementarity relationship also termed duality that arises between the irreps of the su 3 and u 2 lie algebras when their direct sum su 3 u 2 is embedded into a larger u 6 algebra and single row irreps of the latter are considered is extended to the corresponding q algebras suq 3 and uq 2 it is demonstrated by explicitly constructing the unique q boson state that is simultaneously maximal in suq 3 and uq 2 for a given u q 2 weight in addition the relations between the suq 3 and uq 2 casimir operators resulting from their complementarity are explicitly found together with the q bargmann representation of q boson operators the complementarity relationship is then used to construct a gel fand tseitlin basis for arbitrary suq 3 irreps in terms of q boson operators

application of the mesh independence principle to mesh refinement the mesh independence principle mip for a newton iteration applied to an operator equation and its discretization for different stepsizes h states for a fixed starting point the number of iterations of newton s method to obtain a fixed tolerance is eventually independent of h this mip is used to formulate an efficient strategy for the solution of nonlinear equations amounting to the work equivalent of two or three newton iterates for the smallest h examples are given

gazeau klauder coherent states for trigonometric rosen morse potential the gazeau klauder coherent states for the trigonometric rosen morse potential are constructed it is shown that the resolution of unity temporal stability and action identity conditions are satisfied for the coherent states the mandel parameter is also calculated for the weighting distribution function corresponding to the coherent states

generalized coherent states for associated hypergeometric type functions we introduce a right inverse for the annihilation operator which appears in the factorization of associated hypergeometric type operators this makes possible the definition of generalized coherent states for the associated eigenfunctions these generalized coherent states satisfy the relevant properties i e label continuity overcompleteness temporal stability and action identity required to establish a close connection between the quantum and classical formulations of a given physical system

van der pol s oscillator under delayed feedback the effect of delayed feedback on oscillatory behaviour is investigated for the classical van der pol oscillator it is shown how the presence of delay can change the amplitude of limit cycle oscillations or suppress them altogether the result is compared to the conventional proportional and derivative feedback the derivative like effect of delay is also demonstrated in a modified equation where a delayed term provides the damping

three level coupled systems and parasupersymmetric shape invariance a class of bound state problems which represents the coupling of a three level atom with a two dimensional system involving two shape invariant potentials is introduced we consider second order parasupersymmetric quantum mechanical models and using an algebraic formulation for shape invariant potential systems resolve the eigenvalue problem for these coupled systems considering two possible kinds for the coupling hamiltonian linear and nonlinear in the potential ladder operators an application is given for a couple of shape invariant potentials harmonic oscillator morse potentials

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

an energy minimizing mesh for the schro dinger equation abstract a formula is derived which gives the optimum placement of mesh points in the sense of minimizing the error in energy for a given number of degrees of freedom the wave function is assumed to be given in a finite difference or finite element representation with polynomial completeness to an arbitrary but fixed degree the result depends explicitly on the wave function the kinetic energy operator and the degree of polynomial completeness for the representation but does not depend explicitly on the potential even in the presence of a coulomb singularity the optimum mesh predicted here for the hydrogen atom is compared to the widely used herman skillman mesh a 1 dimensional example is given in which the calculated error in energy displays a sharp minimum at the predicted optimal mesh density the critical role of reproducing the analytic structure of the solution is illustrated with an additional example in one dimension the hydrogen is wave function is considered as a 3 dimensional problem and an optimal mesh density is calculated a singular mesh density is required to account for the cusp while retaining the convergence properties of the basis set a few percent of the available degrees of freedom are devoted to the description of the wave function cusp in the optimal mesh

a completeness relation for the q analogue coherent states by q integration q integration is defined for the q oscillator realization of quantum groups this is used to prove a completeness relation for the q analogue of the usual coherent states these states are overcomplete

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

orientation of particle attachment and local isotropy in diffusion limited aggregation dla we simulate 50 off lattice diffusion limited aggregation dla clusters of one million particles each the probability distribution of the angle of attachment of arriving particles with respect to the local radial direction is obtained numerically for increasing cluster size n the distribution crosses over extremely accurately to a cosine with an amplitude which decreases towards zero as a power law in n from this specific viewpoint asymptotically large dla clusters are locally isotropic

correlation theory of delayed feedback in stochastic systems below andronov hopf bifurcation here we address the effect of large delay on the statistical characteristics of noise induced oscillations in a nonlinear system below andronov hopf bifurcation in particular we introduce a theory of these oscillations that does not involve the eigenmode expansion and can therefore be used for arbitrary delay time in particular we show that the correlation matrix cm oscillates on two different time scales on the scale of the main period of noise induced oscillations and on the scale close to the delay time at large values of the delay time the cm is shown to decay exponentially only for large values of its argument while for the arguments comparable with the value of the delay the cm remains finite disregarding the delay time the definition of the correlation time of the system with delay is discussed

completeness of coherent states associated with self similar potentials and ramanujan s integral extension of the beta function a decomposition of identity is given as a complex integral over the coherent states associated with a class of shape invariant self similar potentials there is a remarkable connection between these coherent states and ramanujan s integral extension of the beta function

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

realizability of a model in infinite statistics following greenberg and others we study a space with a collection of operatorsa k satisfying the q mutator relations a l a k a l k l corresponding forq 1 to classical bose and fermi statistics we show that then n matrixa n q representing the scalar products ofn particle states is positive definite for alln ifq lies between 1 and 1 so that the commutator relations have a hilbert space representation in this case this has also been proved by fivel and by bozejko and speicher we also give an explicit factorization ofa n q as a product of matrices of the form 1 q jt 1 with 1 j n andt a permutation matrix in particular a n q is singular if and only ifq m 1 for some integerm of the formk 2 k 2 k n

an algebraic construction of generalized coherent states associated with q deformed models for primary shape invariant systems generalized coherent states for primary shape invariant potential systems quantum deformed by different models are constructed using an algebraic approach based on supersymmetric quantum mechanics we show that this generalized formalism is able a to supply the essential requirements necessary to establish a connection between classical and quantum formulations of a given system b to reproduce as particular cases results already known for shape invariant systems such as standard harmonic oscillator and p schl teller potentials as well as quantum deformed harmonic oscillator models and c point to a formalism that provides a unified description of the different kind of coherent states for quantum systems deformed or not deformed

time quantization and q deformations we extend to quantum mechanics the technique of stochastic subordination by means of which one can express any semi martingale as a time changed brownian motion as examples we considered two versions of the q deformed harmonic oscillator in both ordinary and imaginary time and show how these various cases can be understood as different patterns of time quantization rules

first passage failure of quasi integrable hamiltonian systems under time delayed feedback control a procedure for studying the first passage failure of quasi integrable hamiltonian systems under time delayed feedback control is proposed the stochastic averaging method for quasi integrable hamiltonian systems under time delayed feedback control is firstly introduced a backward kolmogorov equation governing the conditional reliability function and a set of generalized pontryagin equations governing the conditional moments of first passage time are then established the conditional reliability function the conditional probability density and moments of first passage time are obtained by solving the backward kolmogorov equation and generalized pontryagin equations with suitable initial and boundary conditions an example is given to illustrate the proposed procedure and the results from digital simulation are obtained to verify the effectiveness of the proposed procedure the effects of time delay in feedback control forces on the conditional reliability function conditional probability density and moments of first passage time are analyzed

uniform approximation and coherent state path integrals one possible formulation of mean field approximations is in terms of coherent state path integrals in this paper the construction of uniform semiclassical approximation to coherent state integrals is investigated as a specific example the method is applied to the forced harmonic oscillator

nonlinear lie algebra and ladder operators for orbital angular momentum based on the nonlinear lie algebra a new framework is put forward to treat the problem of angular momentum from this framework the ladder operators for the orbital angular momentum can be solved as simultaneous eigenvectors of the lie derivations ad l2 and ad l2 in an operator space the ladder operators for solvable central potentials can also be found in a united way

stochastic averaging of quasi integrable hamiltonian systems with delayed feedback control abstract a stochastic averaging method for quasi integrable hamiltonian systems with time delayed feedback control is proposed first a quasi integrable hamiltonian system with delayed feedback control subjected to gaussian white noise excitations is formulated and then transformed into ito stochastic differential equations without time delay then the averaged ito stochastic differential equations for the system are derived and the stationary solution of the averaged fokker planck kolmogorov fpk equation associated with the averaged ito equations is obtained for both non resonant and resonant cases finally three examples are worked out in detail to illustrate the application and effectiveness of the proposed method and the effect of time delayed feedback control on the response of the systems

three dimensional quantum groups from contractions of su 2 q contractions of lie algebras and of their representations are generalized to define new quantum groups an explicit and complete exposition is made for the one dimensional heisenberg h 1 q and the two dimensional euclidean quantum group e 2 q obtained by contracting su 2 q

multi parametric deformed heisenberg algebras a route to complexity we introduce a generalization of the heisenberg algebra which is written in terms of a functional of one generator of the algebra f j0 that can be any analytical function when f is linear with slope we show that the algebra in this case corresponds to q oscillators for q2 tan the case where f is a polynomial of order n in j0 corresponds to an n parameter deformed heisenberg algebra the representations of the algebra when f is any analytical function are shown to be obtained through the study of the stability of the fixed points of f and their composed functions the case when f is a quadratic polynomial in j0 the simplest nonlinear scheme which is able to create chaotic behaviour is analysed in detail and special regions in the parameter space give representations that cannot be continuously deformed to representations of heisenberg algebra

generalized q oscillators and their hopf structures we study the relationships among the various forms of the q oscillator algebra and consider the conditions under which it supports a hopf structure we also present a generalization of this algebra together with its corresponding hopf structure its multimode extensions are also considered

higher order adaptive finite element methods for kohn sham density functional theory we present an efficient computational approach to perform real space electronic structure calculations using an adaptive higher order finite element discretization of kohn sham density functional theory dft to this end we develop an a priori mesh adaption technique to construct a close to optimal finite element discretization of the problem we further propose an efficient solution strategy for solving the discrete eigenvalue problem by using spectral finite elements in conjunction with gauss lobatto quadrature and a chebyshev acceleration technique for computing the occupied eigenspace the proposed approach has been observed to provide a staggering 100 200 fold computational advantage over the solution of a generalized eigenvalue problem using the proposed solution procedure we investigate the computational efficiency afforded by higher order finite element discretizations of the kohn sham dft problem our studies suggest that staggering computational savings of the order of 1000 fold relative to linear finite elements can be realized for both all electron and local pseudopotential calculations by using higher order finite element discretizations on all the benchmark systems studied we observe diminishing returns in computational savings beyond the sixth order for accuracies commensurate with chemical accuracy suggesting that the hexic spectral element may be an optimal choice for the finite element discretization of the kohn sham dft problem a comparative study of the computational efficiency of the proposed higher order finite element discretizations suggests that the performance of finite element basis is competing with the plane wave discretization for non periodic local pseudopotential calculations and compares to the gaussian basis for all electron calculations to within an order of magnitude further we demonstrate the capability of the proposed approach to compute the electronic structure of a metallic system containing 1688 atoms using modest computational resources and good scalability of the present implementation up to 192 processors

quantum dynamics of parasupersymmetric and shape invariant coupled systems a class of bound state problems which represents the coupling of a three level atom with a two dimensional system involving two shape invariant potentials was introduced in a previous paper in this paper we considered second order parasupersymmetric quantum mechanical models and two possible kinds for the coupling hamiltonian linear and nonlinear in the potential ladder operators in the present paper using an algebraic formulation for shape invariant potential systems we study the quantum dynamics of these coupled systems and obtain the temporal behaviour of some dynamical variables related with the atom and the coupling potentials an application is given for a couple of shape invariant potentials poschl teller self similar potentials

effects of mass discontinuity on the numerical solutions to quantum wells using the effective mass equation this paper investigates the effects of mass dicontinuity on the numerical solutions to quantum wells using the effective mass equation the numerical methods utilized are the finite element method with first order elements and the finite difference method with the entire truncated solution domain discretized by equally spaced nodes the three hamiltonians explored are the convention hamiltonian the bendaniel and duke hamiltonian and the bastard hamiltonian it is shown that the proper discretization patterns for both numerical schemes may drastically improve the solution accuracy the finite difference representation of the bendaniel and duke hamiltonian using the direct mass average is found more accurate than the one using the harmonic mass average it is further pointed out that at the mass profile discontinuities the commonly accepted interface conditions for the bastard hamiltonian are not natural conditions this observation is critical if the bastard hamiltonian is to be solved numerically

generalized robertson intelligent states and squeezing for supersymmetric and shape invariant systems an algebraic construction we obtain the robertson schrodinger uncertainty relation for shape invariant systems and construct generalized robertson intelligent states for these systems using an algebraic approach based on the supersymmetric quantum mechanics using the variances of generalized quadrature operators we study the coherency and squeezing properties evaluating their dependence on different kinds of generalizations for shape invariant systems with potential parameters related by a translation poschl teller potential and by a scaling self similar potential

relations for clebsch gordan and racah coefficients in suq 2 and yang baxter equations relations are exploited among clebsch gordan cg and racah coefficients in the algebra suq 2 known as a deformation of su 2 these are used to show that the yang baxter yb relation for the irf interaction round a face model results from one of the symmetry relations for the 9 j symbol specific to suq 2 and that in an asymptotic limit this yb relation becomes the yb relation for the two dimensional vertex model the racah coefficient which has a particularly simple dependence on q is efficiently used such that an asymptotic limit of the racah coefficient is the cg coefficient and another limit gives the factorized s matrix of the vertex model

approach of spherical harmonics to the representation of the deformed su 1 1 algebra the m shifting generators of su 2 algebra together with a pair of l shifting ladder symmetry operators have been used in the space of all spherical harmonics ylm in order to introduce a new set of operators expressing the transitions between them it is shown that the space of spherical harmonics whose l 2m or l 2m is given presents negative and positive irreducible representations of a deformed su 1 1 algebra respectively these internal symmetries also suggest new algebraic methods to construct the spherical harmonics in the framework of the spectrum generating algebras

coherent states for the noncompact supergroups osp 2 2n r an analysis of the coherent states for the noncompact supergroup osp 2 2n r is presented in contrast to osp 1 2n r both typical and atypical representations have to be considered the measure of integration in general for osp 2 2n r coherent states is calculated it is then used to construct the decomposition of unity for the special case of osp 2 2 r it is found however that the typical and atypical representations of osp 2 2 r have to be treated separately it is verified that the coherent states for osp 2 2 r are closest to classical in the sense of perelomov

a study of representations of the algebra of functions on the quantum group glq n a q analogue of the root system is constructed for this algebra which is similar to the root system of classical lie algebras it is then used to construct in detail a class of representations of the algebra of functions on the quantum group glq n and a q boson realization of the generators of glq n is given i also construct infinite dimensional hilbert space representations of this algebra the main result of this paper is stated in proposition 8

suq h cross to 0 2 and suq h cross 2 the classical and quantum q deformations of the su 2 algebra ii the hopf algebra the yang baxter equation and multi deformed algebraic structures for pt i see ibid vol 23 p 4185 1990 the suq 2 algebra is realized by means of both the poisson brackets in classical mechanics and commutators in quantum mechanics in a system with q deformed oscillators of two different types the structures of the hopf algebra and the quantum yang baxter equation are also discussed on a quantum level a set of j representations of the quantum algebra suq 2 is constructed based on the type ii q oscillators multi deformations of the oscillators of the two types and multi deformed algebras expressed in poisson brackets as well as in lie brackets are proposed

a simple difference realization of the heisenberg q algebra a realization of the heisenberg q algebra whose generators are first order difference operators on the full real line is discussed herein the eigenfunctions of the corresponding q oscillator hamiltonian are given explicitly in terms of the q 1 hermite polynomials the nonuniqueness of the measure for these q oscillator states is also studied

verma module of the quantum group gl n q and its q boson and heisenberg weyl relation realizations the structure and verma module of the quantum matrix element algebra a n q of the quantum group gl n q are studied the method used here is similar to that for studying the structure and verma module of semisimple lie algebras the concept of the cartan subalgebra raising and lowering operators and their pairs is defined the q boson and the corresponding heisenberg weyl relation realizations are generally studied and the cyclic representations of a n q are obtained the explicit examples a 2 q and a 3 q are discussed in detail

path integral formalism for suq 2 coherent states a path integral formulation in the representation of coherent states for the quantum group suq 2 is introduced an expression for the transition amplitude connecting two suq 2 coherent states is constructed and the corresponding canonical equations of motion are also derived

stochastic stationary responses of a viscoelastic system with impacts under additive gaussian white noise excitation abstract this paper is devoted to investigate the stochastic stationary responses of a viscoelastic system with impacts under additive gaussian white noise excitation first the viscoelastic force is approximated as equivalent stiffness and damping terms and the original system is replaced by a system without viscoelasticity then the stationary responses of the system are obtained analytically by using non smooth transformation and stochastic averaging method the theoretical analyses are verified by numerical results from monte carlo simulations effects of the noise intensity and the nonlinear damping coefficient on the system responses are investigated at last it is worthy noting that the restitution coefficient the linear damping coefficient and the viscoelastic parameters can induce the occurrence of stochastic p bifurcation

a new completeness relation in the q deformed two mode fock space in two mode fock space a new completeness relation for the q analogue of the single complex variable state is proved by virtue of some q deformed combinatorial identities which are also derived here for the first time

quantum dynamics of a two level system coupled to a shape invariant potential the quantum dynamics of a two level system coupled to a shape invariant potential is investigated shape invariant potentials share an integrability condition called shape invariance which identifies an underlying algebraic structure in general infinite dimensional that transforms the potential parameters such as strength range and diffuseness we determine the time evolution operator the density operator of the system and obtain the temporal behaviour of various dynamical variables by considering either pure or mixed initial states of the system constructed with the generalized coherent state of the shape invariant coupling potential we consider specific examples of shape invariant coupling potentials harmonic oscillator poschl teller and self similar potentials the results obtained for all dynamical variables exhibit rapid oscillations which periodically collapse and regenerate in different ways depending on the coupling potential nature

the q t gaussian process the q t fock space fq t h introduced in this paper is a deformation of the q fock space of bozejko and speicher the corresponding creation and annihilation operators now satisfy the commutation relation aq t f aq t g qaq t g aq t f f g htn turn mathjax off a defining relation of the chakrabarti jagannathan deformed quantum oscillator algebra the moments of the deformed gaussian element sq t h aq t h aq t h are encoded by the joint statistics of crossings and nestings in pair partitions the q 0 t specialization yields a natural single parameter deformation of the full boltzmann fock space of free probability with the corresponding semicircular measure variously encoded via the rogers ramanujan continued fraction the t airy function the t catalan numbers of carlitz riordan and the first order statistics of the reduced wigner process

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

a q analogue of bargmann space and its scalar product a q analogue of bargmann space is defined using the properties of coherent states associated with a pair of q deformed bosons the space consists of a class of entire functions of a complex variable z and has a reproducing kernel on this space the q boson creation and annihilation operators are represented as multiplication by z and q differentiation with respect to z respectively a q integral analogue of bargmann s scalar product is defined involving the q exponential as a weight function associated with this is a completeness relation for the q coherent states

q oscillators realization of fq 4 and gq 3 a realization of the quantum superalgebras corresponding to f 4 and g 3 is given in terms of q deformed bosonic and fermionic oscillators

more on the q oscillator algebra and q orthogonal polynomials properties of certain q orthogonal polynomials are connected to the q oscillator algebra the wall and q laguerre polynomials are shown to arise as matrix elements of q exponentials of the generators in a representation of this algebra a realization is presented where the continuous q hermite polynomials form a basis of the representation space various identities are interpreted within this model in particular the connection formula between the continuous big q hermite and the continuous q hermite polynomials is thus obtained and two generating functions for these last polynomials are derived algebraically

the q boson realizations of the quantum group uq sl n 1 c the authors give an explicit expression of the recurrency formulae of canonical realization for quantum enveloping algebras uq sl n 1 c in these formulae the generators of the algebra uq sl n 1 c are expressed by means of n canonical q boson pairs one auxiliary representation of the algebra uq gl n c

slq 2 realizations for kepler and oscillator potentials and q canonical transformations the realizations of the lie algebra corresponding to the dynamical symmetry group so 2 1 of the kepler and oscillator potentials are q deformed the q canonical transformation connecting two realizations is given and a general definition for the q canonical transformation is deduced a q schrodinger equation for a kepler like potential is obtained from the q oscillator schrodinger equation the energy spectrum and the ground state wavefunction are calculated

algebraic nature of shape invariant and self similar potentials self similar potentials generalize the concept of shape invariance which was originally introduced to explore exactly solvable potentials in quantum mechanics in this paper it is shown that the previously introduced algebraic approach to the latter can be generalized to the former the infinite lie algebras introduced in this context are shown to be closely related to the q algebras the associated coherent states are investigated

coherent states for the harmonic oscillator representations of the orthosymplectic supergroup osp 1 2n r coherent states for the harmonic oscillator representations of the noncompact supergroup osp 1 2n r are introduced and the invariant integration measure is calculated by studying transformation properties of supercoset variables the generalized bogoliubov transformation for mixed systems of bosons and fermions is also obtained an example for the simple harmonic oscillator is given

technical communique asymptotic lyapunov stability with probability one of quasi integrable hamiltonian systems with delayed feedback control the asymptotic lyapunov stability with probability one of multi degree of freedom mdof quasi integrable and nonresonant hamiltonian systems with time delayed feedback control subject to multiplicative parametric excitation of gaussian white noise is studied first the time delayed feedback control forces are expressed approximately in terms of the system state variables without time delay and the system is converted into ordinary quasi integrable and nonresonant hamiltonian system then the averaged ito stochastic differential equations are derived by using the stochastic averaging method for quasi integrable hamiltonian systems and the expression for the largest lyapunov exponent of the linearized averaged ito equations is derived finally the necessary and sufficient condition for the asymptotic lyapunov stability with probability one of the trivial solution of the original system is obtained approximately by letting the largest lyapunov exponent to be negative an example is worked out in detail to illustrate the above mentioned procedure and its validity and to show the effect of the time delay in feedback control on the largest lyapunov exponent and the stability of the system

higher order adaptive finite element methods for orbital free density functional theory in the present work we study various numerical aspects of higher order finite element discretizations of the non linear saddle point formulation of orbital free density functional theory we first investigate the robustness of viable solution schemes by analyzing the solvability conditions of the discrete problem we find that a staggered solution procedure where the potential fields are computed consistently for every trial electron density is a robust solution procedure for higher order finite element discretizations we next study the convergence properties of higher order finite element discretizations of orbital free density functional theory by considering benchmark problems that include calculations involving both pseudopotential as well as coulomb singular potential fields our numerical studies suggest close to optimal rates of convergence on all benchmark problems for various orders of finite element approximations considered in the present study we finally investigate the computational efficiency afforded by various higher order finite element discretizations which constitutes the main aspect of the present work by measuring the cpu time for the solution of discrete equations on benchmark problems that include large aluminum clusters in these studies we use mesh coarse graining rates that are derived from error estimates and an a priori knowledge of the asymptotic solution of the far field electronic fields our studies reveal a significant 100 1000 fold computational savings afforded by the use of higher order finite element discretization alongside providing the desired chemical accuracy we consider this study as a step towards developing a robust and computationally efficient discretization of electronic structure calculations using the finite element basis

on a one parameter family of q exponential functions we examine the properties of a family of q exponential functions which depend on an extra parameter these functions have a well defined meaning for both the 0 1 cases if only it is shown that any two members of this family with different values of the parameter are related to each other by a fourier gauss transformation

an adaptive finite element method for linear elliptic problems on propose une methode adaptative d elements finis basee sur une estimation d erreur optimale de norme maxima pour les problemes elliptiques lineaires

an algebraic q deformed form for shape invariant systems a quantum deformed theory applicable to all shape invariant bound state systems is introduced by defining q deformed ladder operators we show that these new ladder operators satisfy new q deformed commutation relations in this context we construct an alternative q deformed model that preserves the shape invariance property presented by the primary system q deformed generalizations of morse scarf and coulomb potentials are given as examples

generalized coherent squeezed and intelligent states for exactly solvable quantum systems and the analogue of the displacement and squeezing operators using an algebraic approach we construct purely coherent and squeezed states for a set of exactly solvable quantum confined systems assuming a generalization of both the ladder operator and the displacement operator methods showing the equivalence between the two procedures we obtain the analogue of the displacement and the squeeze operators and study their basic relations and their connections with the properties of the purely coherent and squeezed states that they produce in a second approach we construct generalized squeezed coherent and intelligent states for these systems considering the successive action of the displacement and the squeeze operators in the first case and the combined action of these operators in the second case we apply the generalized approach for shape invariant systems with potential parameters related by a translation and by a scaling and show that the presence of the generalizing functionals of the potential parameters in the formalism opens a large number of possibilities in the construction of these special quantum states