Related papers: Generalized Coherent States Associated with the $C…
We construct two-parameters family of nonlinear coherent states by replacing the factorial in coefficients $z^n/\sqrt{n!}$ of the canonical coherent states by a specific generalized factorial $x_n^{\gamma,\sigma}!$ where parameters $\gamma$…
Both the coherent states and also the squeezed states of the harmonic oscillator have long been understood from the three classical points of view: the 1) displacement operator, 2) annihilation- (or ladder-) operator, and…
The coherent states for the quantum particle on the circle are introduced. The Bargmann representation within the actual treatment provides the representation of the algebra $[\hat J,U]=U$, where $U$ is unitary, which is a direct…
Starting from a faithful five-dimensional matrix representation of the group of two independent oscillators and applying the R-matrix method we generate some classes of deformed fermionic-bosonic quantum Hopf algebras. The corresponding Lie…
Generalized Intelligent States (coherent and squeezed states) are derived for an arbitrary quantum system by using the minimization of the so-called Robertson-Schr\"odinger uncertainty relation. The Fock-Bargmann representation is also…
We generalize the concept of coherent states, traditionally defined as special families of vectors on Hilbert spaces, to Hilbert modules. We show that Hilbert modules over $C^*$-algebras are the natural settings for a generalization of…
We construct coherent state of the effective mass harmonic oscillator and examine some of its properties. In particular closed form expressions of coherent states for different choices of the mass function are obtained and it is shown that…
Starting with the canonical coherent states, we demonstrate that all the so-called nonlinear coherent states, used in the physical literature, as well as large classes of other generalized coherent states, can be obtained by changes of…
The well-known canonical coherent states are expressed as an infinite series in powers of a complex number $z$ together with a positive sequence of real numbers $\rho(m)=m$. In this article, in analogy with the canonical coherent states, we…
A realization of various algebraic structures in terms of the $C_{\lambda}$-extended oscillator algebras is introduced. In particular, the $C_{\lambda}$-extended oscillator algebras realization of Fairlie-Fletcher-Zachos (FFZ)algebra is…
We establish some of the properties of the states interpolating between number and coherent states denoted by $| n >_{\lambda}$; among them are the reproducing of these states by the action of an operator-valued function on $| n>$ (the…
Recently, based on a supersymmetric approach, new classes of conditionally exactly solvable problems have been found, which exhibit a symmetry structure characterized by non-linear algebras. In this paper the associated ``non-linear''…
We introduce and obtain multimode paraboson coherent states. In appropriate subspaces these coherent states provide a decomposition of unity where the measure, when expressed using the cat-type states, is positive definite. Bicoherent…
A set of coupled complex Ginzburg-landau type amplitude equations which operates near a Hopf-Turing instability boundary is analytically investigated to show localized oscillatory patterns. The spatial structure of those patterns are the…
A new kind of q-deformed charged coherent states is constructed in Fock space of two-mode q-boson system with su_{q}(2) covariance and a resolution of unity for these states is derived. We also present a simple way to obtain these coherent…
The purposes of this work are (1) to show that the appropriate generalizations of the oscillator algebra permit the construction of a wide set of nonlinear coherent states in unified form; and (2) to clarify the likely contradiction between…
We construct a class of generalized phase coherent states indexed by points of the unit circle and depending on three positive parameters "gamma","alpha" and "epsilon" by replacing the labelling coefficients of the canonical coherent states…
A class of generalized coherent states with a new type of the identity resolution are constructed by replacing the labeling parameter zn/n! of the canonical coherent states by Meixner-Pollaczek polynomials with specific parameters. The…
We generalize the fermionic coherent states to the case of Fock-Krein spaces, i.e., Fock spaces with an idefinite inner product of Krein type. This allows for their application in topological or functorial quantum field theory and more…
Vector coherent states (VCS) viewed as a generalization of ordinary coherent states for higher rank tensor Hilbert spaces are investigated. We consider a systematic way of generating classes of VCS which are solvable (i.e., in the present…