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Coherent states in mathematical physics
About: Coherent states in mathematical physics is a research topic. Over the lifetime, 732 publications have been published within this topic receiving 32024 citations.
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TL;DR: In this article, the generalized inverse of q-boson operators is introduced via their action on the q-number states, and a q-analogy of photon-added and photon-depleted coherent states are constructed via the generalized operator actions on q-coherent states.
Abstract: The generalized inverse of q-boson operators are introduced via their action on the q-number states. The q-analogy of photon-added and photon-depleted coherent states are constructed via the generalized inverse of q-boson operator actions on the q-coherent states. Their mathematical and quantum statistical properties are discussed in detail analytically and numerically.
8 citations
TL;DR: In this article, a two-body squeezing operator was introduced to represent the coefficients of the permanent (Slater) decomposition of the bosonic (fermionic) states.
Abstract: Many bosonic (fermionic) fractional quantum Hall states, such as Laughlin, Moore-Read and Read-Rezayi wavefunctions, belong to a special class of orthogonal polynomials: the Jack polynomials (times a Vandermonde determinant). This fundamental observation allows to point out two different recurrence relations for the coefficients of the permanent (Slater) decomposition of the bosonic (fermionic) states. Here we provide an explicit Fock space representation for these wavefunctions by introducing a two-body squeezing operator which represents them as a Jastrow operator applied to reference states, which are in general simple periodic one dimensional patterns. Remarkably, this operator representation is the same for bosons and fermions, and the different nature of the two recurrence relations is an outcome of particle statistics.
8 citations
TL;DR: In this paper, the coherent states for a system of time-dependent singular potentials coupled to inverted CK (Caldirola-Kanai) oscillator are investigated by employing invariant operator method and Lie algebraic approach.
8 citations
TL;DR: In this article, a discrete representation of the nonlinearly deformed SU(1,1) algebra was constructed for the cubic algebra related to the conditionally solvable radial oscillator problem.
Abstract: In a previous paper [{\it J. Phys. A: Math. Theor.} {\bf 40} (2007) 11105], we constructed a class of coherent states for a polynomially deformed $su(2)$ algebra. In this paper, we first prepare the discrete representations of the nonlinearly deformed $su(1,1)$ algebra. Then we extend the previous procedure to construct a discrete class of coherent states for a polynomial su(1,1) algebra which contains the Barut-Girardello set and the Perelomov set of the SU(1,1) coherent states as special cases. We also construct coherent states for the cubic algebra related to the conditionally solvable radial oscillator problem.
8 citations
TL;DR: In this article, the authors define coherent states on the quantum group by using harmonic analysis and representation theory of the algebra of functions on the QG. Semiclassical limit of the quantum algebra is discussed and the crucial role of special states on quantum algebra in an investigation of the SLC is emphasized, and a relavence of contact geometry in this context is pointed out.
Abstract: Coherent states on the quantum group $SU_q(2)$ are defined by using harmonic analysis and representation theory of the algebra of functions on the quantum group. Semiclassical limit $q\rightarrow 1$ is discussed and the crucial role of special states on the quantum algebra in an investigation of the semiclassical limit is emphasized. An approach to $q$-deformation as a $q$-Weyl quantization and a relavence of contact geometry in this context is pointed out. Dynamics on the quantum group parametrized by a real time variable and corresponding to classical rotations is considered.
8 citations