Physica Scripta

Wigner algebra in a unit circle and deformed coherent states

Won Sang Chung, HASSAN HASSANABADI

Published Jun 18, 2019• 0 citations

Abstract

Abstract In this paper the Wigner deformation of the quantum mechanics in a unit circle is discussed. The Wigner deformed algebra in a unit circle is presented with a help of parity operator in a unit circle. The coherent state for the Wigner deformed algebra in a unit circle is also constructed.

DOI: 10.1088/1402-4896/ab2a89

Related papers

Wigner functions and coherent states for the quantum mechanics on a circle

K. Kowalski, Karol Ławniczak

Abstract The Wigner functions for the coherent states of a particle on a circle are discussed. The nontrivial analytic forms of these functions are derived. The classicality of the circular coherent states existing in the literature as well as the new ones constructed by means of the Fourier transformation of the Gaussian is compared based on negativity of the Wigner function.

Journal of Physics A Mathematical and TheoreticalJun 10, 20219 citations

ON THE REPRESENTATION OF THE WIGNER ALGEBRA AND WIGNER DEFORMATION OF THE FERMION ALGEBRA

Won Sang Chung

In this paper, we investigate the representation of the Wigner algebra by using the q-calculus like approach. For this algebra, the coherent state is constructed and the uncertainty relation for the ground state is discussed. Following Wigner's approach, the Wigner deformation of the fermion algebra is obtained and its Fock space is shown to have finite dimension.

Modern Physics Letters AMay 30, 20132 citations

Coherent states for the q-deformed quantum mechanics on a circle

K. Kowalski, J Rembieli ski

The q -deformed coherent states for a quantum particle on a circle are introduced and their properties investigated.

arXiv:quant-ph/0412150Journal of Physics A Mathematical and GeneralNov 11, 20047 citations

Two types of q‐deformed Wigner algebra

Won Sang Chung

Abstract In this paper we introduce two types of q‐deformed Wigner algebras. One is q‐deformation of Wigner algebra with q‐reflection symmetry and another is q‐deformation of Wigner algebra with reflection symmetry. For two types of q‐deformed Wigner algebras, we investigate the representation and the eigenvalue of the position operator. Like q‐calculus, we introduce the (q; ν)‐ numbers, (q; ν)‐derivatives and (q; ν)‐Hermite polynomials for two algebras. For the deformation parameter q = 1 ‐ ϵ with small ϵ, we discuss the thermodynamics of the particle obeying the q‐deformed Wigner algebra.

Fortschritte der PhysikMay 7, 20141 citation

Phase space picture of Morse-like coherent states based upon the Wigner function

O de los Santos-Sánchez, J. Récamier

Using the Wigner distribution function, we analyze the behavior on phase space of generalized coherent states associated with the Morse potential (Morse-like coherent states). Within the f -deformed oscillator formalism, such states are constructed by means of the following two definitions: (i) as deformed displacement operator coherent states and (ii) as deformed photon-added coherent states.

arXiv:1801.04876Journal of Physics A Mathematical and TheoreticalOct 2, 20126 citations

Wigner Quasiprobability of Coherent Phase States

Alfred Wünsche

The Wigner quasiprobability, along with some of its essentialproperties, is introduced and discussed in two versions, first covering real canonical variables such as W(q,p) and second a pair of complex conjugate coordinates such as W(α,α*). The reconstruction of the density operator ϱ of states is also given. Building upon the Susskind–Glogower concept of quantum phase operators, further aspects of phase operator algebras in the quantum optics of a harmonic oscillator are discussed in relation to the realization of the su(1,1) Lie algebra. Coherent phase states |ε⟩ are introduced in analogy to the common coherent states |α⟩ in two ways, as both eigenstates of certain operators and as states generated from a ground state |0⟩ by operators of the Lie group SU(1,1). The limiting transition to the non-normalizable Fritz London phase states |eiφ⟩ on the unit circle and an (over)-completeness relation for the coherent phase states are derived. The Wigner quasiprobability W(q,p) for the coherent phase states is calculated and graphically represented. From the Wigner quasiprobability, a phase distribution W(φ) is calculated by integrating over the radius, and its uncertainty is defined and presented. The Hilbert–Schmidt distance is discussed as a measure of the non-classicality of states, where most of our with Viktor Dodonov work was carried out.

PhysicsApr 8, 20261 citation