Some aspects of a weak Weyl–Heisenberg algebra deformation

2005 ◽  
Vol 83 (9) ◽  
pp. 929-939
Author(s):  
N Boucerredj ◽  
N Mebarki ◽  
A Benslama
Keyword(s):  
Wave Function ◽  
Coherent States ◽  
Deformation Parameter ◽  
Annihilation Operator ◽  
Heisenberg Algebra ◽  
Integral Approach ◽  
Displacement Operator ◽  
Fock Representation ◽  
Generalized Coherent States ◽  
Simple Formalism

In the weak deformation (WD) approximation of the Weyl–Heisenberg algebra, the corresponding generalized coherent states and displacement operator are constructed. It is shown that those states, and contrary to the non-deformed Weyl-Heisenberg algebra, are not eigenstates of the annihilation operator. Moreover, and as an alternative to the Chaïchian et al. Q-deformed path integral approach (where Q is the deformation parameter), using the Bargmann Fock representation, we propose in the WD approximation, a general simple formalism. As an application, we calculate the propagator and the wave function of the harmonic oscillator.PACS Nos.: 03.65.Fd, 31.15.Kb

Photon added coherent states of the parity deformed oscillator

2019 ◽  
Vol 34 (14) ◽  
pp. 1950104 ◽  
Author(s):  
A. Dehghani ◽  
B. Mojaveri ◽  
S. Amiri Faseghandis
Keyword(s):  
Coherent States ◽  
Uncertainty Relation ◽  
Annihilation Operator ◽  
Single Mode ◽  
Heisenberg Algebra ◽  
Uncertainty Relations ◽  
Deformed Oscillator ◽  
Cat States ◽  
Poissonian Statistics ◽  
Creation Operators

Using the parity deformed Heisenberg algebra (RDHA), we first establish associated coherent states (RDCSs) for a pseudo-harmonic oscillator (PHO) system that are defined as eigenstates of a deformed annihilation operator. Such states can be expressed as superposition of an even and odd Wigner cat states.[Formula: see text] The RDCSs minimize a corresponding uncertainty relation, and resolve an identity condition through a positive definite measure which is explicitly derived. We introduce a class of single-mode excited coherent states (PARDCS) of the PHO through “m” times application of deformed creation operators to RDCS. For the states thus constructed, we analyze their statistical properties such as squeezing and sub-Poissonian statistics as well as their uncertainty relations.

Multiphoton Laguerre polynomial state as minimum uncertainty states of intensity-dependent squeezing

2014 ◽  
Vol 92 (9) ◽  
pp. 1016-1020
Author(s):  
Qian-Fan Chen ◽  
Hong-Yi Fan
Keyword(s):  
Coherent State ◽  
Lie Algebra ◽  
Explicit Form ◽  
Coherent States ◽  
Fock Space ◽  
Laguerre Polynomial ◽  
Annihilation Operator ◽  
Nonlinear Realization ◽  
Generalized Coherent States ◽  
Minimum Uncertainty

For a general multiphoton annihilation operator, F = f(N)ap, where N = a†a, we find the explicit form of an operator, G†, which satisfies [F, G†] = 1. Based on the nonlinear realization of the SU(1,1) Lie algebra whose generators are [Formula: see text], [Formula: see text], and R0 = [N/p] + 1/2. We introduce the concept of intensity-dependent multiphoton squeezing and find that the state Lm(–yR†)|j⟩, 0 ≤ j ≤ p, where Lm(x) is a Laguerre polynomial, is a minimum uncertainty state for intensity-dependent multiphoton squeezing. We also construct the phase states for multiphoton operator, which turn out to be SU(1,1) generalized coherent states. Additionally, we show that the photon-added coherent state |α, m⟩ (m is a non-negative integer), which can be interpreted as a nonlinear coherent state, can be expressed as [Formula: see text] in the whole Fock space.

scholarly journals Uncertainty Relations in the Madelung Picture

Entropy ◽  
2021 ◽  
Vol 24 (1) ◽  
pp. 20
Author(s):  
Moise Bonilla-Licea ◽  
Dieter Schuch
Keyword(s):  
Wave Function ◽  
Quantum System ◽  
Momentum Space ◽  
Coherent States ◽  
Quantum Mechanical ◽  
Uncertainty Relations ◽  
Hydrodynamic Equations ◽  
Generalized Coherent States ◽  
Complex Wave ◽  
Classical Hydrodynamic

Madelung showed how the complex Schrödinger equation can be rewritten in terms of two real equations, one for the phase and one for the amplitude of the complex wave function, where both equations are not independent of each other, but coupled. Although these equations formally look like classical hydrodynamic equations, they contain all the information about the quantum system. Concerning the quantum mechanical uncertainties of position and momentum, however, this is not so obvious at first sight. We show how these uncertainties are related to the phase and amplitude of the wave function in position and momentum space and, particularly, that the contribution from the phase essentially depends on the position–momentum correlations. This will be illustrated explicitly using generalized coherent states as examples.

A MODEL OF QUANTUM OSCILLATOR WITH DISCRETE SPACE

2008 ◽  
Vol 23 (13) ◽  
pp. 943-952
Author(s):  
I. I. KACHURYK ◽  
A. U. KLIMYK
Keyword(s):  
Real Line ◽  
Coherent States ◽  
Hermite Polynomials ◽  
Heisenberg Algebra ◽  
Discrete Space ◽  
Quantum Oscillator ◽  
Fock Representation ◽  
New Model

We construct a new model of the quantum oscillator, which is related to the discrete q-Hermite polynomials of the second type. The position and momentum operators in the model are appropriate operators of the Fock representation of a deformation of the Heisenberg algebra. These operators have a discrete non-degenerate spectra. These spectra are spread over the whole real line. Coordinate and momentum realizations of the model are constructed. Coherent states are explicitly given.

Measure of non-Gaussianity for photon-added nonlinear coherent states

2018 ◽  
Vol 15 (09) ◽  
pp. 1850158
Author(s):  
K. Berrada ◽  
H. Eleuch
Keyword(s):  
Coherent State ◽  
Coherent States ◽  
Deformation Parameter ◽  
Critical Value ◽  
Statistical Properties ◽  
Noncommutative Space ◽  
Mandel’S Parameter ◽  
Generalized Coherent States ◽  
Non Gaussian

In this paper, we study the non-Gaussian character in generalized coherent states in the framework of a noncommutative space by adding photons to deformed coherent states, which is called the photon-added nonlinear coherent states (PANCSs). We find that the non-Gaussianity of PANCSs is enhanced with the increase of the photon-added number and it increases monotonically with the amplitude of the coherent states. Interestingly, we obtain that the maximal value of non-Gaussianity measure occurs at a certain critical value of the coherent state amplitude, where this critical value is determined by the kind of the deformation. Using the Mandel’s parameter, we examine the statistical properties for the PANCSs and show that the Mandel’s parameter may take positive and negative values depending on the choice of the amplitude and deformation parameter, exhibiting sub-Poissonian distribution and super-Poissonian distribution.

scholarly journals Palatial Twistors from Quantum Inhomogeneous Conformal Symmetries and Twistorial DSR Algebras

Symmetry ◽  
2021 ◽  
Vol 13 (8) ◽  
pp. 1309
Author(s):  
Jerzy Lukierski
Keyword(s):  
Phase Space ◽  
Hopf Algebras ◽  
Deformation Parameter ◽  
Heisenberg Algebra ◽  
Planck Length ◽  
Covariant Quantum ◽  
Drinfeld Twist ◽  
Quantum Deformations ◽  
Heisenberg Double ◽  
Conformal Symmetries

We construct recently introduced palatial NC twistors by considering the pair of conjugated (Born-dual) twist-deformed D=4 quantum inhomogeneous conformal Hopf algebras Uθ(su(2,2)⋉T4) and Uθ¯(su(2,2)⋉T¯4), where T4 describes complex twistor coordinates and T¯4 the conjugated dual twistor momenta. The palatial twistors are suitably chosen as the quantum-covariant modules (NC representations) of the introduced Born-dual Hopf algebras. Subsequently, we introduce the quantum deformations of D=4 Heisenberg-conformal algebra (HCA) su(2,2)⋉Hℏ4,4 (Hℏ4,4=T¯4⋉ℏT4 is the Heisenberg algebra of twistorial oscillators) providing in twistorial framework the basic covariant quantum elementary system. The class of algebras describing deformation of HCA with dimensionfull deformation parameter, linked with Planck length λp, is called the twistorial DSR (TDSR) algebra, following the terminology of DSR algebra in space-time framework. We describe the examples of TDSR algebra linked with Palatial twistors which are introduced by the Drinfeld twist and the quantization map in Hℏ4,4. We also introduce generalized quantum twistorial phase space by considering the Heisenberg double of Hopf algebra Uθ(su(2,2)⋉T4).

scholarly journals Generalized coherent states

2014 ◽  
Vol 82 (8) ◽  
pp. 742-748 ◽  
Author(s):  
T. G. Philbin
Keyword(s):  
Coherent States ◽  
Generalized Coherent States

Description of anharmonic effects with generalized coherent states

2004 ◽  
Vol 37 (3) ◽  
pp. 769-779 ◽  
Author(s):  
Atsushi Kuriyama ◽  
Masatoshi Yamamura ◽  
Constança Providência ◽  
João da Providência ◽  
Yasuhiko Tsue
Keyword(s):  
Coherent States ◽  
Anharmonic Effects ◽  
Generalized Coherent States

Equation for a Composite Scalar Particle in (2+1)-D and its Solutions

1997 ◽  
Vol 12 (23) ◽  
pp. 1699-1708 ◽  
Author(s):  
S. I. Kruglov
Keyword(s):  
Wave Function ◽  
Electromagnetic Wave ◽  
Coherent States ◽  
Dimensional Space ◽  
Plane Electromagnetic Wave ◽  
Photon Number ◽  
Scalar Particle ◽  
Linearly Polarized ◽  
External Electromagnetic Fields ◽  
Quantized Electromagnetic Field

A model of a scalar particle in (2+1)-dimensional space with an internal structure in external electromagnetic fields is considered. Exact solutions of the equation for such scalar particle were obtained in the field of a plane electromagnetic wave with the arbitrary polarization and in the quantized electromagnetic field of the linearly polarized wave. The relativistic coherent states of the particle in the field of n photons were constructed. When the photon number goes to infinity, this wave function transforms to the solution corresponding to the external classical electromagnetic wave.

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