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arXiv:1704.02650 · Communications in Theoretical Physics

Coherent States of Nonlinear Oscillators with Position-Dependent Mass: Temporal Stability and Fractional Revivals

Naila Amir, Shahid Iqbal

Published Aug 1, 2017• 21 citations
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Abstract

Abstract We develop generalized coherent states for a class of nonlinear oscillators with position-dependent effective mass in the context of the Gazeau–Klauder formalism and discuss some of their properties. In order to investigate the temporal evolution we first explore the statistical properties by means of weighting distribution and the Mandel parameter. It is found that the temporal evolution of the coherent states may exhibit the phenomena of quantum revivals and fractional revivals for a particular choice of position-dependent mass oscillator.

DOI
10.1088/0253-6102/68/2/181

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Abstract We develop generalized coherent states for a class of nonlinear oscillators with position-dependent effective mass in the context of the Gazeau–Klauder formalism and discuss some of their properties. In order to investigate the temporal evolution we first explore the statistical properties by means of weighting distribution and the Mandel parameter. It is found that the temporal evolution of the coherent states may exhibit the phenomena of quantum revivals and fractional revivals for a particular choice of position-dependent mass oscillator.
A one-dimensional nonlinear harmonic oscillator is studied in the context of generalized coherent states. We develop a perturbative framework to compute the eigenvalues and eigenstates for the quantum nonlinear oscillator and construct the generalized coherent states based on Gazeau-Klauder formalism. We analyze their statistical properties by means of Mandel parameter and second order correlation function. Our analysis reveals that the constructed coherent states exhibit super-Poissonian statistics. Moreover, it is shown that the coherent states mimic the phenomena of quantum revivals and fractional revivals during their time evolution. The validity of our results has been discussed in terms of various parametric bounds imposed by our computational scheme.
We develop generalized coherent states based on the Gazeau–Klauder formalism for a particle with position-dependent mass trapped in an infinite square well. We study the quantum statistical properties of these states by means of the Mandel parameter and the second-order correlation function. Our analysis reveals that the constructed coherent states exhibit sub-Poissonian statistics. Moreover, theoretical investigations of wave packet revivals and fractional revivals for the pertaining system have been performed by means of the autocorrelation function and temporal evolution of probability density.
The revival structures for the X_m exceptional orthogonal polynomials of the Scarf I potential endowed with position-dependent effective mass is studied in the context of the generalized Gazeau-Klauder coherent states. It is shown that in the case of the constant mass, the deduced coherent states mimic full and fractional revivals phenomena. However in the case of position-dependent effective mass, although full revivals take place during their time evolution, there is no fractional revivals as defined in the common sense. These properties are illustrated numerically by means of some specific profile mass functions, with and without singularities. We have also observed a close connection between the coherence time τ_coh^m? and the mass parameter ?.
Abstract The revival structures for X m -exceptional orthogonal polynomials (EOP) of Scarf I potentials endowed with position-dependent effective mass (PDEM) are studied in the context of the generalized Gazeau-Klauder coherent states. It is shown that the deduced coherent states mimic full and fractional revivals phenomena in the case of the constant-mass. However, in the case of position-dependent effective mass, although full revivals take place during their time evolution, there is no trace of fractional revivals as defined in the common sense. These properties are illustrated numerically by means of some specific profiles of the mass-function, with and without singularities. We have also observed a close connection between the coherence time τ coh [ m ] and the mass-parameter λ . We suspect the effect that a larger mass-parameter λ contributes significantly to a longer coherence time τ coh [ m ] .