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Title: Coherent states for nonlinear harmonic oscillator and some of its properties

Abstract

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.

Authors:
;  [1]
  1. School of Natural Sciences, National University of Sciences and Technology, Islamabad (Pakistan)
Publication Date:
OSTI Identifier:
22479690
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Mathematical Physics; Journal Volume: 56; Journal Issue: 6; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ANNIHILATION OPERATORS; CORRELATION FUNCTIONS; EIGENSTATES; EIGENVALUES; HARMONIC OSCILLATORS; NONLINEAR PROBLEMS; OSCILLATORS; STATISTICS

Citation Formats

Amir, Naila, E-mail: naila.amir@live.com, E-mail: naila.amir@sns.nust.edu.pk, and Iqbal, Shahid, E-mail: sic80@hotmail.com, E-mail: siqbal@sns.nust.edu.pk. Coherent states for nonlinear harmonic oscillator and some of its properties. United States: N. p., 2015. Web. doi:10.1063/1.4922606.
Amir, Naila, E-mail: naila.amir@live.com, E-mail: naila.amir@sns.nust.edu.pk, & Iqbal, Shahid, E-mail: sic80@hotmail.com, E-mail: siqbal@sns.nust.edu.pk. Coherent states for nonlinear harmonic oscillator and some of its properties. United States. doi:10.1063/1.4922606.
Amir, Naila, E-mail: naila.amir@live.com, E-mail: naila.amir@sns.nust.edu.pk, and Iqbal, Shahid, E-mail: sic80@hotmail.com, E-mail: siqbal@sns.nust.edu.pk. 2015. "Coherent states for nonlinear harmonic oscillator and some of its properties". United States. doi:10.1063/1.4922606.
@article{osti_22479690,
title = {Coherent states for nonlinear harmonic oscillator and some of its properties},
author = {Amir, Naila, E-mail: naila.amir@live.com, E-mail: naila.amir@sns.nust.edu.pk and Iqbal, Shahid, E-mail: sic80@hotmail.com, E-mail: siqbal@sns.nust.edu.pk},
abstractNote = {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.},
doi = {10.1063/1.4922606},
journal = {Journal of Mathematical Physics},
number = 6,
volume = 56,
place = {United States},
year = 2015,
month = 6
}
  • Wave packets for the quantum nonlinear oscillator are considered in the generalized coherent state framework. To first order in the nonlinearity parameter the coherent state behaves very similar to its classical counterpart. The position expectation value oscillates in a simple harmonic manner. The energy-momentum uncertainty relation is time independent as in a harmonic oscillator. Various features (such as the squeezed state nature) of the coherent state have been discussed.
  • We used the dicrete variable three-dimmensional Charlier oscillator. For a system of molecules interacting with the coherent radiation field the temporal variation of the refractive index has been established.
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