Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1502.08007

Reconstruction and location of fractional revivals of coherent state wave-packets for potentials associated with exceptional Xm Jacobi-polynomials

Sid-Ahmed Yahiaoui, M. Bentaïba

Published Feb 27, 2015• 0 citations
arXivHTMLPDF

Abstract

Gazeau-Klauder coherent states of the extended trigonometric Scarf potential, underlying the quadratic energy spectrum and associated with Jacobi-type Xm exceptional orthogonal polynomials P(a,b,m) n (x), are constructed. The temporal evolution of wave-packet coherent states are performed by means of an autocorrelation function and the full revival properties are investigated in the usual time-domain analysis. This latter seems to be less useful for describing the fractional revivals due to the complicated nature of coherent wave-packet. Fortunately the autocorrelation function revels a little signature of fractional revivals at the vicinity of quarters of the revival time Trev due to the quadratic energy spectrum and the use of the wavelet-based time-frequency analysis of the autocorrelation function provides an analytical and numerical observation of the fractional revivals at different orders of the system.

DOI
10.48550/arxiv.1502.08007

Related papers

Revival structures of coherent states for Xm exceptional orthogonal polynomials of the Scarf I potential within position-dependent effective mass

Sid-Ahmed Yahiaoui, M. Bentaïba

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 ?.

arXiv:1701.04091•Jan 15, 2017•0 citations

X m –EOP/PDEM connection for Scarf I potentials and their coherent states revivals

Sid-Ahmed Yahiaoui, Othmane Cherroud

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 ] .

Physica Scripta•Dec 18, 2024•1 citation

A time–frequency analysis of wave packet fractional revivals

Suranjana Ghosh, J. Banerji

We show that the time frequency analysis of the autocorrelation function is, in many ways, a more appropriate tool to resolve fractional revivals of a wave packet than the usual time domain analysis. This advantage is crucial in reconstructing the initial state of the wave packet when its coherent structure is short-lived and decays before it is fully revived. Our calculations are based on the model example of fractional revivals in a Rydberg wave packet of circular states. We end by providing an analytical investigation which fully agrees with our numerical observations on the utility of time-frequency analysis in the study of wave packet fractional revivals.

arXiv:0706.1576•Journal of Physics B Atomic Molecular and Optical Physics•Aug 28, 2007•15 citations

Manifestations of wave packet fractional revivals in a Morse-like anharmonic system

V.V. Eryomin, S. I. Vetchinkin, И. М. Уманский

The general properties of the time-dependent characteristics of one-dimensional vibrational wave packets in an anharmonic system with the quadratic spectrum are discussed. The local behavior of the autocorrelation function and its square modulus (the survival function) is studied near the moments of fractional revival t=(p/q)Trev, where Trev is the period of the complete revival, p/q is an irreducible fraction, and q is the order of the revival. It is shown that all the wave packets have the same values of the survival function at the moments of fractional revival provided that the number of states in the packet exceeds the order of the revival q. It is also found that for the given packet, all the fractional revivals are identical to each other in the sense that their lifetimes do not depend on the order of the revival. The lifetimes of all fractional revivals are expressed in terms of the parameters of the initial packet (the effective number of states and the period of classical motion of the packet center) and the anharmonicity of the molecular system.

The Journal of Chemical Physics•Dec 15, 1994•19 citations

Fractional Revival Dynamics in Kerr-Type Systems: Angular Momentum Moments and Classical Analogs

Ashish Kumar Patra, Saikumar Krithivasan

Wave packet revivals and fractional revivals are hallmark quantum interference phenomena that arise in systems with nonlinear energy spectra, and their signatures in expectation values of observables have been studied extensively in earlier work. In this article, we build on these studies and extend the analysis in two important directions. First, we investigate fractional revival dynamics in angular momentum observables, deriving explicit expressions for the time evolution of their moments and demonstrating that higher-order angular momentum moments provide clear and selective signatures of fractional revivals. Second, we examine classical analogs of quantum revival phenomena and elucidate structural similarities between quantum fractional revivals and recurrence behavior in representative classical systems. Using the Kerr-type nonlinear Hamiltonian as a paradigmatic model, we analyze the autocorrelation function, moment dynamics, and phase-space structures, supported by visualizations such as quantum carpets. Our results broaden the range of experimentally accessible diagnostics of fractional revivals and provide a unified perspective on revival phenomena across quantum and classical dynamical systems.

quant-pharXiv:2601.09763•Jan 15, 2026•0 citations

Coherent state of a nonlinear oscillator and its revival dynamics

Bikashkali Midya, Barnana Roy, Anjan Biswas

The coherent state of a nonlinear oscillator having a nonlinear spectrum is constructed using Gazeau–Klauder formalism. The weighting distribution and the Mandel parameter are studied. Details of the revival structure arising from different time scales underlying the quadratic energy spectrum are investigated by the phase analysis of the autocorrelation function.

arXiv:0911.0073•Physica Scripta•May 21, 2009•19 citations
Gazeau-Klauder coherent states of the extended trigonometric Scarf potential, underlying the quadratic energy spectrum and associated with Jacobi-type Xm exceptional orthogonal polynomials P(a,b,m) n (x), are constructed. The temporal evolution of wave-packet coherent states are performed by means of an autocorrelation function and the full revival properties are investigated in the usual time-domain analysis. This latter seems to be less useful for describing the fractional revivals due to the complicated nature of coherent wave-packet. Fortunately the autocorrelation function revels a little signature of fractional revivals at the vicinity of quarters of the revival time Trev due to the quadratic energy spectrum and the use of the wavelet-based time-frequency analysis of the autocorrelation function provides an analytical and numerical observation of the fractional revivals at different orders of the system.
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 ] .
We show that the time frequency analysis of the autocorrelation function is, in many ways, a more appropriate tool to resolve fractional revivals of a wave packet than the usual time domain analysis. This advantage is crucial in reconstructing the initial state of the wave packet when its coherent structure is short-lived and decays before it is fully revived. Our calculations are based on the model example of fractional revivals in a Rydberg wave packet of circular states. We end by providing an analytical investigation which fully agrees with our numerical observations on the utility of time-frequency analysis in the study of wave packet fractional revivals.
The general properties of the time-dependent characteristics of one-dimensional vibrational wave packets in an anharmonic system with the quadratic spectrum are discussed. The local behavior of the autocorrelation function and its square modulus (the survival function) is studied near the moments of fractional revival t=(p/q)Trev, where Trev is the period of the complete revival, p/q is an irreducible fraction, and q is the order of the revival. It is shown that all the wave packets have the same values of the survival function at the moments of fractional revival provided that the number of states in the packet exceeds the order of the revival q. It is also found that for the given packet, all the fractional revivals are identical to each other in the sense that their lifetimes do not depend on the order of the revival. The lifetimes of all fractional revivals are expressed in terms of the parameters of the initial packet (the effective number of states and the period of classical motion of the packet center) and the anharmonicity of the molecular system.
Wave packet revivals and fractional revivals are hallmark quantum interference phenomena that arise in systems with nonlinear energy spectra, and their signatures in expectation values of observables have been studied extensively in earlier work. In this article, we build on these studies and extend the analysis in two important directions. First, we investigate fractional revival dynamics in angular momentum observables, deriving explicit expressions for the time evolution of their moments and demonstrating that higher-order angular momentum moments provide clear and selective signatures of fractional revivals. Second, we examine classical analogs of quantum revival phenomena and elucidate structural similarities between quantum fractional revivals and recurrence behavior in representative classical systems. Using the Kerr-type nonlinear Hamiltonian as a paradigmatic model, we analyze the autocorrelation function, moment dynamics, and phase-space structures, supported by visualizations such as quantum carpets. Our results broaden the range of experimentally accessible diagnostics of fractional revivals and provide a unified perspective on revival phenomena across quantum and classical dynamical systems.