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

Europhysics Letters (EPL)

A dynamical signature of quantum chaos in hydrogen atom under strong, oscillating magnetic fields

Mainak Sadhukhan, Bimalendu Deb

Published May 26, 2011• 14 citations
Publisher

Abstract

A dynamical signature of quantum chaos is proposed in terms of the nonlinear growth of time-dependent (TD) distance function between two trajectories, corresponding to two slightly different Hamiltonians, in what is defined as Ehrenfest phase space. Through comparisons of this signature with the TD correlation function and the Loschmidt echo in case of the hydrogen atom in strong, oscillating magnetic fields, the effectiveness of the proposed signature is demonstrated.

DOI
10.1209/0295-5075/94/50008

Related papers

Ehrenfest ‘phase-space’ trajectories and quantum chaos in He atom under strong, oscillating magnetic fields: an application of time-dependent quantum fluid density functional theory (TDQFDFT)

Mainak Sadhukhan, Bimalendu Deb

Using a dynamical signature proposed earlier from our laboratory, quantum chaos in He atom interacting with strong, oscillating magnetic fields has been studied through a comparison between the nonlinear divergence of two neighbouring Ehrenfest ‘phase-space’ (EPS) trajectories differing slightly in initial conditions and the Loschmidt echo. The dynamical EPS signature can detect quantum chaos independently of the Loschmidt echo and in agreement with the latter, even for low-lying states, in the same spirit as that of classical chaos. This time-dependent signature extends the concept of quantum chaos to systems which have no classical counterparts and brings the concept of quantum chaos closer to that of classical chaos.

Molecular Physics•Feb 22, 2017•5 citations

QUANTUM CHAOS IN RYDBERG ATOMS : A QUANTUM POTENTIAL APPROACH

Pratim Kumar Chattaraj, S. Sengupta

The quantum signature of chaos in Rydberg atoms has been sutdied using a quantum theory of motion and quantum fluid dyanamics. A hydtrogen atom in the electronic ground state (n =1) and in an excited elecronic state (n = 20) behaves differently when placed in an external oscillating eletric field. Temporal evolutions of Shannon entrippy, density correlation, phase space distance function of Bohmian trajectories ans associated Kolmogorov-Sinai entropy for these two cses show marked differences.

•Jul 25, 1996•7 citations

Quantum and Classical Description of H Atom Under Magnetic Field and Quadrupole Trap Potential

Jorge Mahecha, J. Pablo Salas

A discussion regarding the energy levels spectrum of quantum systems whose classical analogous has states of chaotic motion is presented. The chaotic dynamics of the classical underlying system has its manifestation in the wave functions (in the form of “scars”) and in the energy levels (in the form of “statistical repulsion” of the energy levels). The above mentioned signatures are named “quantum chaos”. A typical study of quantum chaos requires finding accurate energy eigenvalues of highly excited states, to calculate the nearest neighbors spacing between levels, to perform the “unfolding” of the spectrum in order to separate the fluctuations, and finally to find the probability distribution of the unfolded spectrum. This is exemplified by the hydrogen atom under uniform magnetic field and a quadrupole electric field.

AIP conference proceedings•Jan 1, 2006•0 citations

Quantum phase-space behaviour for the H2molecule in a magnetic field

T. S. Monteiro

The first study of the quantum dynamics for a highly excited ('Rydberg') H 2 molecule in a magnetic field is presented and compared with the well studied atomic case. Wavefunctions from an accurate quantal calculation have been used to obtain the corresponding Wigner functions by means of a transformation to a basis where the latter are analytical. Unlike the atom, the dynamics of the excited electron in the molecular case experiences two, interfering, energy regimes. This study consider the case near electronic scaled energies -0.5 and -2.3, which would correspond to predominantly regular motion in the atomic case. In the molecular case there is evidence for chaotic behaviour in this energy range. Quantum states for the molecule may divide into those where the underlying dynamics is a perturbed version of the hydrogen atom case, and others where different configuration-space and phase-space structures are apparent.

Journal of Physics B Atomic Molecular and Optical Physics•Dec 28, 1992•2 citations

Long-time signatures of chaos in large atom-light frequency ratios Rabi model

Shangyun Wang, Songbai Chen, Jiliang Jing

Abstract As one of the famous effects in the quantum Rabi model (QRM), Rabi oscillation may lead to the occurrence of quantum dynamical behaviors without classical dynamic counterparts, such as quantum collapse and revival effects. In this paper, we focus on studying the long-time quantum signatures of chaos in the large atom-light frequency ratios of the Rabi model. It is shown that the saturated values of the entanglement entropy for initial states located in chaotic sea are higher than that in the regular regions, and the Husimi Q function are more dispersed in phase space. Moreover, we observed that the long-time average entanglement entropy and spin variance correspond well with the semiclassical phase space. Our results imply that the correspondence principle is not invalidated by quantum collapse and revival effects in the large atom-light frequency ratios Rabi model.

arXiv:2407.09802•Communications in Theoretical Physics•Mar 24, 2025•0 citations

Strange attractors and the probabilities of transitions of an anharmonic oscillator in an external time-dependent field

Klimenty N. Yugay, Stanislav D. Tvorogov

A theory allowing to describe of quantum chaos in the term of nonlinear classical dynamics is proposed. It is showed that a solution of a quantum problem in quasiclassical region is connected with a solution of a corresponding classical problem which is the classical limit of the quantum one. It is showed also that the wave function phase is satisfied an own equation of motion and it is a classical dynamic equation. Dynamical chaos of nonlinear classical dynamics results to irregularity of the wave function phase and a strange attractor in a classical dynamics of the wave function phase leads to irregularity in probabilities of transitions of anharmonic oscillator in an external time-dependent field. In the pure quantum and the pure classical region corresponding solutions are independent.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Oct 21, 1998•0 citations
A dynamical signature of quantum chaos is proposed in terms of the nonlinear growth of time-dependent (TD) distance function between two trajectories, corresponding to two slightly different Hamiltonians, in what is defined as Ehrenfest phase space. Through comparisons of this signature with the TD correlation function and the Loschmidt echo in case of the hydrogen atom in strong, oscillating magnetic fields, the effectiveness of the proposed signature is demonstrated.
Using a dynamical signature proposed earlier from our laboratory, quantum chaos in He atom interacting with strong, oscillating magnetic fields has been studied through a comparison between the nonlinear divergence of two neighbouring Ehrenfest ‘phase-space’ (EPS) trajectories differing slightly in initial conditions and the Loschmidt echo. The dynamical EPS signature can detect quantum chaos independently of the Loschmidt echo and in agreement with the latter, even for low-lying states, in the same spirit as that of classical chaos. This time-dependent signature extends the concept of quantum chaos to systems which have no classical counterparts and brings the concept of quantum chaos closer to that of classical chaos.
A discussion regarding the energy levels spectrum of quantum systems whose classical analogous has states of chaotic motion is presented. The chaotic dynamics of the classical underlying system has its manifestation in the wave functions (in the form of “scars”) and in the energy levels (in the form of “statistical repulsion” of the energy levels). The above mentioned signatures are named “quantum chaos”. A typical study of quantum chaos requires finding accurate energy eigenvalues of highly excited states, to calculate the nearest neighbors spacing between levels, to perform the “unfolding” of the spectrum in order to separate the fluctuations, and finally to find the probability distribution of the unfolded spectrum. This is exemplified by the hydrogen atom under uniform magnetic field and a quadrupole electric field.
The first study of the quantum dynamics for a highly excited ('Rydberg') H 2 molecule in a magnetic field is presented and compared with the well studied atomic case. Wavefunctions from an accurate quantal calculation have been used to obtain the corresponding Wigner functions by means of a transformation to a basis where the latter are analytical. Unlike the atom, the dynamics of the excited electron in the molecular case experiences two, interfering, energy regimes. This study consider the case near electronic scaled energies -0.5 and -2.3, which would correspond to predominantly regular motion in the atomic case. In the molecular case there is evidence for chaotic behaviour in this energy range. Quantum states for the molecule may divide into those where the underlying dynamics is a perturbed version of the hydrogen atom case, and others where different configuration-space and phase-space structures are apparent.
Abstract As one of the famous effects in the quantum Rabi model (QRM), Rabi oscillation may lead to the occurrence of quantum dynamical behaviors without classical dynamic counterparts, such as quantum collapse and revival effects. In this paper, we focus on studying the long-time quantum signatures of chaos in the large atom-light frequency ratios of the Rabi model. It is shown that the saturated values of the entanglement entropy for initial states located in chaotic sea are higher than that in the regular regions, and the Husimi Q function are more dispersed in phase space. Moreover, we observed that the long-time average entanglement entropy and spin variance correspond well with the semiclassical phase space. Our results imply that the correspondence principle is not invalidated by quantum collapse and revival effects in the large atom-light frequency ratios Rabi model.
A theory allowing to describe of quantum chaos in the term of nonlinear classical dynamics is proposed. It is showed that a solution of a quantum problem in quasiclassical region is connected with a solution of a corresponding classical problem which is the classical limit of the quantum one. It is showed also that the wave function phase is satisfied an own equation of motion and it is a classical dynamic equation. Dynamical chaos of nonlinear classical dynamics results to irregularity of the wave function phase and a strange attractor in a classical dynamics of the wave function phase leads to irregularity in probabilities of transitions of anharmonic oscillator in an external time-dependent field. In the pure quantum and the pure classical region corresponding solutions are independent.