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

Nanosystems Physics Chemistry Mathematics

Quantum dynamics in a kicked square billiards

S. Rakhmanov, Doniyor Babajanov, O. Karpova, F. Khoshimova

Published Apr 16, 2015• 0 citations
Publisher

Abstract

We study kicked particle dynamics in a rectangular quantum billiard.The kicking potential is chosen as localized at the center of the billiard.The exact solution for the time-dependent Schrödinger equation for a single kicking period is derived.Using this solution, the time-dependence of the average kinetic energy and probability density as a function of spatial coordinates are computed.Different regimes for trapping of the particle in kicking area are analyzed.It is found that depending of the values of kicking parameters, the average kinetic energy can be a periodic or a monotonically growing function of time or can be suppressed.Such behavior is explained in terms of particle trapping regimes.Wave packet dynamics are also studied.

DOI
10.17586/2220-8054-2015-6-2-216-223

Related papers

Kicked particle dynamics in quantum graphs

Jambul Yusupov, Valijon Eshniyozov, O. Karpova +1 more

The quantum dynamics of a delta-kicked driven particle in a star-shaped network is studied by obtaining an exact solution for the time-dependent Schrödinger equation within a single kicking period.The timedependence of the average kinetic energy and the Gaussian wave packet evolution are analyzed.

Nanosystems Physics Chemistry Mathematics•Dec 21, 2015•1 citation

Kicked Dirac particle in a box

V. E. Eshniyazov, Davron U. Matrasulov, Jambul Yusupov

We study quantum dynamics of a kicked relativistic spin-half particle in a one dimensional box. Time-dependence of the average kinetic energy and evolution of the wave packet are explored. Kicking potential is introduced as the Lorentz-scalar, i.e., through the mass-term in the Dirac equation. It is found that depending on the values of the kicking parameters E(t) can be periodic, monotonically growing and non-periodic function of time. Particle transport in the system is studied by considering spatio-temporal evolution of the Gaussian wave packet.Splitting of the packet into two symmetric parts and restoration of the profile of the packet is found.

arXiv:1311.0799•Nov 4, 2013•0 citations

Time-dependent quantum circular billiard

Doniyor Babajanov, Davron U. Matrasulov, Zarifboy A. Sobirov +2 more

The motion of a quantum particle in a time-dependent circular billiard is studied on the basis of the Schrödinger equation with time-dependent boundary conditions.The cases of monotonically expanding (contracting), non-harmonically, harmonically breathing circles the case when billiard wall suddenly disappears are explored in detail.The exact analytical solutions for monotonically expanding and contracting circles are obtained.For all cases, the time-dependence of the quantum average energy is calculated.It is found that for an harmonically breathing circle, the average energy is time-periodic in the adiabatic regime with the same period as that of the oscillation.For intermediate frequencies which are comparable with the initial frequency of the particle in unperturbed billiard, such periodicity is broken.However, for very high frequencies, the average energy once again becomes periodic.A qualitative analysis of the border between adiabatic and non-adiabatic regimes is provided.

Nanosystems Physics Chemistry Mathematics•Apr 16, 2015•2 citations

Quantum wave packet analysis in the rectangular billiard

Lin Sheng-Lu

The use of wave packet to analyze the dynamics of quantum mechanical systems is an increasingly important method to the study of the classical-quantum correspondence.Using the quantum Gaussian wave packet analysis method,we calculate the autocorrelation function of the rectangular billiard,the peak positions of the autocorrelation function match well with the periods of the classical periodic orbits,which show that the period of the classical orbits can be produced by the time-dependent quantum wave packet method.We also discuss wave packet revivals and fractional revivals in the rectangular billiard,the results show that there are exact revival for all wave packet at each revival time.We find additional cases of exact revivals with short revival times for zero-momentum wave packets initially located at special symmetry point inside the billiard.

Journal of Atomic and Molecular Physics•Jan 1, 2007•0 citations

Quantum dynamics of a parity-time-symmetric kicked particle in a 1D box

J Yusupov, S. Rakhmanov, D Matrasulov +1 more

Abstract We study quantum particle dynamics in a box and driven by a parity-time (PT)-symmetric, delta-kicking complex potential. The dynamical characteristics, identified by the average kinetic energy as a function of time, and quasi-energy are computed for different values of the kicking parameters. Breaking of the PT-symmetry at certain values of the non-Hermitian kicking parameter is shown. Experimental realization of the model is also discussed.

arXiv:1807.10966•Journal of Physics A Mathematical and Theoretical•Nov 13, 2018•5 citations

Wave-packet initial motion, spreading, and energy in the periodically kicked pendulum

Boon Leong Lan

The initial quantum dynamics of an initially well-localized, minimum-uncertainty Gaussian wave packet is studied analytically for the periodically kicked pendulum. The general results presented here include our earlier analytic result [Phys. Rev. A 41, 2952 (1990)] as a special case. We find that as long as the packet remains localized, it remains approximately Gaussian, while its center and widths evolve in time approximately according to, respectively, the classical map and a variance map which utilize the instantaneous values of the classical Jacobi matrix. When the classical map is very strongly chaotic, we predict that the average kinetic energy of the well-localized wave packet does not initially grow diffusively (linearly with time). We show that, instead, in the presence of chaos, the deviations initially grow, on the average, exponentially at a rate equal to the corresponding classical Liapunov exponent under the appropriate conditions. The time scale (Ehrenfest time) on which the Ehrenfest-Hamilton correspondence holds in the presence of chaos is estimated and is slightly different from a previous estimate made by Chirikov, Israilev, and Shepelyansky [Sov. Sci. Rev. C 2, 209 (1981)]. Numerical evidence in support of these analytical results is presented.

Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics•Aug 1, 1994•11 citations
We study kicked particle dynamics in a rectangular quantum billiard.The kicking potential is chosen as localized at the center of the billiard.The exact solution for the time-dependent Schrödinger equation for a single kicking period is derived.Using this solution, the time-dependence of the average kinetic energy and probability density as a function of spatial coordinates are computed.Different regimes for trapping of the particle in kicking area are analyzed.It is found that depending of the values of kicking parameters, the average kinetic energy can be a periodic or a monotonically growing function of time or can be suppressed.Such behavior is explained in terms of particle trapping regimes.Wave packet dynamics are also studied.
We study quantum dynamics of a kicked relativistic spin-half particle in a one dimensional box. Time-dependence of the average kinetic energy and evolution of the wave packet are explored. Kicking potential is introduced as the Lorentz-scalar, i.e., through the mass-term in the Dirac equation. It is found that depending on the values of the kicking parameters E(t) can be periodic, monotonically growing and non-periodic function of time. Particle transport in the system is studied by considering spatio-temporal evolution of the Gaussian wave packet.Splitting of the packet into two symmetric parts and restoration of the profile of the packet is found.
The motion of a quantum particle in a time-dependent circular billiard is studied on the basis of the Schrödinger equation with time-dependent boundary conditions.The cases of monotonically expanding (contracting), non-harmonically, harmonically breathing circles the case when billiard wall suddenly disappears are explored in detail.The exact analytical solutions for monotonically expanding and contracting circles are obtained.For all cases, the time-dependence of the quantum average energy is calculated.It is found that for an harmonically breathing circle, the average energy is time-periodic in the adiabatic regime with the same period as that of the oscillation.For intermediate frequencies which are comparable with the initial frequency of the particle in unperturbed billiard, such periodicity is broken.However, for very high frequencies, the average energy once again becomes periodic.A qualitative analysis of the border between adiabatic and non-adiabatic regimes is provided.
The use of wave packet to analyze the dynamics of quantum mechanical systems is an increasingly important method to the study of the classical-quantum correspondence.Using the quantum Gaussian wave packet analysis method,we calculate the autocorrelation function of the rectangular billiard,the peak positions of the autocorrelation function match well with the periods of the classical periodic orbits,which show that the period of the classical orbits can be produced by the time-dependent quantum wave packet method.We also discuss wave packet revivals and fractional revivals in the rectangular billiard,the results show that there are exact revival for all wave packet at each revival time.We find additional cases of exact revivals with short revival times for zero-momentum wave packets initially located at special symmetry point inside the billiard.
The initial quantum dynamics of an initially well-localized, minimum-uncertainty Gaussian wave packet is studied analytically for the periodically kicked pendulum. The general results presented here include our earlier analytic result [Phys. Rev. A 41, 2952 (1990)] as a special case. We find that as long as the packet remains localized, it remains approximately Gaussian, while its center and widths evolve in time approximately according to, respectively, the classical map and a variance map which utilize the instantaneous values of the classical Jacobi matrix. When the classical map is very strongly chaotic, we predict that the average kinetic energy of the well-localized wave packet does not initially grow diffusively (linearly with time). We show that, instead, in the presence of chaos, the deviations initially grow, on the average, exponentially at a rate equal to the corresponding classical Liapunov exponent under the appropriate conditions. The time scale (Ehrenfest time) on which the Ehrenfest-Hamilton correspondence holds in the presence of chaos is estimated and is slightly different from a previous estimate made by Chirikov, Israilev, and Shepelyansky [Sov. Sci. Rev. C 2, 209 (1981)]. Numerical evidence in support of these analytical results is presented.