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:2403.18283 · Physical Review A

PT -symmetric dynamical confinement: Fermi acceleration, quantum force, and Berry phase

S. Rakhmanov, Carsten Trunk, Miloslav Znojil, Davron U. Matrasulov

Published May 15, 2024• 6 citations
arXivHTMLPDF

Abstract

We consider a quantum particle under the dynamical confinement caused by $PT$-symmetric box with a moving wall. The latter is described in terms of the time-dependent Schr\"odinger equation obeying the time-dependent $PT$-symmetric boundary conditions. The class of the functions, describing time dependence of the wall's position and keeping the system as $PT$-symmetric is found. Physically observable characteristics, such as average kinetic energy and the average quantum force are calculated as a function of time. It is found that the behavior of the average kinetic energy as a function of time is completely different than that for of Hermitian counterpart of the model, while the average quantum force behaves similarly to that for Hermitian system. Also, geometric phase is calculated for the harmonically oscillating wall regime. The experimental realization of the proposed model is discussed.

DOI
10.1103/physreva.109.053519

Related papers

Dirac fermion in a time-dependent spherical box

Kuvonchbek Matchonov, Davron U. Matrasulov, J. Dittrich

We consider a Dirac particle in a spherical box with a time-dependent radius. Analytical and numerical solutions of the time-dependent Dirac equation with time-dependent boundary (Dirichlet) conditions are obtained. Using the obtained solutions, physically observable characteristics of the dynamical confinement, such as the average kinetic energy (as a function of time) and average quantum force acting on the particle by the moving wall, are calculated. The trembling motion is analysed by computing the average coordinate of the Dirac particle as a function of time. The absence of the geometric phase is shown by direct calculation.

Acta Polytechnica•Nov 7, 2025•0 citations

Quantum dynamics of hydrogen-like atom in one-dimensional box with oscillating walls

S. Rakhmanov, O. Karpova, D.R. Rakhimboeva +2 more

The quantum dynamics of a hydrogen-like atom confined in one-dimensional box with oscillating walls is studied.The description of the system is reduced to a one-dimensional Schrödinger equation for Coulomb potential with time-dependent boundary conditions, which is solved numerically.Using the obtained solution, the average kinetic energy and binding energies are calculated as a function of time.It is found that both the average kinetic energy and the binding energies are periodic in time with the period depending on the wall's oscillation parameters.The probability density is also analyzed as a function of time and coordinate.

Nanosystems Physics Chemistry Mathematics•Dec 21, 2015•2 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

Non-Hermitian quantum Fermi accelerator

Andreas Fring, Takano Taira

We exactly solve a quantum Fermi accelerator model consisting of a time-independent non-Hermitian Hamiltonian with time-dependent Dirichlet boundary conditions. A Hilbert space for such systems can be defined in two equivalent ways, either by first constructing a time-independent Dyson map and subsequently unitarily mapping to fixed boundary conditions or by first unitarily mapping to fixed boundary conditions followed by the construction of a time-dependent Dyson map. In turn, this allows to construct time-dependent metric operators from a time-independent metric and two time-dependent unitary maps that freeze the moving boundaries. From the time-dependent energy spectrum, we find the known possibility of oscillatory behavior in the average energy in the $\mathcal{P}\mathcal{T}$ regime, whereas in the spontaneously broken $\mathcal{P}\mathcal{T}$ regime we observe the feature of a one-time depletion of the energy. We show that the $\mathcal{P}\mathcal{T}$ broken regime is mended with a moving boundary, equivalently to mending it with a time-dependent Dyson map.

arXiv:2304.07950•Physical Review A•Jul 31, 2023•5 citations

THE BERRY PHASE OF THE QUANTUM STATE OF A HARMONIC OSCILLATOR WITH TIME-DEPENDENT FREQUENCY AND BOUNDARY CONDITIONS

Liu Deng-yun, 山西师范大学物理系，临汾 041004

The problem of a harmonic oscillator of time-dependent frequency confined in a one-dimensional infinite square well with a moving wall is studied.It is shown that the exact solution and the Lewis invariant operator of the system can be obtained by performing two consecutive gauge transformations on the time-dependent Schrdinger equation.On the basis of the exact solution the Berry phases for the system are calculated by using the geometric concepts such as the geometric distance and geometric length of the curve.

Acta Physica Sinica•Jan 1, 1998•2 citations

Jahn-Teller effect and driven binary oscillators in PT -symmetric potentials

Jing Wu, Xiao-Tao Xie

The dynamics of driven binary oscillators in the $\mathcal{PT}$-symmetric harmonic potential is investigated and the corresponding analytical solutions of the time-dependent wave function are obtained. Our numerical results exhibit that there is the population oscillation, which is different from the case of normal dissipation or gain systems. After studying the motion of driven harmonic oscillators which are coupled via the $E⨂e$ Jahn-Teller effect in the Hermitian potential, we find that the dynamics behavior of these two systems is similar under certain conditions. As we know, the oscillation behavior is induced by the exchange interaction in the oscillator system with Jahn-Teller coupling. Our study shows that the binary quantum systems with $\mathcal{PT}$-symmetric Hamiltonians may be used to approximately describe the dynamics of coupling quantum systems and the quantum transport process in few-particle or other systems.

Physical Review A•Sep 14, 2012•14 citations
We consider a quantum particle under the dynamical confinement caused by PTPTPT-symmetric box with a moving wall. The latter is described in terms of the time-dependent Schr"odinger equation obeying the time-dependent PTPTPT-symmetric boundary conditions. The class of the functions, describing time dependence of the wall's position and keeping the system as PTPTPT-symmetric is found. Physically observable characteristics, such as average kinetic energy and the average quantum force are calculated as a function of time. It is found that the behavior of the average kinetic energy as a function of time is completely different than that for of Hermitian counterpart of the model, while the average quantum force behaves similarly to that for Hermitian system. Also, geometric phase is calculated for the harmonically oscillating wall regime. The experimental realization of the proposed model is discussed.
We consider a Dirac particle in a spherical box with a time-dependent radius. Analytical and numerical solutions of the time-dependent Dirac equation with time-dependent boundary (Dirichlet) conditions are obtained. Using the obtained solutions, physically observable characteristics of the dynamical confinement, such as the average kinetic energy (as a function of time) and average quantum force acting on the particle by the moving wall, are calculated. The trembling motion is analysed by computing the average coordinate of the Dirac particle as a function of time. The absence of the geometric phase is shown by direct calculation.
The quantum dynamics of a hydrogen-like atom confined in one-dimensional box with oscillating walls is studied.The description of the system is reduced to a one-dimensional Schrödinger equation for Coulomb potential with time-dependent boundary conditions, which is solved numerically.Using the obtained solution, the average kinetic energy and binding energies are calculated as a function of time.It is found that both the average kinetic energy and the binding energies are periodic in time with the period depending on the wall's oscillation parameters.The probability density is also analyzed as a function of time and coordinate.
We exactly solve a quantum Fermi accelerator model consisting of a time-independent non-Hermitian Hamiltonian with time-dependent Dirichlet boundary conditions. A Hilbert space for such systems can be defined in two equivalent ways, either by first constructing a time-independent Dyson map and subsequently unitarily mapping to fixed boundary conditions or by first unitarily mapping to fixed boundary conditions followed by the construction of a time-dependent Dyson map. In turn, this allows to construct time-dependent metric operators from a time-independent metric and two time-dependent unitary maps that freeze the moving boundaries. From the time-dependent energy spectrum, we find the known possibility of oscillatory behavior in the average energy in the PT\mathcal{P}\mathcal{T}PT regime, whereas in the spontaneously broken PT\mathcal{P}\mathcal{T}PT regime we observe the feature of a one-time depletion of the energy. We show that the PT\mathcal{P}\mathcal{T}PT broken regime is mended with a moving boundary, equivalently to mending it with a time-dependent Dyson map.
The problem of a harmonic oscillator of time-dependent frequency confined in a one-dimensional infinite square well with a moving wall is studied.It is shown that the exact solution and the Lewis invariant operator of the system can be obtained by performing two consecutive gauge transformations on the time-dependent Schrdinger equation.On the basis of the exact solution the Berry phases for the system are calculated by using the geometric concepts such as the geometric distance and geometric length of the curve.
The dynamics of driven binary oscillators in the PT\mathcal{PT}PT-symmetric harmonic potential is investigated and the corresponding analytical solutions of the time-dependent wave function are obtained. Our numerical results exhibit that there is the population oscillation, which is different from the case of normal dissipation or gain systems. After studying the motion of driven harmonic oscillators which are coupled via the E⨂eE⨂eE⨂e Jahn-Teller effect in the Hermitian potential, we find that the dynamics behavior of these two systems is similar under certain conditions. As we know, the oscillation behavior is induced by the exchange interaction in the oscillator system with Jahn-Teller coupling. Our study shows that the binary quantum systems with PT\mathcal{PT}PT-symmetric Hamiltonians may be used to approximately describe the dynamics of coupling quantum systems and the quantum transport process in few-particle or other systems.