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:1612.02152

Dirac phase and replicating adiabaticity in isotropically moving wall confinement

Mohammad Mehrafarin, Reza Torabi

Published Dec 7, 2016• 0 citations
arXivHTMLPDF

Abstract

Geometric phase in the wave function is important with regard to quantum non-locality and adiabatic evolution. We study the confinement of a particle by three-dimensional isotropically moving walls, of relevance to experimental trapping techniques, via a proposed approach that explains the physical origin of the geometric Dirac phase induced in the wave function. This phase depends only on the relative rate of change of the spatial scale factor. The approach also yields the class of external potentials that replicate adiabatic evolution in finite time. As illustrative examples, we consider uniform and accelerating walls, and the case where the Dirac phase is due to cosmic expansion.

DOI
10.48550/arxiv.1612.02152

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

Single particle nonlocality, geometric phases and time-dependent boundary conditions

A. Matzkin

Abstract We investigate the issue of single particle nonlocality in a quantum system subjected to time-dependent boundary conditions. We discuss earlier claims according to which the quantum state of a particle remaining localized at the center of an infinite well with moving walls would be specifically modified by the change in boundary conditions due to the wall’s motion. We first prove that the evolution of an initially localized Gaussian state is not affected nonlocally by a linearly moving wall: as long as the quantum state has negligible amplitude near the wall, the boundary motion has no effect. This result is further extended to related confined time-dependent oscillators in which the boundary’s motion is known to give rise to geometric phases: for a Gaussian state remaining localized far from the boundaries, the effect of the geometric phases is washed out and the particle dynamics shows no traces of a nonlocal influence that would be induced by the moving boundaries.

arXiv:1706.08617•Journal of Physics A Mathematical and Theoretical•Feb 6, 2018•8 citations

Perturbative calculation of the adiabatic geometric phase and particle in a well with moving walls

Ali Mostafazadeh

We use the Rayleigh-Schrödinger perturbation theory to calculate the corrections to the adiabatic geometric phase due to a perturbation of the Hamiltonian. We show that these corrections are at least of second order in the perturbation parameter. As an application of our general results we address the problem of the adiabatic geometric phase for a one-dimensional particle which is confined to an infinite square well with moving walls.

arXiv:quant-ph/9910104•Journal of Physics A Mathematical and General•Nov 11, 1999•6 citations

Topology and Geometric Phase

Ole Keller

An introduction to topology in electrodynamics and the geometric phase con- cept is given. The form-invariance of the field-coupled Dirac equation is demon- strated, and it is shown, starting from the free Dirac equation, that demand of local phase invariance of the wave function dictates the presence of an elec- tromagnetic field. Afterwards the Dirac phase factor, Φ( C ), for a fixed-time loop is defined and discussed. It appears from The Principle of Local Phase Invariance that only the transverse part of the vector potential contributes to Φ( C ). The conditions ∇ × A T = 0 and ∇ · A T = 0 [A T being the transverse vector potential] in a certain finite spatial domain Ω do not imply that A T = 0 necessarily in Ω, as a certain integration involving A T over the domain outside Ω shows. The vector potential of a magnetic string with curvature and torsion is derived, and from this potential the result for a rectilinear magnetic string is obtained, In turn the Aharonov-Bohm effect is derived for a magnetic flux tube. Starting from the evolution operator in quantum physics an adiabatic theorem is established, and Berry's adiabatic geometric phase is introduced and discussed. An extended discussion shows that a geometric phase, called the Aharonov-Anandan phase, not restricted by the adiabatic principle can be introduced.

CRC Press eBooks•Aug 6, 2024•0 citations

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

S. Rakhmanov, Carsten Trunk, Miloslav Znojil +1 more

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.

arXiv:2403.18283•Physical Review A•May 15, 2024•6 citations

Fast forward of adiabatic quantum dynamics: an application to planar Dirac systems

Iwan Setiawan, Riska Ekawita, Ryan Sugihakim +1 more

We study a scheme of fast-forward adiabatic quantum dynamics of a (2 + 1) Dirac particle. This scheme was originally proposed by Masuda and Nakamura. In this scheme, we include the adiabatic parameter that maintains the adiabatic motion of the particle and fast forward its motion by introducing a time scaling parameter. The fast forward adiabatic state is obtained by determining the regularization term and driving potential. We introduce the proposed method to the system with the Dirac particle using a (2 + 1) dimensiontime- dependent Dirac equation and obtain the regularization term, the driving scalar potential VFF and the driving vector potential AFF . By tuning the driving electric field, this method can accelerate the adiabatic dynamics of an electron as a Dirac particle trapped in the ground state in the plane xy and an electric field in the x direction and a constant magnetic field in the y direction. This acceleration will preserve the ground state of the wave function from the initial time to the final time.

Nanosystems Physics Chemistry Mathematics•Jun 29, 2025•0 citations
Geometric phase in the wave function is important with regard to quantum non-locality and adiabatic evolution. We study the confinement of a particle by three-dimensional isotropically moving walls, of relevance to experimental trapping techniques, via a proposed approach that explains the physical origin of the geometric Dirac phase induced in the wave function. This phase depends only on the relative rate of change of the spatial scale factor. The approach also yields the class of external potentials that replicate adiabatic evolution in finite time. As illustrative examples, we consider uniform and accelerating walls, and the case where the Dirac phase is due to cosmic expansion.
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.
Abstract We investigate the issue of single particle nonlocality in a quantum system subjected to time-dependent boundary conditions. We discuss earlier claims according to which the quantum state of a particle remaining localized at the center of an infinite well with moving walls would be specifically modified by the change in boundary conditions due to the wall’s motion. We first prove that the evolution of an initially localized Gaussian state is not affected nonlocally by a linearly moving wall: as long as the quantum state has negligible amplitude near the wall, the boundary motion has no effect. This result is further extended to related confined time-dependent oscillators in which the boundary’s motion is known to give rise to geometric phases: for a Gaussian state remaining localized far from the boundaries, the effect of the geometric phases is washed out and the particle dynamics shows no traces of a nonlocal influence that would be induced by the moving boundaries.
An introduction to topology in electrodynamics and the geometric phase con- cept is given. The form-invariance of the field-coupled Dirac equation is demon- strated, and it is shown, starting from the free Dirac equation, that demand of local phase invariance of the wave function dictates the presence of an elec- tromagnetic field. Afterwards the Dirac phase factor, Φ( C ), for a fixed-time loop is defined and discussed. It appears from The Principle of Local Phase Invariance that only the transverse part of the vector potential contributes to Φ( C ). The conditions ∇ × A T = 0 and ∇ · A T = 0 [A T being the transverse vector potential] in a certain finite spatial domain Ω do not imply that A T = 0 necessarily in Ω, as a certain integration involving A T over the domain outside Ω shows. The vector potential of a magnetic string with curvature and torsion is derived, and from this potential the result for a rectilinear magnetic string is obtained, In turn the Aharonov-Bohm effect is derived for a magnetic flux tube. Starting from the evolution operator in quantum physics an adiabatic theorem is established, and Berry's adiabatic geometric phase is introduced and discussed. An extended discussion shows that a geometric phase, called the Aharonov-Anandan phase, not restricted by the adiabatic principle can be introduced.
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 study a scheme of fast-forward adiabatic quantum dynamics of a (2 + 1) Dirac particle. This scheme was originally proposed by Masuda and Nakamura. In this scheme, we include the adiabatic parameter that maintains the adiabatic motion of the particle and fast forward its motion by introducing a time scaling parameter. The fast forward adiabatic state is obtained by determining the regularization term and driving potential. We introduce the proposed method to the system with the Dirac particle using a (2 + 1) dimensiontime- dependent Dirac equation and obtain the regularization term, the driving scalar potential VFF and the driving vector potential AFF . By tuning the driving electric field, this method can accelerate the adiabatic dynamics of an electron as a Dirac particle trapped in the ground state in the plane xy and an electric field in the x direction and a constant magnetic field in the y direction. This acceleration will preserve the ground state of the wave function from the initial time to the final time.