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Acta Polytechnica

Dirac fermion in a time-dependent spherical box

Kuvonchbek Matchonov, Davron U. Matrasulov, J. Dittrich

Published Nov 7, 2025• 0 citations
Publisher

Abstract

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.

DOI
10.14311/ap.2025.65.0546

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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 quantum dynamics of one-electron atom confined in a spherical impenetrable box with time-dependent radius. The behavior of the atomic electron interacting with the moving walls of the box is analyzed by computing average binding energy, average force and pressure. Linearly extending, contracting and harmonically breathing boxes are considered in the non-adiabatic regime i.e. when the wall of the box moves with high velocities. It is shown that linearly extending box leads to de-excitation of the atom, while the rapidly contracting box causes the creation of very high pressure on the atom and transition of the atomic electron into the unbound state. In harmonically breathing box diffusive excitation of atomic electron and ionization may occur in analogy with that for atom in a microwave field.
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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.