Classical and quantum dynamics of a kicked relativistic particle in a box

TL;DR

This paper investigates the classical and quantum behavior of a relativistic particle in a box under periodic kicks, revealing how chaos, regularity, and quantum effects influence energy growth and particle transport.

Contribution

It provides an exact quantum solution for a kicked relativistic particle in a box and analyzes its energy dynamics and transport properties.

Findings

Chaotic classical motion leads to energy growth over time.

Quantum energy can be quasi-periodic or fluctuate, depending on parameters.

Particle transport exhibits trembling motion and depends on kicking parameters.

Abstract

We study classical and quantum dynamics of a kicked relativistic particle confined in a one dimensional box. It is found that in classical case for chaotic motion the average kinetic energy grows in time, while for mixed regime the growth is suppressed. However, in case of regular motion energy fluctuates around certain value. Quantum dynamics is treated by solving the time-dependent Dirac equation for delta-kicking potential, whose exact solution is obtained for single kicking period. In quantum case, depending on the values of the kicking parameters the average kinetic energy can be quasi periodic or, fluctuating around some value. Particle transport is studied by considering spatio-temporal evolution of the Gaussian wave packet and by analyzing trembling motion.