Wigner dynamics of quantum semi-relativistic oscillator

TL;DR

This paper presents an exact solution to the Wigner-Liouville equation for a semi-relativistic quantum oscillator using Monte Carlo and molecular dynamics, revealing relativistic effects and unexpected distribution features.

Contribution

It introduces an exact solution method for the semi-relativistic quantum oscillator's Wigner dynamics, highlighting relativistic effects on quantum distributions.

Findings

Relativistic effects significantly influence Wigner distribution evolution.

Unexpected 'protuberances' observed in distribution functions.

Relativistic proper time dilation calculated for the oscillator.

Abstract

The integral Wigner - Liouwille equation describing time evolution of the semi-relativistic quantum 1D harmonic oscillator have been exactly solved by combination of the Monte-Carlo procedure and molecular dynamics methods. The strong influence of the relativistic effects on the time evolution of the momentum, velocity and coordinate Wigner distribution functions and the average values of quantum operators have been studied. Unexpected 'protuberances' in time evolution of the distribution functions were observed. Relativistic proper time dilation for oscillator have been calculated.