On the Wigner function of the relativistic finite-difference oscillator in an external field

TL;DR

This paper develops a phase-space representation for a relativistic finite-difference oscillator in an external field, deriving explicit Wigner functions for stationary and thermal states, and analyzing their limits.

Contribution

It introduces a novel phase-space framework for a relativistic oscillator with external fields using finite-difference equations, providing explicit Wigner functions and their limiting behaviors.

Findings

Explicit Wigner functions for stationary states derived

Wigner functions for thermodynamical equilibrium obtained

Correct limiting behaviors demonstrated

Abstract

The phase-space representation for a relativistic linear oscillator in a homogeneous external field expressed through the finite-difference equation is constructed. Explicit expressions of the relativistic oscillator Wigner quasi-distribution function for the stationary states as well as of states of thermodynamical equilibrium are obtained and their correct limits are shown.