Nonclassical phase-space trajectories for the damped harmonic quantum oscillator

TL;DR

This paper explores the phase-space path-integral approach to the damped harmonic oscillator beyond the Markovian approximation, revealing nonclassical trajectories and their impact on the Wigner propagator.

Contribution

It demonstrates the existence of nonclassical trajectory pairs influencing the Wigner function and explains broadening via time-nonlocal heat bath interactions.

Findings

Pairs of nonclassical trajectories contribute to the Wigner propagator.

Sum coordinate of trajectory pairs obeys classical equations.

Broadening of the Wigner function is due to nonlocal heat bath effects.

Abstract

The phase-space path-integral approach to the damped harmonic oscillator is analyzed beyond the Markovian approximation. It is found that pairs of nonclassical trajectories contribute to the path-integral representation of the Wigner propagating function. Due to the linearity of the problem, the sum coordinate of a pair still satisfies the classical equation of motion. Furthermore, it is shown that the broadening of the Wigner propagating function of the damped oscillator arises due to the time-nonlocal interaction mediated by the heat bath.