Computing characteristic functions of quantum work in phase space

TL;DR

This paper derives analytical characteristic functions for various quantum harmonic oscillators in phase space and introduces a numerical method for approximating CFs of general quantum systems, enhancing understanding of quantum work distributions.

Contribution

It provides a unified analytical approach for specific harmonic oscillators and proposes a numerical method for general quantum systems' characteristic functions.

Findings

Analytical CFs for forced and time-dependent harmonic oscillators.

Numerical method approximates CFs to order 2 for general systems.

Application to systems with time-dependent potentials.

Abstract

In phase space, we analytically obtain the characteristic functions (CFs) of a forced harmonic oscillator [Talkner et al., Phys. Rev. E, 75, 050102 (2007)], a time-dependent mass and frequency harmonic oscillator [Deffner and Lutz, Phys. Rev. E, 77, 021128 (2008)], and coupled harmonic oscillators under driving forces in a simple and unified way. For general quantum systems, a numerical method that approximates the CFs to $\hbar^2$ order is proposed. We exemplify the method with a time-dependent frequency harmonic oscillator and a family of quantum systems with time-dependent even power-law potentials.