Work distribution for the driven harmonic oscillator with time-dependent strength: Exact solution and slow driving

TL;DR

This paper provides an exact solution for the work distribution of a driven harmonic oscillator with time-dependent strength, revealing non-Gaussian behavior with exponential tails and analyzing the transition to Gaussian distribution under slow driving.

Contribution

It derives an exact solution for the work distribution in a time-dependent harmonic oscillator and examines the Gaussian limit under slow driving conditions.

Findings

Work distribution has exponential tails and is non-Gaussian.

Numerical solutions of coupled differential equations describe the moment generating function.

Distribution approaches Gaussian form under slow but finite driving.

Abstract

We study the work distribution of a single particle moving in a harmonic oscillator with time-dependent strength. This simple system has a non-Gaussian work distribution with exponential tails. The time evolution of the corresponding moment generating function is given by two coupled ordinary differential equations that are solved numerically. Based on this result we study the behavior of the work distribution in the limit of slow but finite driving and show that it approaches a Gaussian distribution arbitrarily well.