Statistics of work performed on a forced quantum oscillator

TL;DR

This paper analyzes the statistical properties of work done on a quantum harmonic oscillator by an external force, providing explicit formulas for different initial states and confirming fluctuation theorems.

Contribution

It introduces two parameters to fully characterize the force protocol and derives explicit characteristic functions and probability distributions for various initial states.

Findings

Work distributions vary significantly with initial state

Explicit formulas for characteristic functions and probabilities

Fluctuation and work theorems are confirmed

Abstract

Various aspects of the statistics of work performed by an external classical force on a quantum mechanical system are elucidated for a driven harmonic oscillator. In this special case two parameters are introduced that are sufficient to completely characterize the force protocol. Explicit results for the characteristic function of work and the respective probability distribution are provided and discussed for three different types of initial states of the oscillator: microcanonical, canonical and coherent states. Depending on the choice of the initial state the probability distributions of the performed work may grossly differ. This result in particular holds also true for identical force protocols. General fluctuation and work theorems holding for microcanonical and canonical initial states are confirmed.