Study of work on a quantum harmonic oscillator

Abstract

We define the work probability distribution that is done to a quantum system during some process, from which the average work, its variance and the irreversible work can be obtained. Two limits are introduced according to whether the system evolves adiabatically or it undergoes an instantaneous quench. The time evolution of this system is obtained by solving numerically the time dependent Schrödinger equation through the Crank-Nicolson method. The two limit situations are explored for the simple case of a quantum harmonic oscillator with a time dependent Hamiltonian, as well as the intermediate regime between both limits. The results for the average work done during the process and its variance agree with the analytical expressions for the two limits. Finally, we study the work probability distribution during a shortcut to adiabacity protocol.