The Statistics of the Work Done on a Quantum Critical System by Quenching a Control Parameter

TL;DR

This paper investigates the statistical properties of work done during quenches in a quantum critical system, revealing a connection to Loschmidt echo and identifying edge singularities in work distribution.

Contribution

It introduces a novel relation between work statistics and Loschmidt echo, and analyzes local and global quenches in a quantum Ising chain at criticality.

Findings

Work distribution exhibits edge singularities for local quenches at criticality.

Connection established between work statistics and Loschmidt echo.

Analysis of work distribution shapes depending on quench type.

Abstract

We study the statistics of the work done on a quantum critical system by quenching a control parameter in the Hamiltonian. We elucidate the relation between the probability distribution of the work and the Loschmidt echo, a quantity emerging usually in the context of dephasing. Using this connection we characterize the statistics of the work done on a quantum Ising chain by quenching locally or globally the transverse field. We show that for local quenches starting at criticality the probability distribution of the work displays an interesting edge singularity.