Universal energy distribution of quasi-particles emitted in a local time dependent quench

TL;DR

This paper analyzes the universal energy distribution of quasi-particles emitted during a local, time-dependent quench in a critical 1D Quantum Ising chain, revealing a protocol-independent power law behavior at low energies.

Contribution

It provides an exact analysis of quasi-particle emission and work statistics under generic time-dependent local perturbations in a critical quantum chain, highlighting universal features.

Findings

Work distribution follows a universal power law at low energies.

The power law exponent depends only on the final perturbation value.

Results are valid for generic time-dependent protocols.

Abstract

We study the emission of quasi-particles in the scaling limit of the 1d Quantum Ising chain at the critical point perturbed by a time dependent local transverse field. We compute \it exactly \rm and for a \it generic \rm time dependence the average value of the transverse magnetization, its correlation functions, as well as the statistic of both the inclusive and exclusive work. We show that, except for a cyclic perturbation, the probability distribution of the work at low energies is a power law whose exponent is universal, i.e. does not depend on the specific time dependent protocol, but only on the final value attained by the perturbation.