Measuring effective temperatures in a generalized Gibbs ensemble

TL;DR

This paper proposes a method to determine effective temperatures in integrable quantum systems' generalized Gibbs ensembles using fluctuation-dissipation relations, facilitating experimental access to these parameters.

Contribution

It introduces a practical approach to identify temperature-like parameters in generalized Gibbs ensembles through fluctuation-dissipation relationships in simple models.

Findings

Effective temperatures can be determined from response and correlation functions.

Method applies to simple integrable models.

Accessible through experimental measurements.

Abstract

The local physical properties of an isolated quantum statistical system in the stationary state reached long after a quench are generically described by the Gibbs ensemble, which involves only its Hamiltonian and the temperature as a parameter. If the system is instead integrable, additional quantities conserved by the dynamics intervene in the description of the stationary state. The resulting generalized Gibbs ensemble involves a number of temperature-like parameters, the determination of which is practically difficult. Here we argue that in a number of simple models these parameters can be effectively determined by using fluctuation-dissipation relationships between response and correlation functions of natural observables, quantities which are accessible in experiments.