Dynamics of large deviations in the hydrodynamic limit: Non-interacting systems

TL;DR

This paper analyzes the energy transfer fluctuations in quantum chains with non-interacting particles, deriving exact large deviation functions and interpreting results via a semi-classical quasi-particle picture.

Contribution

It provides an exact calculation of the scaled cumulant generating function for energy transfer in non-interacting quantum chains within the hydrodynamic limit, highlighting differences between fermionic and bosonic systems.

Findings

Exact scaled cumulant generating function derived for energy transfer

Large deviation functions characterized for fermionic and bosonic chains

Semi-classical interpretation of ballistic quasi-particle dynamics

Abstract

We study the dynamics of the statistics of the energy transferred across a point along a quantum chain which is prepared in the inhomogeneous initial state obtained by joining two identical semi-infinite parts thermalized at two different temperatures. In particular, we consider the transverse field Ising and harmonic chains as prototypical models of non-interacting fermionic and bosonic excitations, respectively. Within the so-called hydrodynamic limit of large space-time scales we first discuss the mean values of the energy density and current, and then, aiming at the statistics of fluctuations, we calculate exactly the scaled cumulant generating function of the transferred energy. From the latter, the evolution of the associated large deviation function is obtained. A natural interpretation of our results is provided in terms of a semi-classical picture of quasi-particles moving ballistically along classical trajectories. Similarities and differences between the transferred energy scaled cumulant and the large deviation functions in the cases of non-interacting fermions and bosons are discussed.