Large deviations of energy transfers in nonequilibrium CFT and asymptotics of non-local Riemann-Hilbert problems

TL;DR

This paper rigorously proves the large deviation principle for energy transfer statistics in nonequilibrium conformal field theories by analyzing the asymptotics of a non-local Riemann-Hilbert problem.

Contribution

It provides the first rigorous proof of the large deviation principle for energy transfers in nonequilibrium CFTs, connecting statistical mechanics with complex analysis.

Findings

Established the large deviation principle for energy transfer statistics.

Linked the generating function to a non-local Riemann-Hilbert problem.

Performed long-time asymptotic analysis of the Riemann-Hilbert problem.

Abstract

A wide class of $1+1$ dimensional unitary conformal field theories allows for an explicit construction of nonequilibrium "profile states" interpolating smoothly between different equilibria on the left and on the right. It has been recently established that the generating function for the full counting statistics of energy transfers in such states may be expressed in terms of the solution to a non-local Riemann-Hilbert problem. Following earlier works on the statistics of energy transfers, in particular the ones of Bernard-Doyon on the "partitioning protocol" in conformal field theory, the full counting statistics of energy transfers in the profile states was conjectured to satisfy a large deviation principle in the limit of long transfer-times. The present paper establishes rigorously this conjecture by carrying out the long-time asymptotic analysis of the underlying non-local Riemann-Hilbert problem.