Two-time free energy distribution function in the KPZ problem

TL;DR

This paper derives an explicit expression for the two-time free energy distribution in 1D directed polymers using Bethe ansatz, representing it as a generalized two-dimensional Fredholm determinant.

Contribution

It introduces a novel explicit formula for the two-time distribution function in the KPZ problem using Bethe ansatz and Fredholm determinants.

Findings

Explicit two-time free energy distribution function derived

Representation as a generalized two-dimensional Fredholm determinant

Advances understanding of temporal correlations in KPZ universality class

Abstract

The explicit expression for the two time free energy distribution function in one-dimensional random directed polymers is derived in terms of the Bethe ansatz replica technique. It is show that such type of the distribution function can be represented in the form of a generalized "two-dimensional" Fredholm determinant.