Two-time free energy distribution function in (1+1) directed polymers

TL;DR

This paper derives an explicit formula for the joint distribution of free energies at two different times in a (1+1)-dimensional directed polymer model using Bethe ansatz and quantum boson mapping.

Contribution

It introduces a novel explicit expression for the two-time free energy distribution in directed polymers, advancing understanding of their temporal correlations.

Findings

Explicit two-time free energy distribution formula derived

Mapping to quantum boson system enables analytical progress

Provides insights into temporal correlations in directed polymers

Abstract

The explicit expression for the two-time free energy distribution function in one-dimensional directed polymers in random potential is derived in terms of the Bethe ansatz replica technique by mapping the replicated problem to the $N$-particle quantum boson system with attractive interactions.