Transition probabilities and dynamic structure factor in the ASEP conditioned on strong flux

TL;DR

This paper analyzes the ASEP conditioned on extreme flux, deriving exact transition probabilities and structure factors, revealing a different dynamical exponent than in typical regimes, with implications for understanding large current fluctuations.

Contribution

It provides exact solutions for the ASEP under extreme flux conditions using quantum fermion techniques, revealing a dynamical exponent of z=1.

Findings

Dynamical exponent in extreme current regime is z=1.

Exact transition probabilities and structure factors are derived.

Results extend to partially asymmetric and symmetric exclusion processes.

Abstract

We consider the asymmetric simple exclusion processes (ASEP) on a ring constrained to produce an atypically large flux, or an extreme activity. Using quantum free fermion techniques we find the time-dependent conditional transition probabilities and the exact dynamical structure factor under such conditioned dynamics. In the thermodynamic limit we obtain the explicit scaling form. This gives a direct proof that the dynamical exponent in the extreme current regime is $z=1$ rather than the KPZ exponent $z=3/2$ which characterizes the ASEP in the regime of typical currents. Some of our results extend to the activity in the partially asymmetric simple exclusion process, including the symmetric case.