Exact density profile in a tight-binding chain with dephasing noise

TL;DR

This paper provides an exact analytical solution for the density profile in a quantum chain with dephasing noise, revealing diffusive transport and decay behaviors, and connecting quantum dynamics to classical exclusion processes.

Contribution

It derives the exact long-time density profiles for a dephasing-affected quantum chain using Bethe ansatz, highlighting diffusive transport and decay phenomena.

Findings

Diffusive transport emerges for any positive dephasing strength.

Density exhibits oscillatory or over-damped decay depending on dissipation.

Asymptotic forms approach those of the symmetric simple exclusion process.

Abstract

We theoretically investigate the many-body dynamics of a tight-binding chain with dephasing noise on the infinite interval. We obtain the exact solution of an average particle-density profile for the domain wall and the alternating initial conditions via the Bethe ansatz, analytically deriving the asymptotic expressions for the long time dynamics. For the domain wall initial condition, we obtain the scaling form of the average density, elucidating that the diffusive transport always emerges in the long time dynamics if the strength of the dephasing, no matter how small, is positive. For the alternating initial condition, our exact solution leads to the fact that the average density displays oscillatory decay or over-damped decay depending on the strength of the dissipation. Furthermore, we demonstrate that the asymptotic forms approach those of the symmetric simple exclusion process, identifying corrections from it.