Exceptional stationary state in a dephasing many-body open quantum system

TL;DR

This paper investigates a unique stationary state in a dephasing quantum many-body system that retains initial information, contrasting with the typical infinite-temperature state, and explores its dynamics and implications as quantum scars.

Contribution

It identifies and characterizes an exceptional pure stationary state in an open quantum system that preserves initial conditions, introducing a classical membrane model and hydrodynamic theory.

Findings

The system hosts a pure stationary state distinct from the infinite-temperature state.

The exceptional state retains memory of initial conditions, unlike typical states.

Stationary properties emerge on size-dependent timescales with finite decay rates.

Abstract

We study a dephasing many-body open quantum system that hosts, together with the infinite-temperature state, another additional stationary state. The latter is exceptional in many respects, as it is pure and retains memory of the initial condition, whereas any orthogonal state evolves towards the infinite-temperature state erasing any information on the initial state. We discuss the approach to stationarity of the model focusing in particular on the fate of interfaces between the two states; a simple classical model based on a membrane picture helps developing an effective hydrodynamic theory even if the dynamics does not feature any conserved quantity. The fact that the model reaches stationary properties on timescales that depend on the system size while the asymptotic decay rate is finite is duly highlighted. We point out the reasons for considering these exceptional stationary states as quantum many-body scars in the open system framework.