# Dissipative random quantum spin chain with boundary-driving and bulk-dephasing: magnetization and current statistics in the Non-Equilibrium-Steady-State

## TL;DR

This paper investigates the non-equilibrium steady states of a disordered quantum spin chain with boundary driving and bulk dephasing, mapping the problem to a classical disordered exclusion process to analyze magnetization and current statistics.

## Contribution

It extends classical exclusion process methods to quantum disordered spin chains under strong disorder or dephasing, providing explicit steady-state properties.

## Key findings

- Magnetization profiles and correlations are explicitly characterized.
- Mean current and fluctuations depend on disorder realizations.
- Effective classical mapping simplifies analysis of complex quantum dynamics.

## Abstract

The Lindblad dynamics with dephasing in the bulk and magnetization-driving at the two boundaries is studied for the quantum spin chain with random fields $h_j$ and couplings $J_j$ (that can be either uniform or random). In the regime of strong disorder in the random fields, or in the regime of strong bulk-dephasing, the effective dynamics can be mapped onto a classical Simple Symmetric Exclusion Process with quenched disorder in the diffusion coefficient associated to each bond. The properties of the corresponding Non-Equilibrium-Steady-State in each disordered sample between the two reservoirs are studied in detail by extending the methods that have been previously developed for the Symmetric Exclusion Process without disorder. Explicit results are given for the magnetization profile, for the two-point correlations, for the mean current and for the current fluctuations, in terms of the random fields and couplings defining the disordered sample.