# Boundary-driven Lindblad dynamics of random quantum spin chains : strong disorder approach for the relaxation, the steady state and the current

## TL;DR

This paper investigates the non-equilibrium dynamics of a disordered quantum spin chain under boundary-driven Lindblad evolution, providing explicit calculations of the steady-state magnetization profile and current using a strong disorder renormalization approach.

## Contribution

It introduces a strong disorder boundary-strong-disorder renormalization method to analyze relaxation, steady states, and currents in boundary-driven disordered quantum spin chains.

## Key findings

- Magnetization follows a step profile in localized chains.
- Explicit formulas for the magnetization step and current are derived.
- The approach applies to systems with large random fields and various couplings.

## Abstract

The Lindblad dynamics of the XX quantum chain with large random fields $h_j$ (the couplings $J_j$ can be either uniform or random) is considered for boundary-magnetization-drivings acting on the two end-spins. Since each boundary-reservoir tends to impose its own magnetization, we first study the relaxation spectrum in the presence of a single reservoir as a function of the system size via some boundary-strong-disorder renormalization approach. The non-equilibrium-steady-state in the presence of two reservoirs can be then analyzed from the effective renormalized Linbladians associated to the two reservoirs. The magnetization is found to follow a step profile, as found previously in other localized chains. The strong disorder approach allows to compute explicitly the location of the step of the magnetization profile and the corresponding magnetization-current for each disordered sample in terms of the random fields and couplings.