# Stochastic dissipative quantum spin chains (I) : Quantum fluctuating discrete hydrodynamics

## TL;DR

This paper investigates how dissipative effects influence quantum spin chains coupled to quantum noise, revealing a transition to slow mode dynamics and deriving an effective stochastic quantum description.

## Contribution

It introduces a framework for analyzing dissipative quantum spin chains using quantum stochastic differential equations and characterizes the slow mode dynamics under strong friction.

## Key findings

- Dissipative friction localizes spin chain states on a slow mode manifold.
- Effective stochastic quantum dynamics of slow modes are derived.
- Application to quantum stochastic Heisenberg spin chain demonstrates the approach.

## Abstract

Motivated by the search for a quantum analogue of the macroscopic fluctuation theory, we study quantum spin chains dissipatively coupled to quantum noise. The dynamical processes are encoded in quantum stochastic differential equations. They induce dissipative friction on the spin chain currents. We show that, as the friction becomes stronger, the noise induced dissipative effects localize the spin chain states on a slow mode manifold, and we determine the effective stochastic quantum dynamics of these slow modes. We illustrate this approach by studying the quantum stochastic Heisenberg spin chain.