Equilibration of quantum hard rods in one dimension

TL;DR

This paper investigates the non-equilibrium dynamics of a quantum spin chain mapped to classical hard rods, deriving a Master equation that describes both the evolution and equilibrium properties of the system.

Contribution

It introduces a Master equation approach for quantum hard rods, linking quantum dynamics to classical equilibrium states and non-equilibrium evolution.

Findings

System approaches a microcanonical ensemble of classical hard rods

Master equation accurately describes non-equilibrium dynamics

Results hold for varying sizes of hard rods

Abstract

We study the out-of-equilibrium evolution of a strongly interacting quantum spin chain which is mapped on a system of hard rods that are coherently deposited on and removed from a lattice. We show that this closed quantum system approaches an equilibrium steady state which strongly resembles a microcanonical ensemble of classical hard rods. Starting from the fully coherent evolution equation we derive a Master equation for the evolution of the number of hard rods on the lattice. This equation does not only capture properties of the equilibrium state but also describes the dynamical non-equilibrium evolution into it for the majority of initial conditions. We analyze this in detail for hard rods of varying size.