Open quantum reaction-diffusion dynamics: absorbing states and relaxation

TL;DR

This paper extends classical reaction-diffusion models to open quantum systems, analyzing their relaxation dynamics, steady states, and fluctuation effects in one dimension through theoretical classification and numerical simulations.

Contribution

It introduces a quantum generalization of classical RD models, classifies the structure of their steady states, and reveals slower relaxation due to quantum fluctuations.

Findings

Relaxation towards dark states is slower than mean-field predictions.

Decay of density follows a power law with exponent between 1/2 and 1.

Complete classification of recurrent subspace and steady states.

Abstract

We consider an extension of classical stochastic reaction-diffusion (RD) dynamics to open quantum systems. We study a class of models of hard core particles on a one-dimensional lattice whose dynamics is generated by a quantum master operator and where particle hopping is coherent while reactions, such as pair annihilation or pair coalescence, are dissipative. These are quantum open generalisations of the $A+A \to \varnothing$ and $A+A \to A$ classical RD models. We characterise the relaxation of the state towards the stationary regime via a decomposition of the system Hilbert space into transient and recurrent subspaces. We provide a complete classification of the structure of the recurrent subspace (and the non-equilibrium steady states) in terms of the dark states associated to the quantum master operator and its general spectral properties. We also show that, in one dimension, relaxation towards these absorbing dark states is slower than that predicted by a mean-field analysis due to fluctuation effects, in analogy with what occurs in classical RD systems. Numerical simulations of small systems suggest that the decay of the density in one dimension, in both the open quantum $A+A \to \varnothing$ and $A+A \to A$ cases, may go asymptotically as $t^{-b}$ with $1/2 < b < 1$.