Kinetics of Quantum Reaction-Diffusion systems

TL;DR

This paper extends classical reaction-diffusion models to quantum systems using the Keldysh path integral, deriving kinetic equations for particle reactions and analyzing entropy dynamics in trapped cold atom setups.

Contribution

It introduces a quantum generalization of reaction-diffusion dynamics, deriving kinetic equations for quantum particles and analyzing entropy evolution in inhomogeneous systems.

Findings

Particle density decays algebraically, depending on particle statistics.

Entropy decays algebraically in confining traps, saturates in deconfined cases.

Derived kinetic equations for quantum binary annihilation reactions.

Abstract

We discuss many-body fermionic and bosonic systems subject to dissipative particle losses in arbitrary spatial dimensions $d$, within the Keldysh path-integral formulation of the quantum master equation. This open quantum dynamics represents a generalisation of classical reaction-diffusion dynamics to the quantum realm. We first show how initial conditions can be introduced in the Keldysh path integral via boundary terms. We then study binary annihilation reactions $A+A\to\emptyset$, for which we derive a Boltzmann-like kinetic equation. The ensuing algebraic decay in time for the particle density depends on the particle statistics. In order to model possible experimental implementations with cold atoms, for fermions in $d=1$ we further discuss inhomogeneous cases involving the presence of a trapping potential. In this context, we quantify the irreversibility of the dynamics studying the time evolution of the system entropy for different quenches of the trapping potential. We find that the system entropy features algebraic decay for confining quenches, while it saturates in deconfined scenarios.