Precursors for a nonequilibrium theory of diffusion in open quantum systems

Ming-Bao Yu

Ohad Shpielberg

The macroscopic fluctuation theory provides a complete hydrodynamic description of nonequilibrium classical diffusive systems. As a first step towards a diffusive theory of open quantum systems, we propose a microscopic open quantum system model —the selective dephasing model. It exhibits genuine quantum diffusive scaling. Namely, the dynamics is diffusive and the density matrix remains entangled at large length scales and long time scales.

I. Knežević, David K. Ferry

Merlijn van Horssen, Juan P. Garrahan

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. Particle hopping is coherent while reactions, such as pair annihilation or pair coalescence, are dissipative. These are quantum open generalizations of the A+A→⌀ and A+A→A classical RD models. We characterize 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 nonequilibrium 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→⌀ and A+A→A systems, behaves asymptotically as t-b with 1/2<b<1.

Paweł Danielewicz

P. Danielewicz. Nuclear Science Division