Natural nonequilibrium states in quantum statistical mechanics

TL;DR

This paper develops a framework for describing natural nonequilibrium states in quantum spin systems with heat flow, extending the concept of equilibrium states and deriving a linear response formula valid far from equilibrium.

Contribution

It introduces a new formalism for quantum nonequilibrium states based on a diffusion assumption, and derives a linear response formula applicable far from equilibrium.

Findings

Defined a natural nonequilibrium state in quantum spin systems

Showed the nonequilibrium state retains some analyticity similar to equilibrium states

Derived a linear response formula valid far from equilibrium

Abstract

A quantum spin system is discussed, where a heat flow between infinite reservoirs takes place in a finite region. A time dependent force may also be acting. Our analysis is based on a simple technical assumption concerning the time evolution of infinite quantum spin systems. This assumption, physically natural but currently proved for few specific systems only, says that quantum information diffuses in space-time in such a way that the time integral of the commutator of local observables converges: $\int_{-\infty}^0dt ||[B,\alpha^tA]||<\infty$. In this setup one can define a natural nonequilibrium state. In the time independent case, this nonequilibrium state retains some of the analyticity which characterizes KMS equilibrium states. A linear response formula is also obtained which remains true far from equilibrium. The formalism presented here does not cover situations where (for time independent forces) the time translation invariance and uniqueness of the natural nonequilibrium state are broken.