Quantum statistical mechanics in infinitely extended systems ($C^*$ algebraic approach)

TL;DR

This paper reviews the application of $C^*$ algebra to infinite quantum systems, discusses nonequilibrium steady states, and rigorously derives the Landauer formula for quadratic systems.

Contribution

It provides a concise review of $C^*$ algebra in quantum statistical mechanics and offers a rigorous derivation of the Landauer formula in quadratic systems.

Findings

Review of $C^*$ algebra in equilibrium and nonequilibrium systems

Introduction of recent results on NESS

Rigorous derivation of Landauer formula for quadratic systems

Abstract

The derivation of macroscopic irreversible dynamics of nonequilibrium systems from microscopic equations was recently revisited from the point of view of infinitely extended quantum systems. Here we have briefly reviewed the $C^*$ algebra and its application to equilibrium systems as well as introduced some recent results on NESS. In addition, we have demonstrated the derivation of Landauer formula rigorously for quadratic systems but using a more physical presentation.