Interacting Fermi systems in the tracial state

TL;DR

This paper investigates the asymptotic behavior of interacting Fermi systems in the tracial state, revealing they are either weakly asymptotically abelian or $ ext{ exteta}$-abelian, but not norm asymptotically abelian.

Contribution

It establishes a novel classification of the time evolution of Fermi systems under certain symmetries in the tracial state.

Findings

Time evolution is weakly asymptotically abelian or $ ext{ exteta}$-abelian in the tracial state.

Time evolution is not norm asymptotically abelian.

Results apply to lattice and continuum Fermi systems with Galilei-invariant interactions.

Abstract

We argue that for Fermi systems on lattices or the continuum with interaction invariant under a kind of Galilei transformation the time evolution is either weakly asymptotically abelian or at least $\eta$-abelian in the tracial state but not norm asymptotically abelian.