Time asymptotics for interacting systems

TL;DR

This paper investigates the long-term behavior of Fermi systems with Galilei invariant interactions, showing that their time evolution becomes weakly but not norm asymptotically abelian in time invariant states, impacting the understanding of invariant states.

Contribution

It demonstrates the weak asymptotic abelianness of Fermi systems with Galilei invariance and discusses implications for invariant states, a novel insight into their time evolution.

Findings

Time evolution is weakly asymptotically abelian in invariant states.

Time evolution is not norm asymptotically abelian.

Implications for the existence of invariant states.

Abstract

We argue that for Fermi systems with Galilei invariant interaction the time evolution is weakly asymptotically abelian in time invariant states but not norm asymptotically abelian.Consequences for the existence of invariant states are discussed.