Are interacting systems norm asymptotic abelian?

Jan Dereziński

Heide Narnhofer

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.

Heide Narnhofer

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 $η$-abelian in the tracial state but not norm asymptotically abelian.

Jonas Kahn, Mădălin Guţǎ

Laurent Bruneau, Alain Joye, Marco Merkli

Heide Narnhofer

We study the behaviour of continuous automorphism groups of quantum spin systems on the lattice. Whereas the shift is norm asymptotically abelian continuous automorphism groups can lead only to delocalization but not to norm asymptotic abelianess. As a consequence the shift does not allow a continuous extension.