Typical ground states for large sets of interactions

TL;DR

This paper explores the characteristics of ground states in systems with generic interactions, highlighting their spectral and mixing properties based on recent theoretical results.

Contribution

It applies Morris's recent findings to describe the spectral and mixing behavior of ground states for generic interactions.

Findings

Ground states have singular spectrum.

Ground states are weak mixing but not mixing.

Behavior aligns with that of generic measures.

Abstract

We discuss what ground states for generic interactions look like. We note that a recent result, due to Morris, implies that the behaviour of ground-state measures for generic interactions is similar to that of generic measures. In particular, it follows from his observation that they have singular spectrum and that they are weak mixing, but not mixing.