Dynamical typicality of isolated many-body quantum systems

TL;DR

This paper explores the concept of dynamical typicality in isolated many-body quantum systems, establishing conditions under which similar initial states evolve to exhibit similar observable expectations over time.

Contribution

It unifies and generalizes previous results on dynamical typicality, providing necessary and sufficient conditions related to initial expectation values and the spectrum of observables.

Findings

Identifies conditions for dynamical typicality in high-dimensional quantum systems

Provides a unified framework for previous results

Highlights the importance of initial expectation values and observable spectra

Abstract

Dynamical typicality refers to the property that two pure states, which initially exhibit (almost) the same expectation value for some given observable $A$, are very likely to exhibit also very similar expectation values when evolving in time according to the pertinent Schr\"odinger equation. We unify and generalize a variety of previous findings of this type for sufficiently high dimensional quantum mechanical model systems. Particular emphasize is put on the necessary and sufficient conditions, which the initial expectation value and the spectrum of $A$ have to fulfill.