Slow dynamics for self-adjoint semigroups and unitary evolution groups

TL;DR

This paper investigates slow dynamical behavior in self-adjoint semigroups and unitary groups, focusing on orbit dynamics and average return probabilities, with applications to quantum systems exhibiting purely absolutely continuous spectra.

Contribution

It introduces new results on slow dynamics for self-adjoint semigroups and unitary groups, particularly in quantum systems with absolutely continuous spectra.

Findings

Demonstrates slow orbit dynamics in self-adjoint semigroups

Establishes slow decay of average return probability in unitary groups

Applies results to quantum systems with purely absolutely continuous spectra

Abstract

We obtain slow dynamics for self-adjoint semigroups and unitary evolution groups. For semigroups, the slow dynamics is for orbits, and for the average return probability in the case of unitary evolution groups. We present an application to the quantum dynamics of purely absolutely continuous systems