On the asymptotic dynamics of 2-D magnetic quantum systems

TL;DR

This paper investigates the long-term spatial localization and angular momentum growth in 2-D magnetic quantum systems with symmetry-breaking perturbations, providing theoretical insights into their asymptotic dynamics.

Contribution

It offers new results on dynamical localization and angular momentum growth in 2-D magnetic quantum systems with symmetry-breaking perturbations.

Findings

Demonstrates conditions for dynamical localization in 2-D magnetic systems.

Provides estimates for angular momentum operator growth over time.

Analyzes the impact of symmetry-breaking perturbations on system dynamics.

Abstract

In this work we provide results on the long time localisation in space (dynamical localisation) of certain two-dimensional magnetic quantum systems. The underlying Hamiltonian may have the form $H=H_0+W$, where $H_0$ is rotationally symmetric, has dense point spectrum, and $W$ is a perturbation that breaks the rotational symmetry. In the latter case, we also give estimates for the growth of the angular momentum operator in time.