Path topology dependence of adiabatic time evolution

TL;DR

This paper explores how the topology of adiabatic paths influences the evolution of quantum systems, revealing a topological dependence in eigenspace connections during slow parameter changes.

Contribution

It introduces a topological framework for understanding the dependence of eigenspace connections on adiabatic path topology in quantum systems.

Findings

Eigenspace connections depend on the topological properties of adiabatic paths.

Topological analysis of quantum holonomy explains path-dependent eigenspace evolution.

Application to periodically driven systems demonstrates the topological effects.

Abstract

An adiabatic time evolution of a closed quantum system connects eigenspaces of initial and final Hermitian Hamiltonians for slowly driven systems, or, unitary Floquet operators for slowly modulated driven systems. We show that the connection of eigenspaces depends on a topological property of the adiabatic paths for given initial and final points. An example in slowly modulated periodically driven systems is shown. These analysis are based on the topological analysis of the exotic quantum holonomy in adiabatic closed paths.