Normal Transport Behavior in Finite One-Dimensional Chaotic Quantum Systems

TL;DR

This paper demonstrates that in finite 1D chaotic quantum systems, energy and magnetization transport exhibit a sharp transition from non-normal to normal behavior, coinciding with a transition from integrability to chaos, studied through direct Schrödinger equation solutions.

Contribution

It provides a direct numerical analysis of transport in finite 1D quantum systems without relying on traditional transport analysis techniques, revealing the link between transport behavior and spectral statistics.

Findings

Sharp transition from non-normal to normal transport

Transition from integrability to chaos correlates with transport change

Transport behavior analyzed through direct Schrödinger equation solutions

Abstract

We investigate the transport of energy, magnetization, etc. in several finite one-dimensional (1D) quantum systems only by solving the corresponding time-dependent Schroedinger equation. We explicitly renounce on any other transport-analysis technique. Varying model parameters we find a sharp transition from non-normal to normal transport and a transition from integrability to chaos, i.e., from Poissonian to Wigner-like level statistics. These transitions always appear in conjunction with each other. We investigate some rather abstract design models and a (locally perturbed) Heisenberg spin chain.