Quantum Localization in Open Chaotic Systems

TL;DR

This paper investigates how quantum localization behaves in open chaotic systems, specifically in a delta-kicked rotor with absorbing boundaries, revealing a relationship between localization length and decay rate.

Contribution

It introduces a relation between localization length and decay rate in open quantum systems and explains it through finite time diffusion, applicable to similar models.

Findings

Localization lengths decrease near absorbing boundaries.

Decay rates are significantly increased near boundaries.

Localization length scales as the inverse square root of decay rate.

Abstract

We study a quasi-Floquet state of a $\delta$-kicked rotor with absorbing boundaries focusing on the nature of the dynamical localization in open quantum systems. The localization lengths $\xi$ of lossy quasi-Floquet states located near the absorbing boundaries decrease as they approach the boundary while the corresponding decay rates $\Gamma$ are dramatically enhanced. We find the relation $\xi \sim \Gamma^{-1/2}$ and explain it based upon the finite time diffusion, which can also be applied to a random unitary operator model. We conjecture that this idea is valid for the system exhibiting both the diffusion in classical dynamics and the exponential localization in quantum mechanics.