Universal Quantum Localizing Transition of a Partial Barrier in a Chaotic Sea

TL;DR

This paper investigates the quantum localization transition in systems with partial barriers, revealing a universal transition curve governed by the ratio of flux to Planck's constant, and introduces a local coupling model for better understanding.

Contribution

It introduces a controllable quantum map with an isolated partial barrier and demonstrates a universal transition curve for quantum transport based on local coupling.

Findings

Quantum transport follows a universal transition curve as a function of flux over Planck's constant.

The transition curve is symmetric around the ratio of one, spanning two orders of magnitude.

A simple 2x2 phenomenological model accurately describes the transition.

Abstract

Generic 2D Hamiltonian systems possess partial barriers in their chaotic phase space that restrict classical transport. Quantum mechanically the transport is suppressed if Planck's constant h is large compared to the classical flux, h >> Phi, such that wave packets and states are localized. In contrast, classical transport is mimicked for h << Phi. Designing a quantum map with an isolated partial barrier of controllable flux Phi is the key to investigating the transition from this form of quantum localization to mimicking classical transport. It is observed that quantum transport follows a universal transition curve as a function of the expected scaling parameter Phi/h. We find this curve to be symmetric to Phi/h=1, having a width of two orders of magnitude in Phi/h, and exhibiting no quantized steps. We establish the relevance of local coupling, improving on previous random matrix models relying on global coupling. It turns out that a phenomenological 2x2-model gives an accurate analytical description of the transition curve.