Universal quantum localizing transition of a partial barrier in a chaotic sea.
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>>Φ, such that wave packets and states are localized. In contrast, classical transport is mimicked for h<<Φ. Designing a quantum map with an isolated partial barrier of controllable flux Φ 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 Φ/h. We find this curve to be symmetric to Φ/h=1, having a width of 2 orders of magnitude in Φ/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 2×2 model gives an accurate analytical description of the transition curve.
Institut für Theoretische Physik, Technische Universität Dresden, 01062 Dresden, Germany.
Matthias
M
Michler
Arnd
A
Bäcker
Roland
R
Ketzmerick
Hans-Jürgen
HJ
Stöckmann
Steven
S
Tomsovic