2012/06/30 by Matthias Michler, Arnd Bäcker, Roland Ketzmerick +3 · 25 citations
Physics and Astronomy · #Chaotic #Classical limit #Cold Atom Physics and Bose-Einstein Condensates #Geometry #Hamiltonian (control theory) #Parameter space #Physics #Planck constant #Quantum #Quantum chaos #Quantum chaos and dynamical systems #Quantum dynamics #Quantum many-body systems #Quantum mechanics #Quantum phase transition #Scaling #Statistical physics #Wave packet #nlin.CD
paper · pdf · doi:10.1103/physrevlett.109.234101
published in Physical Review Letters 109(23), 234101 (American Physical Society) · 5 pages, 4 figures
arxiv created 2012/10/23 · openalex publication_date 2012/12/03 · arxiv updated 2014/01/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.