1998/12/09 by Joachim Asch, Andreas Knauf
Mathematics · Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #Quantum and electron transport phenomena #Quantum chaos and dynamical systems #cond-mat #math-ph #math.DS #math.MP
paper · pdf · doi:10.1007/s002200050670
21 pages
arxiv created 1998/12/09 · openalex publication_date 1999/08/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Although quantum tunneling between phase space tori occurs, it is suppressed in the semiclassical limit ℏ\searrow 0 for the Schrödinger equation of a particle in \bRd under the influence of a smooth periodic potential. In particular this implies that the distribution of quantum group velocities near energy E converges to the distribution of the classical asymptotic velocities near E, up to a term of the order \cO(1/√(E)).