Volume 102, Number 1, April 2013
|Number of page(s)||6|
|Published online||23 April 2013|
Complex paths for regular-to-chaotic tunnelling rates
1 Institut für Theoretische Physik, Technische Universität Dresden - 01062 Dresden, Germany, EU
2 Max-Planck-Institut für Physik komplexer Systeme - Nöthnitzer Straße 38, 01187 Dresden, Germany, EU
3 OncoRay - National Center for Radiation Research in Oncology, Technische Universität Dresden Fetscherstraße 74, 01307 Dresden, Germany, EU
4 Department of Physics, Tokyo Metropolitan University - Minami-Osawa, Hachioji, Tokyo 192-0397, Japan
Received: 30 January 2013
Accepted: 21 March 2013
For generic non-integrable systems we show that a semiclassical prediction of tunnelling rates between regular and chaotic phase-space regions is possible. Our prediction is based on complex paths which can be constructed despite the obstacle of natural boundaries. The semiclassically obtained tunnelling rates are in excellent agreement with numerical tunnelling rates for the standard map where few complex paths dominate. This gives a semiclassical foundation of the long-conjectured and often-observed exponential scaling with Planck's constant of regular-to-chaotic tunnelling rates.
PACS: 05.45.Mt – Quantum chaos; semiclassical methods / 03.65.Sq – Semiclassical theories and applications
© EPLA, 2013
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