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Dynamical tunneling in systems with a mixed phase space

Abstract

Tunneling is one of the most prominent features of quantum mechanics. While the tunneling process in one-dimensional integrable systems is well understood, its quantitative prediction for systems with a mixed phase space is a long-standing open challenge. In such systems regions of regular and chaotic dynamics coexist in phase space, which are classically separated but quantum mechanically coupled by the process of dynamical tunneling. We derive a prediction of dynamical tunneling rates which describe the decay of states localized inside the regular region towards the so-called chaotic sea. This approach uses a fictitious integrable system which mimics the dynamics inside the regular domain and extends it into the chaotic region. Excellent agreement with numerical data is found for kicked systems, billiards, and optical microcavities, if nonlinear resonances are negligible. Semiclassically, however, such nonlinear resonance chains dominate the tunneling process. Hence, we combine our approach with an improved resonance-assisted tunneling theory and derive a unified prediction which is valid from the quantum to the semiclassical regime. We obtain results which show a drastically improved accuracy of several orders of magnitude compared to previous studies. (orig.)
Authors:
Publication Date:
Apr 22, 2010
Product Type:
Thesis/Dissertation
Report Number:
INIS-DE-1102
Resource Relation:
Other Information: TH: Diss. (Dr.rer.nat.)
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; CHAOS THEORY; DE-EXCITATION; PHASE SPACE; QUANTUM MECHANICS; RESONANCE; SEMICLASSICAL APPROXIMATION; TUNNEL EFFECT
OSTI ID:
21423628
Research Organizations:
Technische Univ. Dresden (Germany). Inst. fuer Theoretische Physik
Country of Origin:
Germany
Language:
English
Other Identifying Numbers:
TRN: DE11F5166
Availability:
Commercial reproduction prohibited; INIS; OSTI as DE21423628
Submitting Site:
DEN
Size:
247 pages
Announcement Date:
May 14, 2011

Citation Formats

Loeck, Steffen. Dynamical tunneling in systems with a mixed phase space. Germany: N. p., 2010. Web.
Loeck, Steffen. Dynamical tunneling in systems with a mixed phase space. Germany.
Loeck, Steffen. 2010. "Dynamical tunneling in systems with a mixed phase space." Germany.
@misc{etde_21423628,
title = {Dynamical tunneling in systems with a mixed phase space}
author = {Loeck, Steffen}
abstractNote = {Tunneling is one of the most prominent features of quantum mechanics. While the tunneling process in one-dimensional integrable systems is well understood, its quantitative prediction for systems with a mixed phase space is a long-standing open challenge. In such systems regions of regular and chaotic dynamics coexist in phase space, which are classically separated but quantum mechanically coupled by the process of dynamical tunneling. We derive a prediction of dynamical tunneling rates which describe the decay of states localized inside the regular region towards the so-called chaotic sea. This approach uses a fictitious integrable system which mimics the dynamics inside the regular domain and extends it into the chaotic region. Excellent agreement with numerical data is found for kicked systems, billiards, and optical microcavities, if nonlinear resonances are negligible. Semiclassically, however, such nonlinear resonance chains dominate the tunneling process. Hence, we combine our approach with an improved resonance-assisted tunneling theory and derive a unified prediction which is valid from the quantum to the semiclassical regime. We obtain results which show a drastically improved accuracy of several orders of magnitude compared to previous studies. (orig.)}
place = {Germany}
year = {2010}
month = {Apr}
}