Name: From Open Quantum Systems to Open Quantum Maps
Keywords: FOS: Computer and information sciences, Computer Science - Machine Learning, resonances, fractal repeller, FOS: Physical sciences, Statistical and Nonlinear Physics, Mathematical Physics (math-ph), Dynamical Systems (math.DS), [PHYS.MPHY] Physics [physics]/Mathematical Physics [math-ph], Nonlinear Sciences - Chaotic Dynamics

descriptionPublicationkeyboard_double_arrow_right Article , Preprint , Other literature type 09 Mar 2011Embargo end date: 01 Jan 2010 English Publisher:Springer Science and Business Media LLCJournal:Communications in Mathematical Physics, volume 304, pages 1-48 (issn: 0010-3616, eissn: 1432-0916,

Authors: Nonnenmacher, Stéphane; Sjoestrand, Johannes; Zworski, Maciej;

doi: 10.1007/s00220-011-1214-0 , 10.48550/arxiv.1004.3361

arXiv: http://arxiv.org/abs/1004.3361

From Open Quantum Systems to Open Quantum Maps

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Abstract

For a class of quantized open chaotic systems satisfying a natural dynamical assumption, we show that the study of the resolvent, and hence of scattering and resonances, can be reduced to the study of a family of open quantum maps, that is of finite dimensional operators obtained by quantizing the Poincar�� map associated with the flow near the set of trapped trajectories.

53 pages, 8 figures

Related Organizations

Direction des Sciences de la Matière
France
University of Paris-Saclay
France
University of California, Berkeley
United States
University of California, San Francisco
United States
Centre national de la recherche scientifique
France

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Keywords

FOS: Computer and information sciences, Computer Science - Machine Learning, resonances, fractal repeller, FOS: Physical sciences, Statistical and Nonlinear Physics, Mathematical Physics (math-ph), Dynamical Systems (math.DS), [PHYS.MPHY] Physics [physics]/Mathematical Physics [math-ph], Nonlinear Sciences - Chaotic Dynamics, Machine Learning (cs.LG), [NLIN.NLIN-CD] Nonlinear Sciences [physics]/Chaotic Dynamics [nlin.CD], Mathematics - Analysis of PDEs, FOS: Mathematics, open quantum map, [MATH.MATH-MP] Mathematics [math]/Mathematical Physics [math-ph], [MATH.MATH-AP] Mathematics [math]/Analysis of PDEs [math.AP], Mathematics - Dynamical Systems, Chaotic Dynamics (nlin.CD), quantum chaotic scattering, Mathematical Physics, Analysis of PDEs (math.AP)

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