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Mathematics > Analysis of PDEs

Title: From open quantum systems to open quantum maps

Authors: Stéphane Nonnenmacher (IPHT), Johannes Sjoestrand (IMB), Maciej Zworski (UC Berkeley Maths)
(Submitted on 20 Apr 2010 (v1), last revised 28 Feb 2011 (this version, v3))
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\'e map associated with the flow near the set of trapped trajectories.
Comments: 53 pages, 8 figures
Subjects: Analysis of PDEs (math.AP); Machine Learning (cs.LG); Mathematical Physics (math-ph); Dynamical Systems (math.DS); Chaotic Dynamics (nlin.CD)
DOI: 10.1007/s00220-011-1214-0
Cite as: arXiv:1004.3361 [math.AP]
  (or arXiv:1004.3361v3 [math.AP] for this version)

Submission history

From: Stephane Nonnenmacher [view email]
[v1] Tue, 20 Apr 2010 07:02:20 GMT (491kb)
[v2] Tue, 11 May 2010 17:34:00 GMT (491kb)
[v3] Mon, 28 Feb 2011 11:21:36 GMT (589kb)
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