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  Partial Weyl law for billiards

Backer, A., Ketzmerick, R., Lock, S., & Schanz, H. (2011). Partial Weyl law for billiards. EPL, 94(3): 30004.

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Backer, A.1, Author           
Ketzmerick, R.1, Author           
Lock, S.1, Author           
Schanz, H.1, Author           
Affiliations:
1Max Planck Institute for the Physics of Complex Systems, Max Planck Society, ou_2117288              

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 MPIPKS: YB 2012
 Abstract: For two-dimensional quantum billiards we derive the partial Weyl law, i.e. the average density of states, for a subset of eigenstates concentrating on an invariant region G of phase space. The leading term is proportional to the area of the billiard times the phase-space fraction of G. The boundary term is proportional to the fraction of the boundary where parallel trajectories belong to G. Our result is numerically confirmed for the mushroom billiard and the generic cosine billiard, where we count the number of chaotic and regular states, and for the elliptical billiard, where we consider rotating and oscillating states. Copyright (C) EPLA, 2011

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 Dates: 2011-05
 Publication Status: Issued
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 Identifiers: eDoc: 608253
ISI: 000290226900004
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Title: EPL
Source Genre: Journal
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Pages: - Volume / Issue: 94 (3) Sequence Number: 30004 Start / End Page: - Identifier: ISSN: 0295-5075