Near integrable systems

Details Near integrable systems Near integrable systems

2009-02-12

arxiv.org/abs/0902.2089v2

Journal of Physics A vol.42, p.335102 (2009)

Nonlinear Sciences

Chaotic Dynamics

27 pages, 10 figures

Scientific paper

A two-dimensional circular quantum billiard with unusual boundary conditions introduced by Berry and Dennis (\emph{J Phys A} {\bf 41} (2008) 135203) is considered in detail. It is demonstrated that most of its eigenfunctions are strongly localized and the corresponding eigenvalues are close to eigenvalues of the circular billiard with Neumann boundary conditions. Deviations from strong localization are also discussed. These results agree well with numerical calculations.

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