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Amplitude distribution of eigenfunctions in mixed systems

Arnd Bäcker1,2 and Roman Schubert3

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We study the amplitude distribution of irregular eigenfunctions in systems with mixed classical phase space. For an appropriately restricted random wave model, a theoretical prediction for the amplitude distribution is derived and a good agreement with numerical computations for the family of limaçon billiards is found. The natural extension of our result to more general systems, e.g. with a potential, is also discussed.


PACS

03.65.Sq Semiclassical theories and applications

05.45.Mt Quantum chaos; semiclassical methods

02.50.Ey Stochastic processes

MSC

81S30 Phase space methods including Wigner distributions, etc.

81Q20 Semiclassical techniques including WKB and Maslov methods

Subjects

Computational physics

Statistical physics and nonlinear systems

Quantum information and quantum mechanics

Dates

Issue 3 (25 January 2002)

Received 20 April 2001, in final form 14 September 2001

Published 11 January 2002



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