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Spectral statistics in chaotic systems with a point interaction

Martin Sieber

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We consider quantum systems with a chaotic classical limit that are perturbed by a point-like scatterer. The spectral form factor K(τ) for these systems is evaluated semiclassically in terms of periodic and diffractive orbits. It is shown for order τ2 and τ3 that off-diagonal contributions to the form factor which involve diffractive orbits cancel exactly the diagonal contributions from diffractive orbits, implying that the perturbation by the scatterer does not change the spectral statistic. We further show that parametric spectral statistics for these systems are universal for small changes of the strength of the scatterer.


PACS

05.45.Mt Quantum chaos; semiclassical methods

03.65.Yz Decoherence; open systems; quantum statistical methods

03.65.Sq Semiclassical theories and applications

MSC

81Q20 Semiclassical techniques including WKB and Maslov methods

81Q50 Quantum chaos (See also 37Dxx)

81S05 Commutation relations and statistics

Subjects

Quantum information and quantum mechanics

Statistical physics and nonlinear systems

Dates

Issue 36 (15 September 2000)

Received 8 March 2000



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