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Statistics of resonances and delay times in random media: beyond random matrix theory

Tsampikos Kottos

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We review recent developments in quantum scattering from mesoscopic systems. Various spatial geometries whose closed analogues show diffusive, localized or critical behaviour are considered. These are the features that cannot be described by the universal random matrix theory results. Instead, one has to go beyond this approximation and incorporate them in a non-perturbative way. Here, we pay particular attention to the traces of these non-universal characteristics, in the distribution of the Wigner delay times and resonance widths. The former quantity captures time-dependent aspects of quantum scattering while the latter is associated with the poles of the scattering matrix.


PACS

03.65.Nk Scattering theory

02.10.Yn Matrix theory

05.45.Mt Quantum chaos; semiclassical methods

MSC

81U20 S-matrix theory, etc.

15A52 Random matrices

Subjects

Mathematical physics

Statistical physics and nonlinear systems

Quantum information and quantum mechanics

Dates

Issue 49 (9 December 2005)

Received 29 July 2005, in final form 5 October 2005

Published 22 November 2005



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