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| VOLUME 82 | ISSUE 8 |
PAGE 603
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| Universal statistics of the local Green function in wave chaotic systems with absorption
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D. V. Savin, H.-J. Sommers, Y. V. Fyodorov*+
Fachbereich Physik, Universität Duisburg-Essen, 45117 Essen, Germany
*School of Mathematical Sciences, University of Nottingham, Nottingham NG7 2RD, United Kingdom
+ Petersburg Nuclear Physics Institute RAS, 188300 Gatchina, Russia
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PACS: 05.45.Mt, 73.23.-b, 42.25.Bs
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Abstract
We establish a general relation between the statistics
of the local Green function for systems with chaotic wave
scattering and uniform energy loss (absorption) and the two-point
correlator of its resolvents for the same system without
absorption. Within the random matrix approach this kind of a
fluctuation dissipation relation allows us to derive the explicit
analytic expression for the joint distribution function of the
real and imaginary part of the local Green function for all
symmetry classes as well as at an arbitrary degree of
time-reversal symmetry breaking in the system. The outstanding
problem of orthogonal symmetry is further reduced to simple
quadratures. The results can be applied, in particular, to the
experimentally accessible impedance and reflection in a microwave
cavity attached to a single-mode antenna.
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