Random-matrix theory of amplifying and absorbing resonators with PT or PTT' symmetry

Birchall, Chris and Schomerus, Henning (2012) Random-matrix theory of amplifying and absorbing resonators with PT or PTT' symmetry. Journal of Physics A: Mathematical and Theoretical, 45. ISSN 1751-8113

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Abstract

We formulate Gaussian and circular random-matrix models representing a coupled system consisting of an absorbing and an amplifying resonator, which are mutually related by a generalized time-reversal symmetry. Motivated by optical realizations of such systems we consider a PT or a PTT' time-reversal symmetry, which impose different constraints on magneto-optical effects, and then focus on five common settings. For each of these, we determine the eigenvalue distribution in the complex plane in the short-wavelength limit, which reveals that the fraction of real eigenvalues among all eigenvalues in the spectrum vanishes if all classical scales are kept fixed. Numerically, we find that the transition from real to complex eigenvalues in the various ensembles display a different dependence on the coupling strength between the two resonators. These differences can be linked to the level spacing statistics in the Hermitian limit of the considered models.

Item Type:
Journal Article
Journal or Publication Title:
Journal of Physics A: Mathematical and Theoretical
Uncontrolled Keywords:
/dk/atira/pure/subjectarea/asjc/2600/2613
Subjects:
ID Code:
61504
Deposited By:
Deposited On:
02 Jan 2013 16:25
Refereed?:
Yes
Published?:
Published
Last Modified:
01 Jan 2020 08:16