Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
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TY - JOUR
T1 - Random-matrix theory of amplifying and absorbing resonators with PT or PTT' symmetry
AU - Birchall, Chris
AU - Schomerus, Henning
PY - 2012
Y1 - 2012
N2 - We formulate Gaussian and circular random-matrix models representing acoupled system consisting of an absorbing and an amplifying resonator, whichare mutually related by a generalized time-reversal symmetry. Motivated byoptical realizations of such systems we consider a PT or a PTT' time-reversalsymmetry, which impose different constraints on magneto-optical effects, andthen focus on five common settings. For each of these, we determine theeigenvalue distribution in the complex plane in the short-wavelength limit,which reveals that the fraction of real eigenvalues among all eigenvalues in thespectrum vanishes if all classical scales are kept fixed. Numerically, we find thatthe transition from real to complex eigenvalues in the various ensembles displaya different dependence on the coupling strength between the two resonators.These differences can be linked to the level spacing statistics in the Hermitianlimit of the considered models.
AB - We formulate Gaussian and circular random-matrix models representing acoupled system consisting of an absorbing and an amplifying resonator, whichare mutually related by a generalized time-reversal symmetry. Motivated byoptical realizations of such systems we consider a PT or a PTT' time-reversalsymmetry, which impose different constraints on magneto-optical effects, andthen focus on five common settings. For each of these, we determine theeigenvalue distribution in the complex plane in the short-wavelength limit,which reveals that the fraction of real eigenvalues among all eigenvalues in thespectrum vanishes if all classical scales are kept fixed. Numerically, we find thatthe transition from real to complex eigenvalues in the various ensembles displaya different dependence on the coupling strength between the two resonators.These differences can be linked to the level spacing statistics in the Hermitianlimit of the considered models.
U2 - 10.1088/1751-8113/45/44/444006
DO - 10.1088/1751-8113/45/44/444006
M3 - Journal article
VL - 45
JO - Journal of Physics A: Mathematical and Theoretical
JF - Journal of Physics A: Mathematical and Theoretical
SN - 1751-8113
M1 - 444006
ER -