On the Density of Complex Eigenvalues of Wigner Reaction Matrix in a Disordered or Chaotic System with Absorption

Y.V. Fyodorov AFFSTART King's College London, Department of Mathematics, London WC2R 2LS, United Kingdom

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In an absorptive system, the Wigner reaction K-matrix (directly related to the impedance matrix in acoustic or electromagnetic wave scattering) is non-selfadjoint, hence its eigenvalues are complex. The most interesting regime arises when the absorption, taken into account as an imaginary part of the spectral parameter, is of the order of the mean level spacing. I will show how to derive the mean density of the complex K-matrix eigenvalues for the M-channel reflection problem in disordered or chaotic systems with broken time-reversal invariance. The computations have been done in the framework of the nonlinear σ-model approach, assuming fixed M and the dimension of the underlying Hamiltonian matrix N→∞. Some explicit formulas are provided for zero-dimensional quantum chaotic system as well as for a semi-infinite quasi-1D system with fully operative Anderson localization.

DOI:10.12693/APhysPolA.144.447 topics: quantum chaotic scattering, random matrix theory, non-Hermitian matrices.\\vs*{6pt}