2023/08/10 by Yan V. Fyodorov, Fyodorov, Yan V.
Physics and Astronomy · #Chaotic Dynamics (nlin.CD) #Disordered Systems and Neural Networks (cond-mat.dis-nn) #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum chaos and dynamical systems #Quantum optics and atomic interactions #Random lasers and scattering media
paper · pdf · doi:10.48550/arxiv.2308.05682
openalex publication_date 2023/08/10 · openalex created_date 2023/08/18 · openalex updated_date 2026/07/28
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 show how to derive the mean density of the complex eigenvalues for reflection problems in disordered or chaotic systems with broken time-reversal invariance. The computations are done in the framework of nonlinear σ- model approach, assuming fixed M and 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.