2012/07/31 by Henning Schomerus · 1 citation
Physics and Astronomy · #Complex system #Energy (signal processing) #Homogeneous space #Mesoscopic physics #Nonlinear Waves and Solitons #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #Resonator #Scattering #Scattering theory #physics.optics #quant-ph
paper · pdf · doi:10.1098/rsta.2012.0194
published as Phil. Trans. R. Soc. A 371, 20120194 (2013) · 10 pages, 5 figures, minireview for a theme issue, Philosophical Transactions of the Royal Society A
openalex publication_date 2013/03/19 · arxiv created 2013/04/17 · arxiv updated 2013/04/18 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
I review how methods from mesoscopic physics can be applied to describe the multiple wave scattering and complex wave dynamics in non-Hermitian PT-symmetric resonators, where an absorbing region is coupled symmetrically to an amplifying region. Scattering theory serves as a convenient tool to classify the symmetries beyond the single-channel case and leads to effective descriptions that can be formulated in the energy domain (via Hamiltonians) and in the time domain (via time evolution operators). These models can then be used to identify the mesoscopic time and energy scales that govern the spectral transition from real to complex eigenvalues. The possible presence of magneto-optical effects (a finite vector potential) in multi-channel systems leads to a variant (termed PTT' symmetry) that imposes the same spectral constraints as PT symmetry. I also provide multi-channel versions of generalized flux-conservation laws.