From scattering theory to complex wave dynamics in non-Hermitian PT -symmetric resonators

I review how methods from mesoscopic physics can be applied to describe the multiple wave scattering and complex wave dynamics in non-Hermitian -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 symmetry) that imposes the same spectral constraints as symmetry. I also provide multi-channel versions of generalized flux-conservation laws.