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

TL;DR

This paper reviews how mesoscopic physics methods can describe wave scattering and dynamics in non-Hermitian PT-symmetric resonators, highlighting spectral transitions and symmetry classifications.

Contribution

It introduces effective models in energy and time domains for PT-symmetric resonators, extending symmetry classification and flux conservation laws to multichannel systems.

Findings

Identification of mesoscopic scales governing spectral transitions.

Extension of symmetry classifications to include PTT' symmetry.

Development of multichannel flux-conservation laws.

Abstract

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 which 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 which govern the spectral transition from real to complex eigenvalues. The possible presence of magneto-optical effects (a finite vector potential) in multichannel systems leads to a variant (termed PTT' symmetry) which imposes the same spectral constraints as PT symmetry. I also provide multichannel versions of generalized flux-conservation laws.