Symmetry-Breaking Transition and Spectral Singularity in Coupled $\mathcal{PT}$-Symmetric Quantum Potentials

TL;DR

This paper investigates how coupling multiple $ ext{PT}$-symmetric quantum potentials affects their spectral singularities and phase transitions, revealing the impact of connection modes on transport properties.

Contribution

It introduces a transfer matrix formalism for coupled $ ext{PT}$-symmetric potentials and analyzes how different connection configurations influence spectral singularities and phase transitions.

Findings

Spectral singularities can be observed in coupled systems at specific parameters.

Connection mode significantly affects transport properties like anisotropic transmission.

Coupled systems exhibit $ ext{PT}$-symmetry transitions similar to single potentials.

Abstract

We study the scattering properties of $N$ identical one-dimensional localized $\mathcal{PT}$-symmetric potentials, connected in series as well as in parallel. We derive a general transfer matrix formalism for parallel coupled quantum scatterers, and apply that theory to demonstrate that the spectral singularities and $\mathcal{PT}$-symmetric transitions of single scattering cells may be observed in coupled systems, at the same or distinct values of the critical parameters, depending on the connection modes under which the scattering objects are coupled. We analyse the influences of the connection configuration on the related transport properties such as spectral singularities and anisotropic transmission resonances.