Breaking of PT-symmetry in bounded and unbounded scattering systems

TL;DR

This paper investigates PT-symmetry breaking in scattering systems, linking unbounded and bounded cases, and shows that PT-transitions are largely unaffected by coupling strength, with implications for experimental testing.

Contribution

It establishes a relation between PT-symmetry breaking points in unbounded scattering systems and bounded systems, revealing the robustness of PT-transitions against coupling variations.

Findings

PT-symmetry breaking points relate to Robin boundary conditions

PT-transitions are insensitive to coupling strength

Results can be visualized using Smith charts

Abstract

PT-symmetric scattering systems with balanced gain and loss can undergo a symmetry-breaking transition in which the eigenvalues of the non-unitary scattering matrix change their phase shifts from real to complex values. We relate the PT-symmetry breaking points of such an unbounded scattering system to those of underlying bounded systems. In particular, we show how the PT-thresholds in the scattering matrix of the unbounded system translate into analogous transitions in the Robin boundary conditions of the corresponding bounded systems. Based on this relation, we argue and then confirm that the PT-transitions in the scattering matrix are, under very general conditions, entirely insensitive to a variable coupling strength between the bounded region and the unbounded asymptotic region, a result that can be tested experimentally and visualized using the concept of Smith charts.