PT-symmetry, indefinite damping and dissipation-induced instabilities

TL;DR

This paper explores how PT-symmetry in systems with indefinite damping relates to stability, exceptional points, and dissipation-induced instabilities, with implications for experimental PT-symmetric circuits.

Contribution

It analyzes the stability boundaries of PT-symmetric systems with indefinite damping and proposes experiments to observe dissipation-induced destabilization effects.

Findings

PT-symmetric systems can be marginally stable with a pure imaginary spectrum.

Exceptional points mark the transition where stability is lost.

Singularities in parameter space govern dissipation-induced destabilization.

Abstract

With perfectly balanced gain and loss, dynamical systems with indefinite damping can obey the exact PT-symmetry being marginally stable with a pure imaginary spectrum. At an exceptional point where the symmetry is spontaneously broken, the stability is lost via passing through a non-semisimple 1:1 resonance. In the parameter space of a general dissipative system, marginally stable PT-symmetric ones occupy singularities on the boundary of the asymptotic stability. To observe how the singular surface governs dissipation-induced destabilization of the PT-symmetric system when gain and loss are not matched, an extension of recent experiments with PT-symmetric LRC circuits is proposed.