PT-symmetry, indefinite damping and dissipation-induced instabilities

Details PT-symmetry, indefinite damping and dissipation-induced instabilities PT-symmetry, indefinite damping and dissipation-induced instabilities

2011-09-30

arxiv.org/abs/1110.0018v2

Physics Letters A 376 (2012), pp. 1244-1249

Physics

Mathematical Physics

15 pages, 5 figures

Scientific paper

10.1016/j.physleta.2012.02.055

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.

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