Wednesday, February 22, 2012

1110.0018 (Oleg N. Kirillov)

PT-symmetry, indefinite damping and dissipation-induced instabilities    [PDF]

Oleg N. Kirillov
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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