October 2011
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Day October 4, 2011

PT-symmetry, indefinite damping and dissipation-induced instabilities

Oleg N. Kirillov

When gain and loss are in perfect balance, dynamical systems with indefinite damping can obey the exact PT-symmetry and therefore be marginally stable with a pure imaginary spectrum. At an exceptional point where the exact PT-symmetry is spontaneously broken, the stability is lost via a Krein collision of eigenvalues just as it happens at the Hamiltonian Hopf bifurcation. In the parameter space of a general dissipative system, marginally stable PT-symmetric ones occupy singularities on the boundary of the asymptotic stability domain. 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.

Mathematical Physics (math-ph); Other Condensed Matter (cond-mat.other); Spectral Theory (math.SP); Quantum Physics (quant-ph)