Stabilizing and destabilizing perturbations of PT-symmetric indefinitely damped systems

Kirillov, Oleg (2013) Stabilizing and destabilizing perturbations of PT-symmetric indefinitely damped systems. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 371 (1989). p. 20120051. ISSN 1364-503X

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Official URL: http://dx.doi.org/10.1098/rsta.2012.0051

Abstract

Eigenvalues of a potential dynamical system with damping forces that are described by an indefinite real symmetric matrix can behave as those of a Hamiltonian system when gain and loss are in a perfect balance. This happens when the indefinitely damped system obeys parity–time (PT) symmetry. How do pure imaginary eigenvalues of a stable PT-symmetric indefinitely damped system behave when variation in the damping and potential forces destroys the symmetry? We establish that it is essentially the tangent cone to the stability domain at the exceptional point corresponding to the Whitney umbrella singularity on the stability boundary that manages transfer of instability between modes.

Item Type: Article
Uncontrolled Keywords: indefinite damping, PT-symmetry, Krein signature, dissipation-induced instabilities, exceptional point, modulational instability
Subjects: F300 Physics
G100 Mathematics
Department: Faculties > Engineering and Environment > Mathematics and Information Sciences
Depositing User: Oleg Kirillov
Date Deposited: 10 Jan 2017 10:23
Last Modified: 11 Jan 2017 09:43
URI: http://nrl.northumbria.ac.uk/id/eprint/29035

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