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Exceptional and diabolical points in stability questions
“I never satisfy myself until I can make a mechanical model of a thing” - guided by this motto of Lord Kelvin we would like to invite a reader to look at some modern concepts such as a non-Hermitian Hamiltonian, exceptional points, the geometric phase, and PT -symmetry, through the prism of the classical mechanics and stability theory. Mathematical and historical parallels discussed in the paper evidence that positions occupied by the non-Hermitian physics and non-conservative mechanics are closer to each other than one might expect.
Keywords: Non-Hermitian Hamiltonian; exceptional point; stability; non-conservative system; modulational instability
Fortschritte der Physik - Progress of Physics 61(2013)2-3, 205-224
Online First (2013) DOI: 10.1002/prop.201200068