Exceptional and diabolical points in stability questions

Abstract

Abstract“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.