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Exceptional and diabolical points in stability questions
Author(s) -
Kirillov O.N.
Publication year - 2013
Publication title -
fortschritte der physik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.469
H-Index - 71
eISSN - 1521-3978
pISSN - 0015-8208
DOI - 10.1002/prop.201200068
Subject(s) - parallels , theoretical physics , hermitian matrix , hamiltonian (control theory) , classical mechanics , physics , stability (learning theory) , symmetry (geometry) , mathematics , calculus (dental) , geometry , quantum mechanics , computer science , engineering , machine learning , mechanical engineering , medicine , mathematical optimization , dentistry
“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 ‐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.