Exceptional points in quantum and classical dynamics

Abstract

We notice that, when a quantum system involves exceptional points, i.e. the special values of parameters where the Hamiltonian loses its self-adjointness and acquires the Jordan block structure, the corresponding classical system also exhibits a singular behaviour associated with restructuring of classical trajectories. The system with the crypto-Hermitian Hamiltonian H = (p^2+z^2)/2 -igz^5 and hyper-ellictic classical dynamics is studied in details. Analogies with supersymmetric Yang-Mills dynamics are elucidated.

References added. Final version to be published in J. Phys. A

References in corpus (1)

• Cryptogauge symmetry and cryptoghosts for crypto-Hermitian Hamiltonians

Cited by in corpus (2)

• Classical oscillator with position-dependent mass in a complex domain
• An Alternative Canonical Approach to the Ghost Problem in a Complexified Extension of the Pais-Uhlenbeck Oscillator