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

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• Quantum catastrophes: a case study
• Chaotic systems in complex phase space
• Quantum tunneling as a classical anomaly
• Probability Density in the Complex Plane
• Scattering amplitudes for the rationally extended P T symmetric complex potentials
• Classical oscillator with position-dependent mass in a complex domain
• Periodic orbits for classical particles having complex energy
• An Alternative Canonical Approach to the Ghost Problem in a Complexified Extension of the Pais-Uhlenbeck Oscillator
• Parsing skin effect in a non-Hermitian spinless BHZ-like model
• $\mathcal{P}\mathcal{T}$-Symmetric Generalized Extended Momentum Operator