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Journal Article

Exceptional points in quantum and classical dynamics

MPS-Authors

Smilga,  Andrei V.
Quantum Gravity & Unified Theories, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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Fulltext (public)

a9_9_095301.pdf
(Publisher version), 138KB

0808.0575v1.pdf
(Preprint), 150KB

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Citation

Smilga, A. V. (2009). Exceptional points in quantum and classical dynamics. Journal of Physics A: Mathematical and Theoreticaljournal of Physics A: Mathematical and Theoretical, 42(9): 095301. doi:10.1088/1751-8113/42/9/095301.


Cite as: http://hdl.handle.net/11858/00-001M-0000-0013-458C-D
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 = (p2+z2)/2 -igz5 and hyper-ellictic classical dynamics is studied in details. Analogies with supersymmetric Yang-Mills dynamics are elucidated.