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2008

Exceptional points in quantum and classical dynamics

Smilga, A. V.

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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.

Exceptional points in quantum and classical dynamics · Around

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A. Pais and G.E. Uhlenbeck, Phys. Rev. 79
1950
Earlier work this paper cites.
E.T. Whittaker and G.N. Watson, A course of modern analysis
1965
Earlier work this paper cites.
I. Affleck, M. Dine, and N. Seiberg, Phys. Lett. B137
1984
Earlier work this paper cites.
C.L. Siegel, Topics in complex function theory, Vol.2: Automorphic functions and Abelian integrals
1988
Earlier work this paper cites.
J.B. Bronzan, J.A. Shapiro, and R.L. Sugar, Phys. Rev. D14
1992
Earlier work this paper cites.
N. Seiberg and E. Witten, Nucl. Phys. B426
1994
Earlier work this paper cites.
P.C. Argyres and M.R. Douglas, Nucl. Phys. B448
1995
Earlier work this paper cites.
A. Kovner and M.A. Shifman, Phys. Rev. D56
1997
Earlier work this paper cites.

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A.V. Smilga, arXiv: 0808.0139 [quant-ph]

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