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Day January 7, 2011

Study of classical mechanical systems with complex potentials

A. Sinha, D. Dutta, P. Roy

We apply the factorization technique developed by Kuru and Negro [Ann. Phys. 323 (2008) 413] to study complex classical systems. As an illustration we apply the technique to study the classical analogue of the exactly solvable PT symmetric Scarf II model, which exhibits the interesting phenomenon of spontaneous breakdown of PT symmetry at some critical point. As the parameters are tuned such that energy switches from real to complex conjugate pairs, the corresponding classical trajectories display a distinct characteristic feature – the closed orbits become open ones.

http://arxiv.org/abs/1101.0909
Quantum Physics (quant-ph)
Physics Letters A : vol. 375 (2011) p 452-457

Cryptohermitian Hamiltonians on graphs. II. Hermitizations.

Miloslav Znojil

Non-hermitian quantum graphs possessing real (i.e., in principle, observable) spectra are studied via their discretization. The discretized Hamiltonians are assigned, constructively, an elementary pseudometric and/or a more complicated metric. Both these constructions make the Hamiltonian Hermitian, respectively, in an auxiliary (Krein or Pontryagin) vector space or in a less friendly (but more useful) Hilbert space of quantum mechanics.

http://arxiv.org/abs/1101.1015
Quantum Physics (quant-ph); Mathematical Physics (math-ph)