Category University of Stellenbosch

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Spectral singularities in PT-symmetric Bose-Einstein condensates

Mar 4, ’13 6:16 AM

W. D. Heiss, H. Cartarius, G. Wunner, J. Main

We consider the model of a PT-symmetric Bose-Einstein condensate in a delta-functions double-well potential. We demonstrate that analytic continuation of the primarily non-analytic term \(|\psi|^2 \psi\) – occurring in the underlying Gross-Pitaevskii equation – yields new branch points where three levels coalesce. We show numerically that the new branch points exhibit the behaviour of exceptional points of second and third order. A matrix model which confirms the numerical findings in analytic terms is given.

http://arxiv.org/abs/1303.0132
Quantum Physics (quant-ph); Quantum Gases (cond-mat.quant-gas); Chaotic Dynamics (nlin.CD)

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PT-symmetric quantum systems with positive P

Jan 25, ’12 7:52 AM

Miloslav Znojil, Hendrik B. Geyer

A new version of PT-symmetric quantum theory is proposed and illustrated by an N-site-lattice Legendre oscillator. The essence of the innovation lies in the replacement of parity P (serving as an indefinite metric in an auxiliary Krein space) by its non-involutory alternative P(positive)=Q>0 playing the role of a positive-definite nontrivial metric in an auxiliary, redundant, unphysical Hilbert space. It is shown that the QT-symmetry of this form remains appealing and technically useful.

http://arxiv.org/abs/1201.5058
Quantum Physics (quant-ph)

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