Spontaneous Breaking of Classical PT Symmetry

Details Spontaneous Breaking of Classical PT Symmetry Spontaneous Breaking of Classical PT Symmetry

2007-03-08

arxiv.org/abs/hep-th/0703072v1

J.Math.Phys.48:042703,2007

Physics

High Energy Physics

High Energy Physics - Theory

16 pages, 17 figures, accepted for publication in the Journal of Mathematical Physics

Scientific paper

10.1063/1.2720279

The classical trajectories of the family of complex PT-symmetric Hamiltonians $H=p^2+x^2(ix)^\epsilon$ ($\epsilon\geq0$) form closed orbits. All such complex orbits that have been studied in the past are PT symmetric (left-right symmetric). The periods of these orbits exhibit an unusual dependence on the parameter $\epsilon$. There are regions in $\epsilon$ of smooth behavior interspersed with regions of rapid variation. It is demonstrated that the onset of rapid variation is associated with strange new kinds of classical trajectories that have never been seen previously. These rare kinds of trajectories are not PT symmetric and occur only for special rational values of $\epsilon$.

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