2007/03/08 by Carl M. Bender, Daniel W. Darg, D. Darg · 4 citations
Physics and Astronomy · #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #hep-th
paper · pdf · doi:10.1063/1.2720279
published as J.Math.Phys.48:042703,2007 · 16 pages, 17 figures, accepted for publication in the Journal of Mathematical Physics
arxiv created 2007/03/08 · openalex publication_date 2007/04/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The classical trajectories of the family of complex PT-symmetric Hamiltonians H=p2+x2(ix)ϵ (ϵ⩾0) 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 ϵ. There are regions in ϵ 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 ϵ.