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Recent work of Bender and collaborators has shown that it is possible to find closed complex-energy classical trajectories for several polynomial potentials. The nature of the topologies of these trajectories was explored in these simple cases and an elegant relationship between the periodicity of the motion and the elliptic functions was shown.
The current talk extends this work to the classical paths associated with the infinite tower of pairs of isospectral Hamiltonians found by Bender and Hook in 2008 (each Hamiltonian in the pair is PT-symmetric, isospectral and the period of classical paths for paired Hamiltonians is isochronous). The complicated topology of complex-energy classical paths is explored and the question of the closure these trajectories (and hence the isochrony and isospectrality properties) is explored for particular cases. |
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