Periodic orbits for classical particles having complex energy

Abstract

This paper revisits earlier work on complex classical mechanics in which it was argued that when the energy of a classical particle in an analytic potential is real, the particle trajectories are closed and periodic, but that when the energy is complex, the classical trajectories are open. Here it is shown that there is a discrete set of eigencurves in the complex-energy plane for which the particle trajectories are closed and periodic.

12 pages, 9 figures

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• The ODE/IM Correspondence
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Cited by in corpus (8)

• PT-symmetric deformations of integrable models
• Formulating the Kramers problem in field theory
• Infinitely many inequivalent field theories from one Lagrangian
• Understanding complex dynamics by means of an associated Riemann surface
• Complex Trajectories in a Classical Periodic Potential
• Classical Trajectories of the Continuum States of the $\mathcal{P}\mathcal{T}$ symmetric Scarf II potential
• Complex Lagrangian dynamics
• Effects of complex parameters on classical trajectories of Hamiltonian systems