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arXiv · math-ph/0602040

Classical Trajectories for Complex Hamiltonians

Carl M. Bender·Jun-Hua Chen·Daniel W. Darg·Kimball A. Milton
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Abstract

It has been found that complex non-Hermitian quantum-mechanical Hamiltonians may have entirely real spectra and generate unitary time evolution if they possess an unbroken $\cP\cT$ symmetry. A well-studied class of such Hamiltonians is $H= p^2+x^2(ix)^ε$ ($ε\geq0$). This paper examines the underlying classical theory. Specifically, it explores the possible trajectories of a classical particle that is governed by this class of Hamiltonians. These trajectories exhibit an extraordinarily rich and elaborate structure that depends sensitively on the value of the parameter $ε$ and on the initial conditions. A system for classifying complex orbits is presented.

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Carl M. Bender, Jun-Hua Chen, Daniel W. Darg, Kimball A. Milton. 2006-02-14. Classical Trajectories for Complex Hamiltonians. https://doi.org/10.1088/0305-4470/39/16/009

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