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arXiv · 2103.04214

$PT$-symmetric classical mechanics

Carl M. Bender·Daniel W. Hook
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Abstract

This paper reports the results of an ongoing in-depth analysis of the classical trajectories of the class of non-Hermitian $PT$-symmetric Hamiltonians $H=p^2+ x^2(ix)^\varepsilon$ ($\varepsilon\geq0$). A variety of phenomena, heretofore overlooked, have been discovered such as the existence of infinitely many separatrix trajectories, sequences of critical initial values associated with limiting classical orbits, regions of broken $PT$-symmetric classical trajectories, and a remarkable topological transition at $\varepsilon=2$. This investigation is a work in progress and it is not complete; many features of complex trajectories are still under study.

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Carl M. Bender, Daniel W. Hook. 2021-03-06. $PT$-symmetric classical mechanics. https://arxiv.org/abs/2103.04214

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