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arXiv · 1911.11626

Construction of the classical time crystal Lagrangians from Sisyphus dynamics and duality description with the Liénard type equation

Partha Guha·A Ghose-Choudhury
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Abstract

We explore the connection between the equations describing Sisyphus dynamics and the generic Liénard type or Liénard equation from the viewpoint of branched Hamiltonians. The former provides the appropriate setting for classical time crystal being derivable from a higher order Lagrangian. However it appears the equations of Sisyphus dynamics have a close relation with the Liénard-II equation when expressed in terms of the `velocity' variable. Another interesting feature of the equations of Sisyphus dynamics is the appearance of velocity dependent "mass function" in contrast to the more commonly encountered position dependent mass. The consequences of such mass functions seem to have connections to cosmological time crystals .

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Partha Guha, A Ghose-Choudhury. 2019-11-25. Construction of the classical time crystal Lagrangians from Sisyphus dynamics and duality description with the Liénard type equation. https://arxiv.org/abs/1911.11626

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