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Quasi Kepler’s third law for quantum many-body systems

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Abstract

The Kepler’s third law is a relation between the period and the energy of two classical particles interacting via a gravitational potential. Recent works showed that this law could be extended, at least approximately, to classical three-body systems, or even many-body classical systems. So, a classical quasi Kepler’s third law seems to exist. In this paper, approximate analytical solutions are computed for quantum self-gravitating particles with different masses. The results give strong indications in favor of the existence of a quasi Kepler’s third law for such systems. The relevance of the proposal is checked with accurate numerical data for the ground state of self-gravitating identical bosons and with numerical estimations for systems with identical particles plus a different one. Connections between the quantum and classical systems are discussed.

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Acknowledgements

This work was supported by the Fonds de la Recherche Scientifique-FNRS under Grant No. 4.45.10.08.

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Authors and Affiliations

  1. Service de Physique Nucléaire et Subnucléaire, UMONS Research Institute for Complex Systems, Université de Mons, Place du Parc 20, 7000, Mons, Belgium

    Claude Semay & Cintia T. Willemyns

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  1. Claude Semay
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  2. Cintia T. Willemyns
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Correspondence to Claude Semay.

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Semay, C., Willemyns, C.T. Quasi Kepler’s third law for quantum many-body systems. Eur. Phys. J. Plus 136, 342 (2021). https://doi.org/10.1140/epjp/s13360-021-01313-2

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  • DOI: https://doi.org/10.1140/epjp/s13360-021-01313-2

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