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A Note on Classical Ground State Energies

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Abstract

The pair-specific ground state energy ε g (N):=ℰ g (N)/(N(N−1)) of Newtonian N body systems grows monotonically in N. This furnishes a whole family of simple new tests for minimality of putative ground state energies ℰ x g (N) obtained through computer experiments. Inspection of several publicly available lists of such computer-experimentally obtained putative ground state energies ℰ x g (N) has yielded several dozen instances of ℰ x g (N) which failed one of these tests; i.e., for those N one concludes that ℰ x g (N)>ℰ g (N) strictly. Although the correct ℰ g (N) is not revealed by this method, it does yield a better upper bound on ℰ g (N) than ℰ x g (N) whenever ℰ x g (N) fails a monotonicity test. The surveyed N-body systems include in particular N point charges with 2- or 3-dimensional Coulomb pair interactions, placed either on the unit 2-sphere or on a 2-torus (a.k.a. Thomson, Fekete, or Riesz problems).

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  1. Department of Mathematics, Rutgers University, Piscataway, NJ, 08854, USA

    Michael K.-H. Kiessling

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  1. Michael K.-H. Kiessling
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Kiessling, M.KH. A Note on Classical Ground State Energies. J Stat Phys 136, 275–284 (2009). https://doi.org/10.1007/s10955-009-9769-2

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