Utterson J, Erban R. Symmetries of many-body systems imply distance-dependent potentials.
Phys Rev E 2023;
108:014122. [PMID:
37583145 DOI:
10.1103/physreve.108.014122]
[Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/31/2023] [Accepted: 06/21/2023] [Indexed: 08/17/2023]
Abstract
Considering an interatomic potential U(q), where q=[q_{1},q_{2},⋯,q_{N}]∈R^{3N} is a vector describing positions q_{i}∈R^{3}, it is shown that U can be defined as a function of the interatomic distance variables r_{ij}=|q_{i}-q_{j}| provided the potential U satisfies some symmetry assumptions. Moreover, the potential U can be defined as a function of a proper subset of the distance variables r_{ij}, provided N>5, with the number of distance variables used scaling linearly with the number of atoms N.
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