What is liquid, from Noether's perspective?

F. Sammüller, S. Hermann, D. de las Heras, M. Schmidt
arXiv, 2301.11221, , (2023)     DOI: 10.48550/arXiv.2301.11221
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Liquid structure carries deep imprints of an inherent thermal invariance against a spatial transformation of the underlying classical many-body Hamiltonian. At first order in the transformation field the Noether theorem yields the local force balance. Three distinct two-body correlation functions emerge at second order, namely the standard two-body density, the localized force-force correlation function, and the localized force gradient. An exact Noether sum rule interrelates these correlators. Simulations of Lennard-Jones and Weeks-Chandler-Andersen liquids, of monatomic water and of a colloidal gel former demonstrate their fundamental role in the characterization of spatial structure.

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