Noether-Constrained Correlations in Equilibrium Liquids

F. Sammüller, S. Hermann, D. de las Heras, M. Schmidt
Phys. Rev. Lett., 130, 268203, (2023)     DOI: 10.1103/PhysRevLett.130.268203
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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 Noether’s 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, Yukawa, soft-sphere dipolar, Stockmayer, Gay-Berne and Weeks-Chandler-Andersen liquids, of monatomic water and of a colloidal gel former demonstrate the fundamental role in the characterization of spatial structure.

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