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Noether-Constrained Correlations in Equilibrium Liquids.

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This study reveals how liquid structures maintain thermal invariance under spatial transformations. It identifies three key two-body correlation functions and an exact sum rule that characterizes liquid structure.

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Area of Science:

  • Condensed matter physics
  • Statistical mechanics
  • Computational physics

Background:

  • Classical many-body Hamiltonians describe liquid behavior.
  • Thermal invariance is a key property of liquid structures.
  • Noether's theorem relates symmetries to conservation laws.

Purpose of the Study:

  • To investigate thermal invariance in liquid structures against spatial transformations.
  • To identify and characterize emergent correlation functions at second order.
  • To establish a unifying sum rule for these correlators.

Main Methods:

  • Theoretical analysis using Noether's theorem.
  • Second-order perturbation theory for spatial transformations.
  • Molecular dynamics simulations of various liquid models.

Main Results:

  • Identified three distinct two-body correlation functions: density, force-force, and force gradient.
  • Derived an exact Noether sum rule connecting these correlation functions.
  • Demonstrated the fundamental role of these correlators in characterizing liquid structure.

Conclusions:

  • Liquid structure exhibits inherent thermal invariance.
  • The identified correlation functions and sum rule provide a fundamental framework for structural characterization.
  • The findings are broadly applicable across diverse liquid systems.