A self-consistent field theory of density correlations in classical fluids

Abstract

More than half of a century has passed since the free energy of classical fluids defined by second Legendre transform was derived as a functional of density-density correlation function. It is now becoming an increasingly significant issue to develop the correlation functional theory that encompasses the liquid state theory, especially for glassy systems where out of equilibrium correlation fields are to be investigated. Here we have formulated a field theoretic perturbation theory that incorporates two-body fields (both of density-density correlation field and its dual field playing the role of two-body interaction potential) into a density functional integral representation of the Helmholtz free energy. Quadratic density fluctuations are only considered in the saddle-point approximation of two-body fields as well as density field. We have obtained a set of self-consistent field equations with respect to these fields, which simply reads a modified mean-field equation of density field where the bare interaction potential in the thermal energy unit is replaced by minus the direct correlation function given in the mean spherical approximation. Such replacement of the interaction potential in the mean-field equation belongs to the same category as the local molecular field theory proposed by Weeks and co-workers. Notably, it has been shown that even the mean-field part of the free energy functional given by the self-consistent field theory includes information on short-range correlations between fluid particles, similarly to the formulation of the local molecular field theory. The advantage of our field theoretic approach is not only that the modified mean-field equation can be improved systematically, but also that fluctuations of two-body fields in nonuniform fluids may be considered, which would be relevant especially for glass-forming liquids.

to be published in Phys. Rev. E (13 pages, 1 table)

References in corpus (17)

• Theoretical perspective on the glass transition and amorphous materials
• Hyperuniform States of Matter
• Local molecular field theory for effective attractions between like charged objects in systems with strong Coulomb interactions
• Decorrelation of the static and dynamic length scales in hard-sphere glass-formers
• The standard mean-field treatment of inter-particle attraction in classical DFT is better than one might expect
• Attraction Between Like-Charged Walls: Short-Ranged Simulations Using Local Molecular Field Theory
• Static replica approach to critical correlations in glassy systems
• Integral equations for simple fluids in a general reference functional approach
• Renormalized phonons in nonlinear lattices: A variational approach
• Static Structural Signatures of Nearly Jammed Disordered and Ordered Hard-Sphere Packings: Direct Correlation Function
• Systematic expansion in the order parameter for replica theory of the dynamical glass transition
• Absence of hyperuniformity in amorphous hard-sphere packings of nonvanishing complexity
• A formally exact field theory for classical systems at equilibrium
• A variational principle behind van der Waals picture of strongly coupled plasmas
• The method of collective variables: a link with the density functional theory
• A mesoscopic field theory of ionic systems versus a collective variable approach
• Bridging the gap between correlation entropy functionals in the mean spherical and the hypernetted chain approximations: a field theoretic description

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• Replica Field Theory for a Generalized Franz--Parisi Potential of Inhomogeneous Glassy Systems: New Closure and the Associated Self-Consistent Equation
• Free-energy functional of instantaneous correlation field in liquids: field-theoretic derivation of the closures