Dynamic correlations in Brownian many-body systems

Abstract

For classical Brownian systems driven out of equilibrium we derive inhomogeneous two-time correlation functions from functional differentiation of the one-body density and current with respect to external fields. In order to allow for appropriate freedom upon building the derivatives, we formally supplement the Smoluchowski dynamics by a source term, which vanishes at the physical solution. These techniques are applied to obtain a complete set of dynamic Ornstein-Zernike equations, which serve for the development of approximation schemes. The rules of functional calculus lead naturally to non-Markovian equations of motion for the two-time correlators. Memory functions are identified as functional derivatives of a unique space- and time-nonlocal dissipation power functional.

10 pages, 67 equations

References in corpus (3)

• The van Hove distribution function for Brownian hard spheres: dynamical test particle theory and computer simulations for bulk dynamics
• Nonlinear rheology of colloidal dispersions
• Stochastic thermodynamics of fluctuating density fields: Non-equilibrium free energy differences under coarse-graining

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