Dresden 2026 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 9: Statistical Physics far from Thermal Equilibrium I

DY 9.6: Talk

Monday, March 9, 2026, 10:45–11:00, ZEU/0160

Volterra Series leads to exact Dynamical Density Functional Theory — •Ion Santra — KU LEUVEN

We derive an exact Volterra series expansion for a mean mesoscopic field of an interacting particle system subject to a potential perturbation, expressing the Volterra expansion kernels in terms of the field’s response functions, to any order. Applying this formalism to the mean particle density of a simple interacting fluid, we identify a form reminiscent of dynamical density functional theory, with, however, fundamental differences: A generally nonlocal mobility kernel appears, and the internal force derives from a functional of the history of mean density. In the limit of a slowly varying external force, the expansion kernels of this functional turn into the equilibrium direct correlation functions of the corresponding order, thereby, in this limit, recovering the equilibrium density functional. We identify a freedom in deriving this expansion, which, e.g., allows different forms of mobility kernels, and we explore two choices: A nonlocal mobility kernel results in a concise ans simple form to linear order. For interacting Brownian particles, a local mobility kernel results in a form reminiscent of previous forms for the density current.

Keywords: Nonlinear response theory; Memory effects; Mean field theory