Uniqueness theorems and analysis of classical density functional theory in nonequilibrium random geometries
Classical density functional theory (DFT) is a sophisticated and versatile tool
to tackle fundamental physical questions regarding the behavior of various
types of equilibrium fluids through a variational principle with respect to the
probability density to find a particle at a certain position. The framework of
DFT has a deep mathematical foundation provided by a rigorous theorem
relating the density of the fluid and the external potential acting on the particles: the knowledge of the density uniquely determines the external potential.
The aim of this research project is to establish the mathematical background
of a dynamical DFT (DDFT), which we understand in the most general ma-
thematical sense as a differential equation for the time-dependent density.
The central question is whether the different random external influences on
the nonequilibrium behavior of a fluid can be uniquely characterized alone in
terms of the density which solves the DDFT equation, in generalization of
the uniqueness theorem in equilibrium. This purely mathematical task is
independent of explicit approximations required for practical purposes. It will
be complemented by developing and employing novel DDFT methods to
describe the complex interplay of different intrinsic and extrinsic forces acting on the particles. A particular focus will lie on nonequilibrium fluid behavior in porous (random) media.
René Wittmann, Hartmut Löwen, Joseph M. Brader:
Order-preserving dynamics in one dimension – single-file diffusion and
caging from the perspective of dynamical density functional theory