Superadiabatic Forces and Dynamic Decay of Liquid Structure

The power functional theory, as a very recently proposed variationalapproach to many-body statistical physics, describes systems of colloidal particles that evolve in time via overdamped Brownian many-body dynamics. The theoretical description rests on the Smoluchowski equation of motion for the many-body distribution function in configuration space. The power functional framework provides an exact variational description of such classical many-body problems. It is formulated on the basis of the use of the one-body particle density and current as trial fields. There exists a unique ``free power'' functional, which is minimal at the physical solution, both for the case of equilibrium dynamics and arbitrarily far from equilibrium, i.e. the theory is not restricted to a linear response regime of small perturbations around equilibrium.While previous investigations of the power functional framework were primarily carried out for very simple (e.g. one-dimensional) test cases, the present project aims at using the theory in order to describe colloidal liquids, for both dense and dilute states. In particular the influence of memory contributions to the dynamics of two-body time correlation functions shall be investigated. A cornerstone of the research is provided by the recently found nonequilibrium Ornstein-Zernike relation, which relates the memory functions to measurable correlation functions, such as the van Hove correlation function.While the motivation of the proposal is deeply routed in theoretical physics, on a methodological level, we primarily intend to carry out Brownian Dynamics computer simulations. The quantities that we aim to calculate possess direct relevance for the power functional theory, such as the current-density and current-current two-body correlation functions. The project aims at obtaining a systematic understanding of the memory effects in liquids, which is a necessary step on the route towards constructing usable and robust approximation for the power functional that describe superadiabatic forces. Having such approximations will permit to study a broad range of interesting and relevant inhomogeneous and driven colloidal systems in the future.

The power functional theory, as a very recently proposed variationalapproach to many-body statistical physics, describes systems of colloidal particles that evolve in time via overdamped Brownian many-body dynamics. The theoretical description rests on the Smoluchowski equation of motion for the many-body distribution function in configuration space. The power functional framework provides an exact variational description of such classical many-body problems. It is formulated on the basis of the use of the one-body particle density and current as trial fields. There exists a unique ``free power'' functional, which is minimal at the physical solution, both for the case of equilibrium dynamics and arbitrarily far from equilibrium, i.e. the theory is not restricted to a linear response regime of small perturbations around equilibrium.While previous investigations of the power functional framework were primarily carried out for very simple (e.g. one-dimensional) test cases, the present project aims at using the theory in order to describe colloidal liquids, for both dense and dilute states. In particular the influence of memory contributions to the dynamics of two-body time correlation functions shall be investigated. A cornerstone of the research is provided by the recently found nonequilibrium Ornstein-Zernike relation, which relates the memory functions to measurable correlation functions, such as the van Hove correlation function.While the motivation of the proposal is deeply routed in theoretical physics, on a methodological level, we primarily intend to carry out Brownian Dynamics computer simulations. The quantities that we aim to calculate possess direct relevance for the power functional theory, such as the current-density and current-current two-body correlation functions. The project aims at obtaining a systematic understanding of the memory effects in liquids, which is a necessary step on the route towards constructing usable and robust approximation for the power functional that describe superadiabatic forces. Having such approximations will permit to study a broad range of interesting and relevant inhomogeneous and driven colloidal systems in the future.