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Power functional theory for many-body dynamics
Reviews of Modern Physics  (IF50.485),  Pub Date : 2022-03-28, DOI: 10.1103/revmodphys.94.015007
Matthias Schmidt

The rich and diverse dynamics of particle-based systems ultimately originates from the coupling of their degrees of freedom via internal interactions. To arrive at a tractable approximation of such many-body problems, coarse graining is often an essential step. Power functional theory provides a unique and microscopically sharp formulation of this concept. The approach is based on an exact one-body variational principle to describe the dynamics of both overdamped and inertial classical and quantum many-body systems. In equilibrium, density-functional theory is recovered, and hence spatially inhomogeneous systems are described correctly. The dynamical theory operates on the level of time-dependent one-body correlation functions. Two- and higher-body correlation functions are accessible via the dynamical test-particle limit and the nonequilibrium Ornstein-Zernike route. The structure of this functional approach to many-body dynamics is described, including much background as well as applications to a broad range of dynamical situations, such as the van Hove function in liquids, flow in nonequilibrium steady states, motility-induced phase separation of active Brownian particles, lane formation in binary colloidal mixtures, and both steady and transient shear phenomena.