09.05.23 - Giovanni Ciccotti "Hydrodynamic limit of the scattering function and Time-dependent Non-equilibrium Molecular Dynamic"

Hydrodynamic limit of the scattering function

and

Time-dependent Non-equilibrium Molecular Dynamic

The derivation of the hydrodynamic limit of the Van Hove function from a rigorous probabilistic approach is presented. Then, after recalling the extension of the standard stationary state (time averages!) Molecular Dynamics to time dependent nonequilibrium situations, we show how the same idea can be used to compute hydrodynamic relaxation processes. The procedure, which we have called Dynamical Non-Equilibrium Molecular Dynamics (D-NEMD), to distinguish it from standard (stationary) NEMD, is based on a generalization of linear response theory. The idea has been implicitly formulated by Onsager in the thirties in metaphysical language; has been given a solid statistical mechanical foundation in the fifties by Green and Kubo (in the linear and nonlinear regime); then has been proven useful in molecular simulation by the present author in collaboration with G.Jacucci and I.R.Mac Donald in the seventies. It has been called the nonlinear Kubo-Onsager relation. It permits to connect dynamical nonequilibrium averages or dynamical relaxations to the final stationary state (the chosen initial distribution, suitably sampled, is the key ingredient of the game). To show the power of the method we apply it to get the hydrodynamic relaxation of an interface between two immiscible liquids.