Superadiabatic Forces in Brownian Many-Body Dynamics

Abstract

Theoretical approaches to nonequilibrium many-body dynamics generally rest upon an adiabatic assumption, whereby the true dynamics is represented as a sequence of equilibrium states. Going beyond this simple approximation is a notoriously difficult problem. For the case of classical Brownian many-body dynamics, we present a simulation method that allows us to isolate and precisely evaluate superadiabatic correlations and the resulting forces. Application of the method to a system of one-dimensional hard particles reveals the importance for the dynamics, as well as the complexity, of these nontrivial out-of-equilibrium contributions. Our findings help clarify the status of dynamical density functional theory and provide a rational basis for the development of improved theories.

Free power dissipation from functional line integration

“…The superadiabatic force has been studied in detail for a simple one-dimensional model, where a non-trivial dependence on particle density was revealed [20].…”

Superadiabatic forces in the dynamics of the one-dimensional Gaussian core model

“…The time-dependent one-body density ρ(r, t) and the two-body density ρ (2) (r, r ′ , t) are obtained by integrating ψ(r N , t) over all but one and all but two particle coordinates, respectively, and multiplying by the appropriate normalizing factor [9],…”

“…This substitution implies the assumption that the relaxation time of particle correlations is short compared to the time scale of the processes of interest. However, this assumption is not justified, e.g., for strongly confined systems, which leads to a failure of DDFT in those cases [9]. In order to accurately describe the dynamics of such systems, superadiabatic forces need to be included.…”

“…However, for equidistant initial particle locations we find large superadiabatic forces, which are out-of-phase with respect to the adiabatic force and tend to grow with temperature. We identify the occupation of density peaks, which in reality correspond to individual particles, by multiple particles [9] to be one of the reasons for the occurrence of these superadiabatic forces.…”

“…In order to accurately describe the dynamics of such systems, superadiabatic forces need to be included. In recent work Fortini et al [9] have proposed a computational scheme for systematically dividing internal forces in a system of Brownian particles into an adiabatic and a superadiabatic contribution. By applying their method to a system of confined hard rods in one dimension, which is a common model system [10,11] for studying dynamical features, these authors found that the superadiabatic part of the force in that system is not a small correction and cannot easily be related to the adiabatic part.…”