The amplitude of the t^(3/2) short-time relaxation of density correlations is exactly set by equilibrium contact geometry in reversible Brownian hard-particle systems.
Numerical solution of the dynamical mean field theory of infinite-dimensional equilibrium liquids
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We present a numerical solution of the dynamical mean field theory of infinite-dimensional equilibrium liquids established in [Phys. Rev. Lett. 116, 015902 (2016)]. For soft sphere interactions, we obtain the numerical solution by an iterative algorithm and a straightforward discretization of time. We also discuss the case of hard spheres, for which we first derive analytically the dynamical mean field theory as a non-trivial limit of the soft sphere one. We present numerical results for the memory function and the mean square displacement. Our results reproduce and extend kinetic theory in the dilute or short-time limit, while they also describe dynamical arrest towards the glass phase in the dense strongly-interacting regime.
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Particle Contacts Generate Fractional Density Relaxation
The amplitude of the t^(3/2) short-time relaxation of density correlations is exactly set by equilibrium contact geometry in reversible Brownian hard-particle systems.