On the Scaling of Langevin and Molecular Dynamics Persistence Times of Non-Homogeneous Fluids

Abstract: The solution of the Langevin equation of an anisotropic fluid [Colmenares P. J; L\'opez F. and Olivares-Rivas W., Phys. Rev E. 2009, 80061123] allowed the evaluation of the position dependent perpendicular and parallel diffusion coefficients, using Molecular Dynamics data. However, the time scale of the Langevin Dynamics and Molecular Dynamics are different and an anzat for the persistence probability relaxation time was needed. Here we show how the solution for the average persistence probability obtained from the Smoluchowski-Fokker-Planck equation (SE), associated to the Langevin Dynamics, scales with the corresponding Molecular Dynamics quantity. Our SE perpendicular persistence time is evaluated in terms of simple integrals over the equilibrium local density. When properly scaled by the perpendicular diffusion coefficient, it gives a good match with that obtained from Molecular Dynamics.