On the relative dynamics of pairs of atoms in simple liquids
type: Item
instance of: scholarly article
title: On the relative dynamics of pairs of atoms in simple liquids
zbMATH Open document ID: 0598.76010
DOI: 10.1016/0378-4371(84)90169-9
author: R. Vallauri
author: H. A. Posch
author: Umberto Balucani
published in: Physica A
publication date: 1984-01-01T00:00:00Z
review text: We have studied the mutual dynamics of pairs of atoms in a dense Lennard- Jones fluid by evaluating relative velocity autocorrelation functions for particle pairs with separation \(r_ 0\) in a given distance range \(a_ 0\leq r_ 0\leq b_ 0\) at time zero using computer simulation. By application of projection operator techniques we have further derived exact generalized Langevin and Fokker-Planck equations for the problem in hand. After introducing simplifying assumptions for the memory kernel of these equations, a generalized Langevin equation is obtained which is solved numerically. Time dependent cross correlations between the relative velocity and the mean force entering this calculation are also evaluated from the MD-data. The resulting memory functions surprisingly prove to be practically independent of the chosen interval \((a_ 0,b_ 0)\) of starting separations of pair trajectories and, consequently, on the sign of the mean force between the test particles at time equal zero. The memory function exhibits a short time initial decay and a weak positive long time tail. Neglecting the latter and approximating the short time regime by a separation independent exponential memory function is it possible to model the pair dynamics by stochastic dynamics techniques. The mutual velocity correlation functions, force-velocity cross correlation functions and relative positional moments obtained from a stochastic dynamics simulation agree semi-quantitatively with the corresponding ''exact'' correlation functions obtained from MD-simulations.
Mathematics Subject Classification ID: 76A05
Mathematics Subject Classification ID: 82B05
zbMATH DE Number: 3965643
zbMATH Keywords: relative dynamics of pairs of atoms
zbMATH Keywords: dense Lennard-Jones fluid
zbMATH Keywords: relative velocity autocorrelation functions
zbMATH Keywords: projection operator techniques
zbMATH Keywords: Fokker-Planck equations
zbMATH Keywords: memory kernel
zbMATH Keywords: generalized Langevin equation
zbMATH Keywords: Time dependent cross correlations
zbMATH Keywords: memory functions
zbMATH Keywords: separations of pair trajectories
zbMATH Keywords: mean force
zbMATH Keywords: short time initial decay
zbMATH Keywords: weak positive long time tail
zbMATH Keywords: separation independent exponential memory function
zbMATH Keywords: stochastic dynamics techniques
zbMATH Keywords: force-velocity cross correlation functions
zbMATH Keywords: relative positional moments
MaRDI profile type: Publication
full work available at URL: 0378-4371(84)90169-9
OpenAlex ID: W2034339037
cites work: Statistical-mechanical theory of random frequency modulations and generalized Brownian motions.
cites work: Numerical integration of the Langevin equation: Monte Carlo simulation
cites work: Q4748912
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description: scientific article; zbMATH DE number 3965643