Computer simulation of some dynamical properties of the Lorentz gas

Abstract

We carried out molecular dynamics simulations of a Lorentz gas, consisting of a lone hydrogen molecule moving in a sea of stationary argon atoms. A Lennard-Jones form was assumed for the H₂-Ar potential. The calculations were performed at a reduced temperatureK ^* =kT/ɛ_{H 2−Ar} = 4.64 and at reduced densitiesρ ^*=ρ _Arσ ³_Ar in the range 0.074−0.414. The placement of Ar atoms was assumed to be random rather than dictated by equilibrium considerations. We followed the trajectories of many H₂ molecules, each of which is assigned in turn a velocity given by the Maxwell-Boltzmann distribution at the temperature of the simulation. Solving the equations of motion classically, we obtained the translational part of the incoherent dynamic structure factor for the H₂ molecule,S _tr(q, ω). This was convoluted with the rotational structure factorS _rot(q, ω) calculated assuming unhindered rotation to obtain the total structure factorS(q, ω). Our results agree well with experimental data on this function obtained by Egelstaffet al. At the highest density (ρ ^*=0.414) we studied the dependence ofS(q, ω) on system size (number of Ar atoms), number of H₂ molecules for which trajectories are generated, and the length of time over which these trajectories are followed.