Analysis of velocity-displacement correlations in correlated random walks on lattices

The question how the velocity-autocorrelation in correlated random walks on lattices itself is correlated with the travelling distance of particles is investigated both by Monte Carlo simulation of the hard-square lattice gas and by analytical treatment of a Markoffian model with preferred backward jumps. In both cases it is found that the negative total of the velocity-autocorrelation function is the sum of relatively large negative and positive contributions from particles with small and large travelling distances, respectively.