Second moment for cooperative diffusion in one-dimensional hard-particle lattice gases

摘要

The diffusion of hard particles that span an arbitrary number oi lattice sites an a one-dimensional lattice can be expressed in terms of a differential equation that contains one term that represents the random walk of independent particles and another term that represents the interaction of particles. The cooperative term involves the gradient of the pair distribution al the distance of closest approach. The moments of the particle distribution can then be expressed as a set of recursion relations that involve moments of the pair distribution at closest approach. For the case of the second moment this reduces to an equation involving the zeroth moment of the pair distribution for particles spanning a single lattice site which is known exactly. The independent-walk part of the second moment has the usual linear dependence with time while the cooperative part introduces a contribution that varies as root t.