Kawasaki-type dynamics: diffusion in the kinetic Gaussian model.

In this Brief Report, we retain the basic idea and at the same time generalize Kawasaki's dynamics, the spin-pair exchange mechanism, to a spin-pair redistribution mechanism, and present a normalized redistribution probability. This serves to unite various order-parameter-conserved processes into a universal framework in microscopics and provides the basis for further treatment. As an example of the applications, we treated the kinetic Gaussian model and obtained the exact diffusion equation. We observed critical slowing down near the critical point and found that the critical dynamic exponent z = 1/v = 2 is independent of space dimensionality and the assumed mechanism, whether Glauber type or Kawasaki type.