Chern-Simons number diffusion with hard thermal loops

We construct an extension of the standard Kogut-Susskind lattice model for classical (3+1) -dimensional Yang-Mills theory, in which ``classical particle'' degrees of freedom are added. We argue that this will correctly reproduce the ``hard thermal loop'' effects of hard degrees of freedom, while giving a local implementation which is numerically tractable. We prove that the extended system is Hamiltonian and has the same thermodynamics as dimensionally reduced hot Yang-Mills theory put on a lattice. We present a numerical update algorithm and study the Abelian theory to verify that the classical gauge theory self-energy is correctly modified. Then we use the extended system to study the diffusion constant for the Chern-Simons number. We verify the Arnold-Son-Yaffe picture that the diffusion constant is inversely proportional to the hard thermal loop strength. Our numbers correspond to a diffusion constant of =296ₖ^5T^4 for m₃^2=11g^2T^2/6.