Thermalization of a strongly interacting closed spin system: From   coherent many-body dynamics to a Fokker-Planck equation
  Thermalization has been shown to occur in a number of closed quantum many-body systems, but the description of the actual thermalization dynamics is prohibitively complex. Here, we present a model - in one and two dimensions - for which we can analytically show that the evolution into thermal equilibrium is governed by a Fokker-Planck equation derived from the underlying quantum dynamics. Our approach does not rely on a formal distinction of weakly coupled bath and system degrees of freedom. The results show that transitions within narrow energy shells lead to a dynamics which is dominated by entropy and establishes detailed balance conditions that determine both the eventual equilibrium state and the non-equilibrium relaxation to it. 
C. Ates and J. P. Garrahan and I. Lesanovsky
quant-ph cond-mat.quant-gas cond-mat.stat-mech physics.atom-ph