DIFFUSION EQUATION FOR ENERGY IN ERGODIC ADIABATIC ENSEMBLES

A diffusion equation is derived for the distribution of energies of an ensemble of systems governed by an ergodic adiabatic Hamiltonian. We compare the predictions of this equation with previously derived results and find some disagreement. We obtain explicit expressions for the degree to which the ergodic adiabatic invariant is conserved. We demonstrate that our equation gives the expected results for two special cases. Finally, we discuss applications and tests of our theory, as well as directions for future study.