A simple direct quantum model which, with no random phase assumptions and with arbitrary initial conditions, evolves to the Boltzman distribution

Abstract

We consider M systems (each an electron in a long square cylinder) uniformly arranged on a ring and with Coulomb interactions. Exact straightforward numerical time-dependent perturbation calculation of a single N-level ($\lesssim 7$) system, with no (random) phase assumptions, system show a Boltzman distribution. We exploit the physical ring symmetry and develop several hierarchical physical equation set so of increasing generality and (computation) speed. Given the impressive history of theoretical quantum-mehanical statistical mechanics, our results might seem surprising, but we observe that accurate calculation of correct physical equations should mimic Nature.