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

TL;DR

This paper presents a straightforward quantum model that, without relying on random phase assumptions, naturally evolves to the Boltzmann distribution, demonstrating consistency with physical principles through numerical simulations.

Contribution

The authors develop a direct quantum model with no random phase assumptions that accurately predicts Boltzmann distribution evolution for systems with arbitrary initial conditions.

Findings

Numerical simulations show systems evolve to Boltzmann distribution.

Hierarchical equations improve computational efficiency.

Model aligns with physical expectations of quantum statistical mechanics.

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.