Quantum thermal equilibration from equipartition

TL;DR

This paper demonstrates that two finite quantum systems initially at different temperatures tend to reach a thermal-like equilibrium through energy exchange, driven by equipartition within energy shells, under weak interaction conditions.

Contribution

It establishes that equipartition in energy shells is sufficient for thermalization in quantum systems, supported by exact diagonalization of various models.

Findings

Energy exchange leads to equipartition within energy shells.

Equipartition suffices for thermalization of quantum systems.

Numerical models confirm the theoretical predictions.

Abstract

The problem of mutual equilibration between two finite, identical quantum systems, A and B, prepared initially at different temperatures is elucidated. We show that the process of energy exchange between the two systems leads to accurate equipartition within energy shells in the Hilbert space of the total non-interacting, composite system, A \otimes B. This scenario occurs under the general condition of a weak interaction between the systems. We predict that the sole hypothesis of such equipartition is sufficient to obtain a relaxation of the peers, A and B, towards a common thermal-like state. This conjecture is fully corroborated by an exact diagonalization of several quantum models.