Quantum thermal equilibration from equipartition

¹ Institute of Physics, University of Augsburg - Universitätstr. 1, D-86159 Augsburg, Germany
² Fachbereich Physik, Universität Osnabrück - Barbarastrasse 7, D-49069 Osnabrück, Germany

Received: 18 January 2012
Accepted: 27 April 2012

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⊗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.