The Existence of the Thermodynamic Limit for the System of Interacting Quantum Particles in Random Media

TL;DR

This paper proves the existence of the thermodynamic limit for the internal energy and entropy of interacting quantum particles in random media, under broad conditions, using subadditive inequalities.

Contribution

It establishes the thermodynamic limit for quantum systems in random media with general assumptions, extending previous results to more complex interactions.

Findings

Energy proportional to system size in the thermodynamic limit

Existence of the thermodynamic limit for energy and entropy

Results hold under broad assumptions on randomness and interactions

Abstract

The thermodynamic limit of the internal energy and the entropy of the system of quantum interacting particles in random medium is shown to exist under the crucial requirements of stability and temperedness of interactions. The energy turns out to be proportional to the number of particles and/or volume of the system in the thermodynamic limit. The obtained results require very general assumptions on the random one-particle model. The methods are mainly based on subadditive type inequalities.