Gaussian quantum fluctuations in interacting many particle systems

TL;DR

This paper demonstrates that in large interacting quantum systems with bounded energy per particle, the energy distribution of most product states approaches a Gaussian distribution as the number of particles grows infinitely large.

Contribution

It establishes a rigorous connection between many-particle quantum systems and Gaussian energy distributions in the thermodynamic limit.

Findings

Energy distribution becomes Gaussian in the large system limit.

Applicable to systems with nearest-neighbor interactions and bounded energy per particle.

Provides potential applications in quantum statistical mechanics.

Abstract

We consider a many particle quantum system, in which each particle interacts only with its nearest neighbours. Provided that the energy per particle has an upper bound, we show, that the energy distribution of almost every product state becomes a Gaussian normal distribution in the limit of infinite number of particles. We indicate some possible applications.