Equipartition principle for Wigner matrices

TL;DR

This paper proves that in large Wigner matrices, the energy of eigenvectors is evenly distributed among the matrices, demonstrating a strong form of the equipartition principle in quantum system models.

Contribution

It establishes a rigorous microcanonical equipartition principle for eigenvectors of sums of independent large Wigner matrices.

Findings

Eigenvector energy is equally distributed among matrices

High-precision equipartition in large Wigner matrices

Supports quantum system modeling with Wigner matrices

Abstract

We prove that the energy of any eigenvector of a sum of several independent large Wigner matrices is equally distributed among these matrices with very high precision. This shows a particularly strong microcanonical form of the equipartition principle for quantum systems whose components are modelled by Wigner matrices.