Gaussian fluctuations in the Equipartition Principle for Wigner matrices

Understand

The total energy of an eigenstate in a composite quantum system tends to be distributed equally among its constituents.

• We identify the quantum fluctuation around this equipartition principle in the simplest disordered quantum system consisting of linear combinations of Wigner matrices.
• As our main ingredient, we prove the Eigenstate Thermalisation Hypothesis and Gaussian fluctuation for general quadratic forms of the bulk eigenvectors of Wigner matrices with an arbitrary deformation.