Single-particle eigenstate thermalization and its effect on nonequlibrium dynamics in many-body systems

Abstract:
First, we introduce the concept of single-particle eigenstate thermalization on the example of a three-dimensional Anderson model in a delocalized regime. Among others, we discuss how the fluctuations of matrix elements of observables in single-particle energy eigenstates scale with the Hilbert space dimension (the system size).

Next, we prove that the observables which exhibit eigenstate thermalization in a single-particle sector equilibrate in many-body sectors of quadratic models. Remarkably, the same observables do not exhibit eigenstate thermalization in many-body sectors (there are exponentially many outliers). Therefore, the generalized Gibbs ensemble is needed to describe their expectation values after equilibration, and it is characterized by Lagrange multipliers that are smooth functions of single-particle energies.