Figure 2

Eigenstate thermalization of spontaneous emissions. (a)-(c) The matrix-elements of the kinetic energy (), , in the energy eigenbasis (sorted in ascending order according to their energy). Different panels are for increasing on-site interaction U. Only in the SF regime ([37]) the diagonal elements vary smoothly with α, and allow for eigenstate thermalization. (d) The difference of the expectations between the diagonal and the canonical ensemble corresponding to the same mean energy after a single spontaneous emission at site in a system of and sites (errorbars are due to the interpolation to find the canonical ensemble corresponding to the correct energy). Although finite size effects are large the change in behavior at the quantum phase transition is evident.