  The nonequilibrium dynamics in chaotic quantum systems denies a fully
understanding up to now, even if thermalization in the long-time asymptotic
state has been explained by the eigenstate thermalization hypothesis which
assumes a universal form of the observable matrix elements in the eigenbasis of
Hamiltonian. It was recently proposed that the density matrix elements have
also a universal form, which can be used to understand the nonequilibrium
dynamics at the whole time scale, from the transient regime to the long-time
steady limit. In this paper, we numerically test these assumptions for density
matrix in the models of spins.
