Roles of energy eigenstates and eigenvalues in equilibration of isolated quantum systems

We show that eigenenergies and energy eigenstates play different roles in the equilibration process of an isolated quantum system. Their roles are revealed numerically by exchanging the eigenenergies between an integrable model and a nonintegrable model. We find that the structure of eigenenergies of a nonintegrable model characterized by nondegeneracy ensures that quantum revival occurs rarely whereas the energy eigenstates of a nonintegrable model suppress the fluctuations for the equilibrated quantum state. Our study is aided with a quantum entropy that describes how randomly a wave function is distributed in quantum phase space. We also demonstrate with this quantum entropy the validity of Berry's conjecture for energy eigenstates. This implies that the energy eigenstates of a nonintegrable model appear indeed random.