INTERACTION-DRIVEN EQUILIBRIUM AND STATISTICAL LAWS IN SMALL SYSTEMS - THE CERIUM ATOM

It is shown that statistical mechanics is applicable to isolated quant um systems with finite numbers of particles, such as complex atoms, at omic clusters, or quantum dots in solids, where the residual two-body interaction is sufficiently strong. This interaction mixes the unpertu rbed shell-model (Hartree-Fock) basis states and produces chaotic many -body eigenstates. As a result, an interaction-induced statistical equ ilibrium emerges in the system. This equilibrium is due to the off-dia gonal matrix elements of the Hamiltonian. We show that it can be descr ibed by means of temperature introduced through the canonical-type dis tribution. However, the interaction between the particles can lead to prominent deviations of the equilibrium distribution of the occupation numbers from the Fermi-Dirac shape. Besides that, the off-diagonal pa rt of the Hamiltonian gives rise to an increase of the effective tempe rature of the system (statistical effect of the interaction). For exam ple, this takes place in the cerium atom, which has four valence elect rons and which is used in our work to compare the theory with realisti c numerical calculations.