  It is shown that statistical mechanics is applicable to isolated quantum
systems with finite numbers of particles, such as complex atoms, atomic
clusters, or quantum dots in solids, where the residual two-body interaction is
sufficiently strong. This interaction mixes the unperturbed shell-model
(Hartree-Fock) basis states and produces chaotic many-body eigenstates. As a
result, an interaction-induced statistical equilibrium emerges in the system.
This equilibrium is due to the off-diagonal matrix elements of the Hamiltonian.
We show that it can be described by means of temperature introduced through the
canonical-type distribution. 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 part of the
Hamiltonian gives rise to the increase of the effective temperature of the
system (statistical effect of the interaction). For example, this takes place
in the cerium atom which has four valence electrons and which is used in our
work to compare the theory with realistic numerical calculations.
