  By means of exact diagonalization, we investigate the onset of 'eigenstate
thermalization' and the crossover to ergodicity in a system of 1D fermions with
increasing interaction. We show that the fluctuations in the expectation values
of the momentum distribution from eigenstate to eigenstate decrease with
increasing coupling strength and system size. It turns out that these
fluctuations are proportional to the inverse participation ratio of eigenstates
represented in the Fock basis. We demonstrate that eigenstate thermalization
should set in even for vanishingly small perturbations in the thermodynamic
limit.
