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A numerical study of a system of spinless fermions on a two dimensional lattice is performed. The system is small enough such that exact diagonalization up to machine precision can be applied. The aim is to study the equilibration and thermalization of closed quantum systems by looking at the expectation values of certain observables, a topic which lies at the foundations of statistical mechanics but has recently become also of great experimental interest. In particular the eigenstate thermalization hypothesis (ETH) is being tested, a proposal that thermalization of quantum systems takes place at the level of individual energy eigenstates and which has been conjectured for Hamiltonians far from integrability. By changing the interactions between the particles the system is moved away from the integrable free fermion model and the validity of the ETH is being inferred. In addition indicators of quantum chaos are being studied. These measure how far a system is from integrability and have been proposed to be tightly linked to eigenstate thermalization.