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We present an elementary, general, and semi-quantitative description ofrelaxation to gaussian and generalized Gibbs states in lattice models offermions or bosons with quadratic hamiltonians. Our arguments apply toarbitrary initial states that satisfy a mild condition on clustering ofcorrelations. We also show that similar arguments can be used to understandrelaxation (or its absence) in systems with time-dependent quadratichamiltonians, and provide a semi-quantitative description of relaxation inquadratic periodically driven (Floquet) systems.

Relaxation to gaussian and generalized Gibbs states in systems of particles with quadratic hamiltonians