Prethermalization for Deformed Wigner Matrices.

We prove that a class of weakly perturbed Hamiltonians of the form , with being a Wigner matrix, exhibits . That is, the time evolution generated by relaxes to its ultimate thermal state via an intermediate prethermal state with a lifetime of order . Moreover, we obtain a general relaxation formula, expressing the perturbed dynamics via the unperturbed dynamics and the ultimate thermal state. The proof relies on a two-resolvent law for the deformed Wigner matrix .