There is a renewed interest in the derivation of statistical mechanics from the dynamics of closed quantum systems. A central part of this program is to understand how far-from-equilibrium closed quantum system can behave as if relaxing to a stable equilibrium. Equilibration dynamics has been traditionally studied with a focus on the so-called quenches of large-scale many-body systems. Alternatively, we consider here the equilibration of a molecular model system describing the double proton transfer reaction in porphine. Using numerical simulations, we show that equilibration in this context indeed takes place and does so very rapidly ($sim !! 200$fs) for initial states induced by pump-dump laser pulse control with energies well above the synchronous tunneling barrier.
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