The Holstein model describes the motion of a tight-binding tracer particle interacting with a field of quantum harmonic oscillators. We consider this model with an on-site random potential. Provided the hopping amplitude for the particle is small, we prove localization for matrix elements of the resolvent, in particle position and in the field Fock space. These bounds imply a form of dynamical localization for the particle position that leaves open the possibility of resonant tunneling in Fock space between equivalent field configurations.
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