Incoherent tunneling excited states

The transition from coherent to incoherent tunneling is most easily understood by considering the ground state of the system and the first excited state. In the systems under consideration the typical energy difference between the ground state and the first excited state is in the range 40-50 meV. At temperatures below 50 K practically only the ground state is populated (nj, < 10-5 d only a small... 

Note that, since the coherences of the reduced density matrix vanish on long timescales, the coupling to the STM electric field disappears from the equations of motion and only the incoherently driven evolution of the system mediated by the non-adiabatic couplings remains. This is consistent with the picture of an ensemble of localized states in quasi-thermal equilibrium that diffuses towards other local minima. Since the zeroth-order vibrational states are non-local by constmction, both tunneling and above-threshold excitations are seamlessly included in this treatment. 

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