Mode-mixing in quantum diffusion

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Abstract
The archetype model for phonon-assisted tunnelling is considered. Two alternative approaches are presented that mutually supplement each other. After parity-ordering (Fulton-Gouterman) a reflective ansatz for the ground state is invoked, which establishes mode-mixing and prevents strict mathematical localisation even in the 'ohmic dissipation' coupling situation. This variational argument is supplemented by a rigorous hierarchical calculation, which confirms the statement about localisation. On the other hand, a Green function technique with Hartree-Fock factorisation is employed, which traces the quantum-diffusion problem back to the solution of the oscillatory Fano problem and thus displays all mode-mixing features of the latter. The HF factorisation is justified by a coincidence argument, which interconnects the two approaches. Numerical results are given for the time evolution and an analytical long-time law ( approximately t-1(lnt)-2) is found for T=0. Furthermore, in the strong-coupling limit analytical estimates are given for the transmission time at T=0 and at low temperatures that deviate from the conventional results in several aspects.