Exact asymptotics for dissipative quantum tunneling

We analyze a simple model of quantum tunneling in a dimerized lattice characteristic of those in which solid-state excimers have been observed. The model we pose proves to be exactly diagonalizable, allowing the time dependence of tunneling within a molecular pair to be determined to quadrature. A straightforward analysis allows the short- and long-time asymptotic behavior to be specified exactly. Oscillatory decay of a localized initial distribution toward a delocalized final distribution is found at both finite and zero temperature. The decay envelope at finite temperatures is eventually exponential, while that found at zero temperature is eventually power law. Localization is not found.