Doublon relaxation in the bose-hubbard model

The decay of a high-energy double occupancy state, doublon, in a narrow-band lattice requires the creation of a coherent many-particle excitation. This leads to an exponentially long relaxation time of such a state. We show that, if the average occupation number is sufficiently small, the corresponding exponent may be evaluated exactly. To this end we develop the quasiclassical approach to calculation of the high-order tree-level decay amplitudes.