Anomalous tunneling of bound pairs in crystal lattices

Abstract

A novel method of solving scattering problems for bound pairs on a lattice is developed. Two different break ups of the hamiltonian are employed to calculate the full Green operator and the wave function of the scattered pair. The calculation converges exponentially in the number of basis states used to represent the non-translation invariant part of the Green operator. The method is general and applicable to a variety of scattering and tunneling problems. As the first application, the problem of pair tunneling through a weak link on a one-dimensional lattice is solved. It is found that at momenta close to πthe pair tunnels much easier than one particle, with the transmission coefficient approaching unity. This anomalously high transmission is a consequence of the existence of a two-body resonant state localized at the weak link.