Europhys. Lett.
Volume 71, Number 3, August 2005
Page(s) 352 - 358
Section General
Published online 14 July 2005
Europhys. Lett., 71 (3), pp. 352-358 (2005)
DOI: 10.1209/epl/i2005-10102-7

Anomalous tunneling of bound pairs in crystal lattices

V. L. Bulatov1 and P. E. Kornilovitch2

1  2970 N. W. Christine St, Corvallis, OR 97330, USA
2  2876 N. W. Audene Drive, Corvallis, OR 97330, USA

received 13 April 2005; accepted in final form 7 June 2005
published online 14 July 2005

A novel non-perturbative 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 the momentum values close to $\pm\pi$ the 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.

03.65.Ge - Solutions of wave equations: bound states.
03.65.Nk - Scattering theory.
71.10.Li - Excited states and pairing interactions in model systems.

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