Transfer of BECs through discrete breathers in an optical lattice

We study the stability of a stationary discrete breather (DB) on a nonlinear trimer in the framework of the discrete nonlinear Schr\"odinger equation (DNLS). In previous theoretical investigations of the dynamics of Bose-Einstein condensates in leaking optical lattices, collisions between a DB and a lattice excitation, e.g. a moving breather (MB) or phonon, were studied. These collisions lead to the transmission of a fraction of the incident (atomic) norm of the MB through the DB, while the DB can be shifted in the direction of the incident lattice excitation. Here we show that there exists a total energy threshold of the trimer, above which the lattice excitation can trigger the destabilization of the DB and that this is the mechanism leading to the movement of the DB. Furthermore, we give an analytic estimate of upper bound to the norm that is transmitted through the DB. Our analysis explains the results of the earlier numerical studies and may help to clarify functional operations with BECs in optical lattices such as blocking and filtering coherent (atomic) beams.