Two-particle scattering in a periodic medium

Yu. P. Chuburin

Teoretičeskaâ i matematičeskaâ fizika, Tome 191 (2017) no. 2, pp. 304-318

Résumé

We consider a two-particle Schrödinger difference operator with a periodic potential perturbed by an exponentially decaying interaction potential for particles on a one-dimensional lattice. We obtain rigorous results for the two-particle scattering problem in the case of a small interaction and low velocities. Here, as in other quasi-one-dimensional models, small interactions can significantly affect the scattering pattern. In particular, we find the probability that the velocities of two particles in a periodic medium (e.g., they can be ultracold atoms in a one-dimensional optical lattice) change their signs during a collision. This probability increases as the relative velocity decreases and also as the absolute value of the matrix element between single-particle unperturbed Bloch states increases.

Détail

Keywords: Schrödinger difference operator, two-particle scattering problem, periodic potential.

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