Two-particle scattering in a~periodic medium
Teoretičeskaâ i matematičeskaâ fizika, Tome 191 (2017) no. 2, pp. 304-318
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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.
Keywords:
Schrödinger difference operator, two-particle scattering problem, periodic potential.
@article{TMF_2017_191_2_a12,
author = {Yu. P. Chuburin},
title = {Two-particle scattering in a~periodic medium},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {304--318},
publisher = {mathdoc},
volume = {191},
number = {2},
year = {2017},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_2017_191_2_a12/}
}
Yu. P. Chuburin. Two-particle scattering in a~periodic medium. Teoretičeskaâ i matematičeskaâ fizika, Tome 191 (2017) no. 2, pp. 304-318. http://geodesic.mathdoc.fr/item/TMF_2017_191_2_a12/