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TMF, 2017, Volume 191, Number 2, Pages 304–318 (Mi tmf9139)  

Two-particle scattering in a periodic medium

Yu. P. Chuburin

Physical-Technical Institute, Urals Branch, RAS, Izhevsk, Russia

Abstract: 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.

Funding Agency Grant Number
Ural Branch of the Russian Academy of Sciences 15-8-2-12
This research is supported in part by the Urals Branch of the Russian Academy of Sciences (Grant No. 15-8-2-12).


DOI: https://doi.org/10.4213/tmf9139

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English version:
Theoretical and Mathematical Physics, 2017, 191:2, 738–751

Bibliographic databases:

Document Type: Article
Received: 24.12.2015
Revised: 26.05.2016

Citation: Yu. P. Chuburin, “Two-particle scattering in a periodic medium”, TMF, 191:2 (2017), 304–318; Theoret. and Math. Phys., 191:2 (2017), 738–751

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  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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