Publication: Lattice two-body problem with arbitrary finite-range interactions
Authors
Valiente Cifuentes, Manuel
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Publisher
American Physical Society
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DOI
https://doi.org/10.1103/PhysRevA.81.042102
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info:eu-repo/semantics/article
Description
© 2010 American Physical Society. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/ This document is the Published Manuscript, version of a Published Work that appeared in final form in Physical Review A . To access the final edited and published work see https://doi.org/10.1103/PhysRevA.81.042102
Abstract
We study the exact solution of the two-body problem on a tight-binding one-dimensional lattice, with pairwise interaction potentials which have an arbitrary but finite range. We show how to obtain the full spectrum, the bound and scattering states, and the “low-energy” solutions by very efficient and easy-to-implement numerical means. All bound states are proven to be characterized by roots of a polynomial whose degree depends linearly on the range of the potential, and we discuss the connections between the number of bound states and the scattering lengths. “Low-energy” resonances can be located with great precision with the methods we introduce. Further generalizations to include more exotic interactions are also discussed.
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Citation
Physical Review A, Vol. 81, 042102 (2010)
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