Lattice two-body problem with arbitrary finite-range interactions

Valiente Cifuentes, Manuel

Publication:
Lattice two-body problem with arbitrary finite-range interactions

dc.contributor.author	Valiente Cifuentes, Manuel
dc.contributor.department	Física
dc.date.accessioned	2025-01-28T09:11:47Z
dc.date.available	2025-01-28T09:11:47Z
dc.date.issued	2010-04-07
dc.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
dc.description.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.
dc.format	application/pdf	es
dc.identifier.citation	Physical Review A, Vol. 81, 042102 (2010)
dc.identifier.doi	https://doi.org/10.1103/PhysRevA.81.042102
dc.identifier.issn	Print: 2469-9926
dc.identifier.issn	Electronic: 2469-9934
dc.identifier.uri	http://hdl.handle.net/10201/149431
dc.language	eng	es
dc.publisher	American Physical Society
dc.relation	EC Marie Curie Network EMALI	es
dc.relation.publisherversion	https://journals.aps.org/pra/abstract/10.1103/PhysRevA.81.042102
dc.rights	info:eu-repo/semantics/openAccess	es
dc.rights	Attribution-NonCommercial-NoDerivatives 4.0 Internacional	*
dc.rights.uri	http://creativecommons.org/licenses/by-nc-nd/4.0/	*
dc.subject.other	CDU::5 - Ciencias puras y naturales	es
dc.title	Lattice two-body problem with arbitrary finite-range interactions	es
dc.type	info:eu-repo/semantics/article	es
dspace.entity.type	Publication	es