Lattice two-body problem with arbitrary finite-range interactions

Manuel Valiente Cifuentes

Research output: Contribution to journalArticle

29 Citations (Scopus)

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.

Original languageEnglish
Article number042102
Number of pages6
JournalPhysical Review A
Volume81
Issue number4
DOIs
Publication statusPublished - Apr 2010

Keywords

  • OPTICAL LATTICES
  • TRANSITION
  • SUPERFLUID
  • INSULATOR
  • PHYSICS
  • GASES
  • ATOMS

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