Lattice two-body problem with arbitrary finite-range interactions
Year: 2010
Type: article
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.
Source: Physical Review A
Author: Manuel Valiente
Institution: FORTH Institute of Electronic Structure and Laser
Language: English
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1998477567