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 language | English |
---|---|
Article number | 042102 |
Number of pages | 6 |
Journal | Physical Review A |
Volume | 81 |
Issue number | 4 |
DOIs | |
Publication status | Published - Apr 2010 |
Keywords
- OPTICAL LATTICES
- TRANSITION
- SUPERFLUID
- INSULATOR
- PHYSICS
- GASES
- ATOMS