Quasi-one-dimensional scattering in a discrete model

TL;DR

This paper investigates quasi-one-dimensional scattering of particles on a discrete lattice, revealing multiple confinement-induced resonances due to non-separability of coordinates, and characterizes effective interactions in these systems.

Contribution

It introduces an exact ansatz for quasi-one-dimensional states on a lattice and uncovers multiple confinement-induced resonances in two-particle scattering.

Findings

Multiple confinement-induced resonances due to non-separability.

Characterization of effective one-dimensional interactions.

Comparison with single-pole approximation models.

Abstract

We study quasi-one-dimensional scattering of one and two particles with short-range interactions on a discrete lattice model in two dimensions. One of the directions is tightly confined by an arbitrary trapping potential. We obtain the collisional properties of these systems both at finite and zero Bloch quasi- momenta, considering as well finite sizes and transversal traps that support a continuum of states. This is made straightforward by using the exact ansatz for the quasi-one-dimensional states from the beginning. In the more interesting case of genuine two-particle scattering, we find that more than one confinement-induced resonance appear due to the non-separability of the center-of-mass and relative coordinates on the lattice. This is done by solving its corresponding Lippmann- Schwinger-like equation. We characterize the effective one-dimensional interaction and compare it with a model that includes only the effect of the dominant, broadest resonance, which amounts to a single-pole approximation for the interaction coupling constant.