Scattering Theory for Quantum Hall Anyons in a Saddle Point Potential

TL;DR

This paper develops a numerical scattering theory for two anyons in a saddle-point potential under a magnetic field, revealing how anyon statistics influence two-particle scattering through phase shifts.

Contribution

It introduces a method to solve the two-anyon scattering problem numerically using a generalized lowest Landau level approximation, highlighting the effects of anyon statistics.

Findings

Scattering phase shifts depend on energy and anyon statistics.

Decoupling of center-of-mass and relative coordinates simplifies analysis.

Numerical method enables detailed study of anyon scattering in saddle potentials.

Abstract

We study the theory of scattering of two anyons in the presence of a quadratic saddle-point potential and a perpendicular magnetic field. The scattering problem decouples in the centre-of-mass and the relative coordinates. The scattering theory for the relative coordinate encodes the effects of anyon statistics in the two-particle scattering. This is fully characterized by two energy-dependent scattering phase shifts. We develop a method to solve this scattering problem numerically, using a generalized lowest Landau level approximation.