Universality of Low-Energy Scattering in 2+1 Dimensions: The Non Symmetric Case

TL;DR

This paper proves that for a broad class of potentials in two dimensions, the low-energy scattering amplitude is universal and follows a specific logarithmic behavior, except when zero-energy bound states are present.

Contribution

It establishes the universality of low-energy scattering in 2+1 dimensions for non-symmetric potentials, extending previous symmetric cases.

Findings

Scattering amplitude behaves as 1/log k at low energies.

Universality holds except when zero-energy bound states exist.

Includes rotationally symmetric potentials as a special case.

Abstract

For a very large class of potentials, $V(\vec{x})$, $\vec{x}\in R^2$, we prove the universality of the low energy scattering amplitude, $f(\vec{k}', \vec{k})$. The result is $f=\sqrt{\frac{\pi}{2}}\{1/log k)+O(1/(log k)^2)$. The only exceptions occur if $V$ happens to have a zero energy bound state. Our new result includes as a special subclass the case of rotationally symmetric potentials, $V(|\vec{x}|)$.