Interactions of Collective Excitations with Vortices in Superfluid Systems

TL;DR

This paper explores how collective excitations interact with vortices in superfluid systems like helium-4 and superconductors, deriving scattering cross-sections and classical equations of motion for different wavelength regimes.

Contribution

It provides a unified theoretical framework for understanding excitation-vortex interactions across different superfluid systems, including explicit formulas for scattering cross-sections.

Findings

Derived a general formula for scattering cross-section in the long-wavelength limit

Obtained classical equations of motion at short wavelengths

Applied the theory to superfluid helium-4 and superconductors

Abstract

We investigate the interactions of collective excitations with vortices in superfluid systems, including $~^4$He and superconductors. The dynamical equations are obtained by the aid of the many-body wavefunction and the density-density correlation function. The scattering cross-section of collective excitations with a vortex is calculated in the Born approximation (valid at long wavelengths), and is expressed in terms of the collective excitation spectrum $ \omega (q) $ by the simple and general formula $ \sigma = \frac{\pi}{2} \frac{q}{[\omega'(q)]^2} \cot^2\frac{\theta}{2} $, where $ q $ is the wave number of the excitation, and $\theta $ is the scattering angle. At short wave lengths, the classical equations of motion are derived.