Quantum dynamics of two-dimensional vortex pairs with arbitrary total vorticity

TL;DR

This paper explores the quantum behavior of two-dimensional vortex pairs with arbitrary vorticity using various algebraic frameworks, revealing insights into their spectra, Berry phase, and scattering properties.

Contribution

It introduces a comprehensive algebraic approach to analyze vortex pair quantum dynamics, including spectrum construction, Berry phase study, and scattering quantization.

Findings

Spectrum constructed within e(2)-like symmetry

Berry phase analyzed via su(1,1) realization

Quantization of scattering from obstacles achieved

Abstract

Quantum dynamics of a vortex pair is investigated by considering the pair Hamiltonian within various, unequivalent algebraic frameworks. First the vortex pair spectrum is constructed in the standard contest of the e(2)-like dynamical symmetry and its degeneracy is thoroughly examined. Then the Berry phase phenomenon is studied through an su(1,1) realization of the pair Hamiltonian when its parameters are assumed to be time-dependent, whereas the Feynman- Onsager quantization conditions are recovered by means of symmetry arguments within a third approach based on a magneticlike description of the vortex pair. Finally, it is shown how recasting the dynamical algebra in terms of two-particle realization of both su(2) and su(1,1) provides the correct approach for the quantization of the model Hamiltonian accounting for the pair scattering from a disklike obstacle.