Generation of a scalar vortex in a rotational frame

TL;DR

This paper investigates the generation of scalar vortices in a rotating frame with magnetic fields, analyzing flux tube configurations and their energy properties through numerical and analytical methods.

Contribution

It introduces a detailed study of scalar field condensation in rotating systems with flux tubes, extending previous uniform magnetic field analyses with new numerical solutions.

Findings

Flux tube configurations have lower condensate energy than uniform magnetic fields.

Numerical solutions align with analytical approximations for critical frequencies.

Condensate properties depend on flux tube radius and rotation frequency.

Abstract

We consider generation from the vacuum of a scalar charged field in a rigidly rotating frame. Adding an external magnetic field opens the way to Bose condensation of the field. This phenomenon has been studied for external uniform magnetic field occupying the whole volume of the uniformly rotating cylindrical system of finite radius $R$ with a Dirichlet boundary condition imposed on it. Besides continuing this study, we consider the field formed by a flux tube of small radius. We find numerical solutions of the Ginzburg-Pitaevskii equation for the charged scalar field, the critical rotation frequencies, the mean radii and the condensate energies, and compare them with those found in a linearization scheme and with approximate analytical solutions. We show that for the same input parameters the energy of the condensate in the case of the flux tube is lower than in the case of uniform magnetic field in the whole cylinder.