Generation of a scalar vortex in a rotational frame

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 an external uniform magnetic field occupying the whole volume of the uniformly rotating cylindrical system of finite radius <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mi>R</a:mi> </a:math> with a Dirichlet boundary condition imposed on it. In addition to continuing this study, we consider the field formed by a flux tube of small radius. We find numerical solutions of the Gross-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.