Quantum Statistical Mechanics of Dissolving Vortices

Abstract

The quantum partition function for dissolving Abelian Higgs vortices is calculated explicitly, using spectral data for the Beltrami Laplacian on the $N$-vortex moduli space ${\mathbb{CP}}^N$ with a scaled Fubini--Study metric. From the partition function, the pressure of the vortex gas is derived. There are three asymptotic regimes -- High, Intermediate and Low Temperature. The phase crossover from Intermediate to Low Temperature is modelled by a Bessel function. In the Low Temperature regime the free energy is not extensive but is proportional to $N^2$.

arXiv comment12 pages, 7 figures

References in corpus (9)

• Bose-Einstein Condensation on the Surface of a Sphere
• Volume of Vortex Moduli Spaces
• On the L^2-metric of vortex moduli spaces
• The dynamics of vortices on S^2 near the Bradlow limit
• Scattering theory and equation of state of a spherical two-dimensional Bose gas
• The Virial Expansion of a Dilute Bose Gas in Two Dimensions
• Thermodynamics of the Noninteracting Bose Gas in a Two-Dimensional Box
• Quantum Statistical Mechanics of Vortices
• The geometry of the space of vortices on a two-sphere in the Bradlow limit