Asymptotic Interactions of Critically Coupled Vortices |
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Authors: | NS Manton JM Speight |
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Institution: | (1) Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, England. E-mail: N.S.Manton@damtp.cam.ac.uk, GB;(2) Department of Pure Mathematics, University of Leeds, Leeds LS2 9JT, England. E-mail: J.M.Speight@leeds.ac.uk, GB |
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Abstract: | At critical coupling, the interactions of Ginzburg-Landau vortices are determined by the metric on the moduli space of static
solutions. Here, a formula for the asymptotic metric for two well separated vortices is obtained, which depends on a modified
Bessel function. A straightforward extension gives the metric for N vortices. The asymptotic metric is also shown to follow from a physical model, where each vortex is treated as a point-like
particle carrying a scalar charge and a magnetic dipole moment of the same magnitude. The geodesic motion of two well separated
vortices is investigated, and the asymptotic dependence of the scattering angle on the impact parameter is determined. Formulae
for the asymptotic Ricci and scalar curvatures of the N-vortex moduli space are also obtained.
Received: 25 June 2002 / Accepted: 7 February 2003
Published online: 17 April 2003
Communicated by A. Kupiainen |
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Keywords: | |
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