Asymptotic limit for condensate solutions in the Abelian Chern-Simons Higgs model

Han, Jongmin

doi:10.1090/S0002-9939-02-06737-0

Asymptotic limit for condensate solutions in the Abelian Chern-Simons Higgs model
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by Jongmin Han

Proc. Amer. Math. Soc. 131 (2003), 1839-1845

DOI: https://doi.org/10.1090/S0002-9939-02-06737-0

Published electronically: October 1, 2002

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Abstract:

In this paper we show that the maximal solutions $(\phi ^\epsilon , A^\epsilon )$ in the Abelian Chern-Simons Higgs model on a ’t Hooft type periodic domain converges to $(\phi _*,A_*)$ and $\phi _*$ is a harmonic map. We also study asymptotic behaviors of the energy density.

References

Fabrice Bethuel, Haïm Brezis, and Frédéric Hélein, Ginzburg-Landau vortices, Progress in Nonlinear Differential Equations and their Applications, vol. 13, Birkhäuser Boston, Inc., Boston, MA, 1994. MR 1269538, DOI 10.1007/978-1-4612-0287-5
Luis A. Caffarelli and Yi Song Yang, Vortex condensation in the Chern-Simons Higgs model: an existence theorem, Comm. Math. Phys. 168 (1995), no. 2, 321–336. MR 1324400, DOI 10.1007/BF02101552
J. Han, Asymptotics for the vortex condensate solutions in Chern-Simons-Higgs theory, Asymptotic Anal. 28 (2001), 31-48.
Jooyoo Hong, Yoonbai Kim, and Pong Youl Pac, Multivortex solutions of the abelian Chern-Simons-Higgs theory, Phys. Rev. Lett. 64 (1990), no. 19, 2230–2233. MR 1050529, DOI 10.1103/PhysRevLett.64.2230
R. Jackiw and Erick J. Weinberg, Self-dual Chern-Simons vortices, Phys. Rev. Lett. 64 (1990), no. 19, 2234–2237. MR 1050530, DOI 10.1103/PhysRevLett.64.2234
Arthur Jaffe and Clifford Taubes, Vortices and monopoles, Progress in Physics, vol. 2, Birkhäuser, Boston, Mass., 1980. Structure of static gauge theories. MR 614447
Gabriella Tarantello, Multiple condensate solutions for the Chern-Simons-Higgs theory, J. Math. Phys. 37 (1996), no. 8, 3769–3796. MR 1400816, DOI 10.1063/1.531601