Topological solutions in the Maxwell-Chern-Simons model with anomalous magnetic moment

Youngae Lee

doi:10.3934/dcds.2018053

Article Contents

2018, Volume 38, Issue 3: 1293-1314. Doi: 10.3934/dcds.2018053

This issue Previous Article Weak regularization by stochastic drift : Result and counter example Next Article Long-time behaviour of a radially symmetric fluid-shell interaction system

Topological solutions in the Maxwell-Chern-Simons model with anomalous magnetic moment

Youngae Lee

National Institute for Mathematical Sciences, Academic exchanges, KT Daeduk 2 Research Center, 70 Yuseong-daero 1689 beon-gil, Yuseong-gu, Daejeon, 34047, Republic of Korea

Received: March 2017

Revised: October 2017

Published: July 2018

Abstract Full Text(HTML) Related Papers Cited by

Abstract

In this paper, we consider a Maxwell-Chern-Simons model with anomalous magnetic moment. Our main goal is to show the existence and uniqueness of topological type solutions to this problem on a flat two torus for any configuration of vortex points. Moreover, we also discuss about the stability of topological solutions.

Keywords:

Mathematics Subject Classification: 35J60.

Citation:

Full Text(HTML)

Related Papers

Cited by

References

	A. A. Abrikosov , On the magnetic properties of superconductors of the second group, Soviet Phys. JETP, 5 (1957) , 1174-1182.
	D. Bartolucci , Y. Lee , C. S. Lin and M. Onodera , Asymptotic analysis of solutions to a gauged $O(3)$ sigma model, Ann. Inst. H. Poincaré Anal. Non Linéaire, 32 (2015) , 651-685. doi: 10.1016/j.anihpc.2014.03.001.
	F. S. A. Cavalcante , M. S. Cunha and C. A. S. Almeida , Vortices in a nonminimal Maxwell-Chern-Simons O(3) sigma model, Phys. Lett. B, 475 (2000) , 315-323. doi: 10.1016/S0370-2693(00)00077-0.
	D. Chae and O. Y. Imanuvilov , The existence of non-topological multivortex solutions in the relativistic self-dual Chern-Simons theory, Commun. Math. Phys., 215 (2000) , 119-142. doi: 10.1007/s002200000302.
	D. Chae and O. Y. Imanuvilov , Non-topological multivortex solutions to the self-dual Maxwell-Chern-Simons-Higgs systems, J. Funct. Anal., 196 (2002) , 87-118. doi: 10.1006/jfan.2002.3988.
	H. Chan , C. C. Fu and C. S. Lin , Non-topological multivortex solutions to the self-dual Chern-Simons-Higgs equation, Commun. Math. Phys., 231 (2002) , 189-221. doi: 10.1007/s00220-002-0691-6.
	X. Chen , S. Hastings , J. McLeod and Y. Yang , A nonlinear elliptic equation arising from gauge field theory and cosmology, Proc. R. Soc. Lond. A, 446 (1994) , 453-478. doi: 10.1098/rspa.1994.0115.
	K. Choe , Self-dual non-topological vortices in a Maxwell-Chern-Simons model with non-minimal coupling, Lett. Math. Phys., 87 (2009) , 47-65. doi: 10.1007/s11005-009-0294-7.
	K. Choe, Uniqueness of the topological multivortex solution in the selfdual Chern-Simons theory, J. Math. Phys., 46 (2005), 012305, 21pp.
	K. Choe , J. Han , Y. Lee and C. S. Lin , Bubbling solutions for the Chern-Simons gauged $O(3)$ sigma model on a torus, Calc. Var. Partial Differential Equations, 54 (2015) , 1275-1329. doi: 10.1007/s00526-015-0825-2.
	H. R. Christiansen , M. S. Cunha , J. A. Helayël-Neto , L. R. U. Manssur and A. L. M. A. Nogueira , $N =2$-Maxwell-Chern-Simons model with anomalous magnetic moment coupling via dimensional reduction, Int. J. Mod. Phys. A, 14 (1999) , 147-159. doi: 10.1142/S0217751X99000075.
	H. R. Christiansen , M. S. Cunha , J. A. Helayël-Neto , L. R. U. Manssur and A. L. M. A. Nogueira , Self-dual vortices in a Maxwell-Chern-Simons model with non-minimal coupling, Int. J. Mod. Phys. A, 14 (1999) , 1721-1735. doi: 10.1142/S0217751X99000877.
	W. Ding , J. Jost , J. Li , X. Peng and G. Wang , Self duality equations for Ginzburg-Landau and Seiberg-Witten type functionals with 6th order potentials, Comm. Math. Phys., 217 (2001) , 383-407. doi: 10.1007/s002200100377.
	G. Dunne, Self-duality and Chern-Simons theories. Lecture Notes in Physics, Springer, Heidelberg, 1995.
	Y. W. Fan , Y. Lee and C. S. Lin , Mixed type solutions of the SU(3) models on a torus, Comm. Math. Phys., 343 (2016) , 233-271. doi: 10.1007/s00220-015-2532-4.
	D. Gilbarg and N. Trudinger, Elliptic partial differential equations of second order, Classics in Mathematics, Springer-Verlag, Berlin, 2001.
	J. Han and H. Huh , Self-dual vortices in a Maxwell-Chern-Simons model with non-minimal coupling, Lett. Math. Phys., 82 (2007) , 9-24. doi: 10.1007/s11005-007-0193-8.
	J. Hong , P. Kim and P. Pac , Multivortex solutions of the abelian Chern-Simons-Higgs theory, Phys. Rev. Lett., 64 (1990) , 2230-2233. doi: 10.1103/PhysRevLett.64.2230.
	G.'t Hooft , A property of electric and magnetic flux in nonabelian gauge theories, Nucl. Phys. B, 153 (1979) , 141-160. doi: 10.1016/0550-3213(79)90595-9.
	R. Jackiw and E. Weinberg , Self-dual Chern-Simons vortices, Phys. Rev. Lett., 64 (1990) , 2234-2237. doi: 10.1103/PhysRevLett.64.2234.
	A. Jaffe and C. H. Taubes, Vortices and Monopoles, Birkh$ä$user, Boston, 1980.
	T. Lee and H. Min , Bogomol'nyi equations for solitons in Maxwell-Chern-Simons gauge theories with the magnetic moment interaction term, Phys. Rev. D, 50 (1994) , 7738-7741. doi: 10.1103/PhysRevD.50.7738.
	C. Lee , K. Lee and H. Min , Self-dual Maxwell-Chern-Simons solitons, Phys. Lett. B, 252 (1990) , 79-83. doi: 10.1016/0370-2693(90)91084-O.
	B. H. Lee , C. Lee and H. Min , Supersymmetric Chern-Simons vortex systems and fermion zero modes, Phys. Rev. D, 45 (1992) , 4588-4599. doi: 10.1103/PhysRevD.45.4588.
	P. Navrátil , $N =2$ supersymmetry in a Chern-Simons system with the magnetic moment interaction, Phys. Lett. B, 365 (1996) , 119-124. doi: 10.1016/0370-2693(95)01254-0.
	H. B. Nielsen and P. Olesen , Vortex-line models for dual-strings, Nucl. Phys. B, 61 (1973) , 45-61.
	S. Paul and A. Khare , Charged vortices in an abelian Higgs model with Chern-Simons term, Phys. Lett. B, 174 (1986) , 420-422. doi: 10.1016/0370-2693(86)91028-2.
	J. Spruck and Y. Yang , The existence of non-topological solitons in the self-dual Chern-Simons theory, Commun. Math. Phys., 149 (1992) , 361-376. doi: 10.1007/BF02097630.
	G. Tarantello , Selfdual Maxwell-Chern-Simons vortices, Milan J. Math., 72 (2004) , 29-80. doi: 10.1007/s00032-004-0030-9.
	G. Tarantello , Uniqueness of self-dual periodic Chern-Simons vortices of topological-type, Calc. Var. P.D.E., 29 (2007) , 191-217. doi: 10.1007/s00526-006-0062-9.
	G. Tarantello, Selfdual gauge field vortices an analytical approach, In Progress in Nonlinear Differential Equations and Their Applications. Birkhäuser, Boston, 2008.
	M. Torres , Bogomol'nyi limit for nontopological solitons in a Chern-Simons model with anomalous magnetic moment, Phys. Rev. D, 46 (1992) , 2295-2298. doi: 10.1103/PhysRevD.46.R2295.
	Y. Yang, Solitons in Field Theory and Nonlinear Analysis, Springer Monograph in Mathematics. Springer, New York, 2001.