Low-energy vortex dynamics in the self-dual Chern-Simons-Higgs model
- 作者：Richard J. Strilka af.doc.mil@gmail.com
- 关键词：Chern&ndash ; Simons&ndash ; Higgs ; Vortex scattering ; Spectral methods ; Numerical simulation
- 刊名：Communications in Nonlinear Science and Numerical Simulation
- 出版年：2012
- 期刊代码：89_10075704
- 类别：ph
- 出版时间：October, 2012
- 卷：17
- 期：10
- 页码：3811-3823
- 文件大小：856 K
摘要
The relativistic Chern-Simons-Higgs theory finds application in anyonic superconductivity and contains topological vortices whose dynamics are poorly understood. The gauge fields are defined by a set of nonlinear constraint equations that can be accurately solved with effective Green鈥檚 functions, spectral methods, and a discretization scheme using lattice gauge techniques. Simulations show that low-energy two-vortex interactions are elastic with final scattering angles sensitive to vortex velocity; furthermore, vortex pairs form rotating breather states for certain impact parameters. In this study, a function that reproduces scattering angles in the adiabatic limit for nontangential collisions is presented. Simulation results are discussed in the context of analytical methods that extract vortex dynamics from low-energy effective Lagrangians, and a numerical method to calculate the effective Lagrangian is suggested. The numerical techniques used can be applied to the study of other Chern-Simon theories.