TIME-DEPENDENT TOPOLOGICAL CHERN-SIMONS SOLITONS IN EXTERNAL MAGNETIC-FIELD

We present a new method to construct time-dependent periodic solutions using static solutions in the (2 + 1)-dimensional Chern-Simons gauge theory with external magnetic field B. We apply this method to vortex solitons, which may be topological or nontopological; topological vortices are identified with Laughlin's quasiparticles or quasiholes in the fractional quantum Hall effect. Our periodic solution represents that vortex solitons make cyclotron motion. After applying the Bohr-Sommerfeld semiclassical quantization, it is found that the quantum soliton is in the Landau level.