Finite difference methods for the one-dimensional Chern-Simons gauged models

Abstract

<p style='text-indent:20px;'>We present finite difference schemes for the one-dimensional Chern-Simons gauged Schrödinger and Dirac equations. We provide two numerical schemes for the Chern-Simons-Schrödinger equations, each of them has its own advantage in total charge preservation and the second-order accuracy. On the other hand, we offer the second-order, total charge-preserving numerical scheme for the Chern-Simons-Dirac equations. We numerically test each method and validate the total charge preserving properties. We also compare the solutions to the Chern-Simons gauged equations with the equations without the gauge effect, illustrating the effect of gauge fields on the dynamics of the matter field.</p>