A fourth-order compact time-splitting method for the Dirac equation with time-dependent potentials

Abstract

In this paper, we present an approach to deal with the dynamics of the Dirac equation with time-dependent electromagnetic potentials using the fourth-order compact time-splitting method ($S_{\text{4c}}$). To this purpose, the time-ordering technique for time-dependent Hamiltonians is introduced, so that the influence of the time-dependence could be limited to certain steps which are easy to treat. Actually, in the case of the Dirac equation, it turns out that only those steps involving potentials need to be amended, and the scheme remains efficient, accurate, as well as easy to implement. Numerical examples in 1D and 2D are given to validate the scheme.

arXiv comment24pages, 8 figures

References in corpus (17)

• Electric Field Effect in Atomically Thin Carbon Films
• The electronic properties of graphene
• Two-Dimensional Gas of Massless Dirac Fermions in Graphene
• Discovery (theoretical prediction and experimental observation) of a large-gap topological-insulator class with spin-polarized single-Dirac-cone on the surface
• Fractional quantum Hall effect and insulating phase of Dirac electrons in graphene
• Non-Abelian optical lattices: Anomalous quantum Hall effect and Dirac Fermions
• Gradient Symplectic Algorithms for Solving the Schroedinger Equation with Time-Dependent Potentials
• Dirac Equation For Cold Atoms In Artificial Curved Spacetimes
• Wave packets in Honeycomb Structures and Two-Dimensional Dirac Equations
• Numerical Solution of the Time-Dependent Dirac Equation in Coordinate Space without Fermion-Doubling
• A time-splitting spectral scheme for the Maxwell-Dirac system
• Fourth Order Gradient Symplectic Integrator Methods for Solving the Time-Dependent Schrödinger Equation
• Resonantly enhanced pair production in a simple diatomic model
• Error estimates of numerical methods for the nonlinear Dirac equation in the nonrelativistic limit regime
• Numerical methods and comparison for the Dirac equation in the nonrelativistic limit regime
• A uniformly accurate (UA) multiscale time integrator pseudospectral method for the Dirac equation in the nonrelativistic limit regime
• Staggered grid leap-frog scheme for the (2+1)D Dirac equation