A fourth-order compact time-splitting method for the Dirac equation with time-dependent potentials. (English) Zbl 07506534
Summary: 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 (\(S_{4\mathrm{c}}\)). 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.
MSC:
| 65Mxx | Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems |
| 35Qxx | Partial differential equations of mathematical physics and other areas of application |
| 81Qxx | General mathematical topics and methods in quantum theory |
Keywords:
Dirac equation; time-dependent potentials; fourth-order compact time-splitting; time-orderingSoftware:
Dirac++References:
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