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

@article{Yin2021AFC,
title={A fourth-order compact time-splitting method for the Dirac equation with time-dependent potentials},
author={Jia Yin},
journal={ArXiv},
year={2021},
volume={abs/2106.09184}
}
• Jia Yin
• Published 2021
• Computer Science, Mathematics
• ArXiv
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 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… Expand
1 Citations

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#### References

SHOWING 1-10 OF 59 REFERENCES
Numerical solution of the time-dependent Dirac equation in coordinate space without fermion-doubling
• Physics, Computer Science
• Comput. Phys. Commun.
• 2012
It is shown that this numerical method for the solution of the time-dependent Dirac equation is free from spurious solutions related to the fermion-doubling problem and that it can be parallelized very efficiently. Expand
An efficient and stable numerical method for the Maxwell-Dirac system
• Mathematics
• 2004
In this paper, we present an explicit, unconditionally stable and accurate numerical method for the Maxwell-Dirac system (MD) and use it to study dynamics of MD. As preparatory steps, we take theExpand
A time-splitting spectral scheme for the Maxwell-Dirac system
• Mathematics, Physics
• 2005
We present a time-splitting spectral scheme for the Maxwell-Dirac system and similar time-splitting methods for the corresponding asymptotic problems in the semi-classical and the non-relativisticExpand
Numerical approach to solve the time-dependent Dirac equation
• Physics
• 1999
We discuss how split-operator techniques may be applied to calculate normalized wave-function solutions to the three-dimensional time-dependent Dirac equation on a space-time lattice grid. ThisExpand
A fourth-order compact time-splitting Fourier pseudospectral method for the Dirac equation
• Mathematics
• 2017
We propose a new fourth-order compact time-splitting ($$S_\mathrm{4c}$$S4c) Fourier pseudospectral method for the Dirac equation by splitting the Dirac equation into two parts together with using theExpand
Gradient symplectic algorithms for solving the Schrödinger equation with time-dependent potentials
• Physics, Chemistry
• 2002
We show that the method of factorizing the evolution operator to fourth order with purely positive coefficients, in conjunction with Suzuki’s method of implementing time-ordering of operators,Expand
Gaussian Beam Methods for the Dirac Equation in the Semi-classical Regime
• Physics, Mathematics
• 2012
The Dirac equation is an important model in relativistic quantum mechanics. In the semi-classical regime $\epsilon\ll1$, even a spatially spectrally accurate time splitting method \cite{HuJi:05}Expand
General solutions of Maxwell-Dirac equations in 1+1-dimensional space-time and a spatially confined solution
The most general solution of the system of massless Maxwell–Dirac equations in 1+1‐dimensional space–time (or classical Schwinger theory) is obtained in terms of four arbitrary functions and oneExpand
Staggered grid leap-frog scheme for the (2+1) D Dirac equation
• Mathematics, Physics
• Comput. Phys. Commun.
• 2014
Several numerical examples, ranging from generic to specific to textured topological insulator surfaces, demonstrate the properties of the scheme which can handle general electromagnetic potential landscapes. Expand
Numerical treatment of the time-dependent Dirac equation in momentum space for atomic processes in relativistic heavy-ion collisions.
• Physics, Medicine
• Physical review. A, Atomic, molecular, and optical physics
• 1996
A numerical method for the solution of the time-dependent Dirac equation to describe atomic processes in relativistic heavy-ion collisions is presented and finds that the enhancement of bound-free pair production as compared to perturbation theory is much smaller than reported previously by others. Expand