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Solving the fully coupled time-dependent Maxwell-Dirac system : a second-order accurate numerical scheme

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Abstract
Owing to their increased carrier velocities, Dirac materials have become a promising option for the integration into nanoelectronics. However, without the aid of simulation software that is able to accurately describe the behavior of these materials, the fabrication of novel devices is extremely challenging. In this work, we present a second-order accurate, multiphysics solution method for the pertinent time-dependent Maxwell-Dirac equations. The numerical stencils of the separate equations are presented, leading to a novel stability criterion for the minimally coupled Dirac equation. Afterwards, the second-order accuracy is demonstrated via a numerical example, in which a Dirac particle is represented as a wave packet.
Keywords
Nanoelectronics, computational electromagnetics, relativistic quantum, mechanics, finite-difference time-domain methods, numerical stability

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Citation

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MLA
Van den Broeck, Jul, et al. “Solving the Fully Coupled Time-Dependent Maxwell-Dirac System : A Second-Order Accurate Numerical Scheme.” 2023 IEEE MTT-S INTERNATIONAL CONFERENCE ON NUMERICAL ELECTROMAGNETIC AND MULTIPHYSICS MODELING AND OPTIMIZATION, NEMO, IEEE, 2023, pp. 91–94, doi:10.1109/nemo56117.2023.10202442.
APA
Van den Broeck, J., Vanderstraeten, E., Decleer, P., & Vande Ginste, D. (2023). Solving the fully coupled time-dependent Maxwell-Dirac system : a second-order accurate numerical scheme. 2023 IEEE MTT-S INTERNATIONAL CONFERENCE ON NUMERICAL ELECTROMAGNETIC AND MULTIPHYSICS MODELING AND OPTIMIZATION, NEMO, 91–94. https://doi.org/10.1109/nemo56117.2023.10202442
Chicago author-date
Van den Broeck, Jul, Emile Vanderstraeten, Pieter Decleer, and Dries Vande Ginste. 2023. “Solving the Fully Coupled Time-Dependent Maxwell-Dirac System : A Second-Order Accurate Numerical Scheme.” In 2023 IEEE MTT-S INTERNATIONAL CONFERENCE ON NUMERICAL ELECTROMAGNETIC AND MULTIPHYSICS MODELING AND OPTIMIZATION, NEMO, 91–94. IEEE. https://doi.org/10.1109/nemo56117.2023.10202442.
Chicago author-date (all authors)
Van den Broeck, Jul, Emile Vanderstraeten, Pieter Decleer, and Dries Vande Ginste. 2023. “Solving the Fully Coupled Time-Dependent Maxwell-Dirac System : A Second-Order Accurate Numerical Scheme.” In 2023 IEEE MTT-S INTERNATIONAL CONFERENCE ON NUMERICAL ELECTROMAGNETIC AND MULTIPHYSICS MODELING AND OPTIMIZATION, NEMO, 91–94. IEEE. doi:10.1109/nemo56117.2023.10202442.
Vancouver
1.
Van den Broeck J, Vanderstraeten E, Decleer P, Vande Ginste D. Solving the fully coupled time-dependent Maxwell-Dirac system : a second-order accurate numerical scheme. In: 2023 IEEE MTT-S INTERNATIONAL CONFERENCE ON NUMERICAL ELECTROMAGNETIC AND MULTIPHYSICS MODELING AND OPTIMIZATION, NEMO. IEEE; 2023. p. 91–4.
IEEE
[1]
J. Van den Broeck, E. Vanderstraeten, P. Decleer, and D. Vande Ginste, “Solving the fully coupled time-dependent Maxwell-Dirac system : a second-order accurate numerical scheme,” in 2023 IEEE MTT-S INTERNATIONAL CONFERENCE ON NUMERICAL ELECTROMAGNETIC AND MULTIPHYSICS MODELING AND OPTIMIZATION, NEMO, Winnipeg, Canada, 2023, pp. 91–94.
@inproceedings{01HA4DSCG3GQBN7HR5H6N2HTHR,
  abstract     = {{Owing to their increased carrier velocities, Dirac materials have become a promising option for the integration into nanoelectronics. However, without the aid of simulation software that is able to accurately describe the behavior of these materials, the fabrication of novel devices is extremely challenging. In this work, we present a second-order accurate, multiphysics solution method for the pertinent time-dependent Maxwell-Dirac equations. The numerical stencils of the separate equations are presented, leading to a novel stability criterion for the minimally coupled Dirac equation. Afterwards, the second-order accuracy is demonstrated via a numerical example, in which a Dirac particle is represented as a wave packet.}},
  author       = {{Van den Broeck, Jul and Vanderstraeten, Emile and Decleer, Pieter and Vande Ginste, Dries}},
  booktitle    = {{2023 IEEE MTT-S INTERNATIONAL CONFERENCE ON NUMERICAL ELECTROMAGNETIC AND MULTIPHYSICS MODELING AND OPTIMIZATION, NEMO}},
  isbn         = {{9798350347401}},
  issn         = {{2575-4769}},
  keywords     = {{Nanoelectronics,computational electromagnetics,relativistic quantum,mechanics,finite-difference time-domain methods,numerical stability}},
  language     = {{eng}},
  location     = {{Winnipeg, Canada}},
  pages        = {{91--94}},
  publisher    = {{IEEE}},
  title        = {{Solving the fully coupled time-dependent Maxwell-Dirac system : a second-order accurate numerical scheme}},
  url          = {{http://doi.org/10.1109/nemo56117.2023.10202442}},
  year         = {{2023}},
}

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