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Volume 34, Issue 1
Frozen Gaussian Approximation for the Dirac Equation in Curved Space with Application to Strained Graphene

Lihui Chai, Lorin Emmanuel & Xu Yang

DOI: 10.4208/cicp.OA-2021-0209

Commun. Comput. Phys., 34 (2023), pp. 18-37.

Published online: 2023-08

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  • Abstract

In this paper, we derive the frozen Gaussian approximation (FGA) for computing the solution to the Dirac equation in curved space in the semi-classical regime. The latter equation is used in particular for modeling electronic scattering on strained graphene surfaces. We present numerical comparisons of the Dirac solutions on curved and flat spaces, illustrating the focusing effect of graphene surfaces, as well as qualitative comparisons with a tight-binding model. A CPU-time comparison shows that FGA becomes more efficient than an IMEX pseudospectral method when the semiclassical parameter is small.

  • Keywords

Dirac equation, semi-classical regime, frozen Gaussian approximation, strained graphene.

  • AMS Subject Headings

35Q41, 81Q05, 81Q20, 78A05

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CiCP-34-18, author = {Chai , LihuiEmmanuel , Lorin and Yang , Xu}, title = {Frozen Gaussian Approximation for the Dirac Equation in Curved Space with Application to Strained Graphene}, journal = {Communications in Computational Physics}, year = {2023}, volume = {34}, number = {1}, pages = {18--37}, abstract = {

In this paper, we derive the frozen Gaussian approximation (FGA) for computing the solution to the Dirac equation in curved space in the semi-classical regime. The latter equation is used in particular for modeling electronic scattering on strained graphene surfaces. We present numerical comparisons of the Dirac solutions on curved and flat spaces, illustrating the focusing effect of graphene surfaces, as well as qualitative comparisons with a tight-binding model. A CPU-time comparison shows that FGA becomes more efficient than an IMEX pseudospectral method when the semiclassical parameter is small.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2021-0209}, url = {http://global-sci.org/intro/article_detail/cicp/21878.html} }
TY - JOUR T1 - Frozen Gaussian Approximation for the Dirac Equation in Curved Space with Application to Strained Graphene AU - Chai , Lihui AU - Emmanuel , Lorin AU - Yang , Xu JO - Communications in Computational Physics VL - 1 SP - 18 EP - 37 PY - 2023 DA - 2023/08 SN - 34 DO - http://doi.org/10.4208/cicp.OA-2021-0209 UR - https://global-sci.org/intro/article_detail/cicp/21878.html KW - Dirac equation, semi-classical regime, frozen Gaussian approximation, strained graphene. AB -

In this paper, we derive the frozen Gaussian approximation (FGA) for computing the solution to the Dirac equation in curved space in the semi-classical regime. The latter equation is used in particular for modeling electronic scattering on strained graphene surfaces. We present numerical comparisons of the Dirac solutions on curved and flat spaces, illustrating the focusing effect of graphene surfaces, as well as qualitative comparisons with a tight-binding model. A CPU-time comparison shows that FGA becomes more efficient than an IMEX pseudospectral method when the semiclassical parameter is small.

Chai , LihuiEmmanuel , Lorin and Yang , Xu. (2023). Frozen Gaussian Approximation for the Dirac Equation in Curved Space with Application to Strained Graphene. Communications in Computational Physics. 34 (1). 18-37. doi:10.4208/cicp.OA-2021-0209
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