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 - <p style="text-align: justify;">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.</p>