100 citations · 495 across the 18 of their papers we have counts for
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Computation of the Time-Dependent Dirac Equation with Physics-Informed Neural Networks
Emmanuel Lorin, Xu Yang
We propose to compute the time-dependent Dirac equation using physics-informed neural networks (PINNs), a new powerful tool in scientific machine learning avoiding the use of appro…
Numerical quasi-conformal transformations for electron dynamics on strained graphene surfaces
F. Fillion-Gourdeau, E. Lorin, S. MacLean
The dynamics of low energy electrons in general static strained graphene surface is modelled mathematically by the Dirac equation in curved space-time. In Cartesian coordinates, a…
Galerkin method for unsplit 3-D Dirac equation using atomically/kinetically balanced B-spline basis
F. Fillion-Gourdeau, E. Lorin, A. D. Bandrauk
A Galerkin method is developed to solve the time-dependent Dirac equation in prolate spheroidal coordinates for an electron-molecular two-center system. The initial state is evalua…
A Split-Step Numerical Method for the Time-Dependent Dirac Equation in 3-D Axisymmetric Geometry
François Fillion-Gourdeau, Emmanuel Lorin, André D. Bandrauk
A numerical method is developed to solve the time-dependent Dirac equation in cylindrical coordinates for 3-D axisymmetric systems. The time evolution is treated by a splitting sch…
Numerical Solution of the Time-Dependent Dirac Equation in Coordinate Space without Fermion-Doubling
Francois Fillion-Gourdeau, Emmanuel Lorin, Andre D. Bandrauk
The validation and parallel implementation of a numerical method for the solution of the time-dependent Dirac equation is presented. This numerical method is based on a split opera…