Dirac++

FFT-split-operator code for solving the Dirac equation in (2+1) dimensions. The main part of the code presented in this work represents an implementation of the split-operator method for calculating the time-evolution of Dirac wave functions. It allows to study the dynamics of electronic Dirac wave packets under the influence of any number of laser pulses and its interaction with any number of charged ion potentials. The initial wave function can be either a free Gaussian wave packet or an arbitrary discretized spinor function that is loaded from a file provided by the user. The latter option includes Dirac bound state wave functions. The code itself contains the necessary tools for constructing such wave functions for a single-electron ion. With the help of self-adaptive numerical grids, we are able to study the electron dynamics for various problems in (2+1) dimensions at high spatial and temporal resolutions that are otherwise unachievable. Along with the position and momentum space probability density distributions, various physical observables, such as the expectation values of position and momentum, can be recorded in a time-dependent way. The electromagnetic spectrum that is emitted by the evolving particle can also be calculated with this code. Finally, for planning and comparison purposes, both the time-evolution and the emission spectrum can also be treated in an entirely classical relativistic way. Besides the implementation of the above-mentioned algorithms, the program also contains a large C++ class library to model the geometric algebra representation of spinors that we use for representing the Dirac wave function. This is why the code is called “Dirac++”.


References in zbMATH (referenced in 17 articles , 1 standard article )

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  1. Schratz, Katharina; Wang, Yan; Zhao, Xiaofei: Low-regularity integrators for nonlinear Dirac equations (2021)
  2. Antoine, Xavier; Fillion-Gourdeau, François; Lorin, Emmanuel; MacLean, Steve: Pseudospectral computational methods for the time-dependent Dirac equation in static curved spaces (2020)
  3. Antoine, Xavier; Lorin, Emmanuel: A simple pseudospectral method for the computation of the time-dependent Dirac equation with perfectly matched layers (2019)
  4. Chai, Lihui; Lorin, Emmanuel; Yang, Xu: Frozen Gaussian approximation for the Dirac equation in semiclassical regime (2019)
  5. Pötz, Walter; Schreilechner, Magdalena: Single-cone finite difference scheme for the ((2+1))D Dirac von Neumann equation (2017)
  6. Fillion-Gourdeau, F.; Lorin, E.; Bandrauk, A. D.: Galerkin method for unsplit 3-D Dirac equation using atomically/kinetically balanced B-spline basis (2016)
  7. Beerwerth, Randolf; Bauke, Heiko: Krylov subspace methods for the Dirac equation (2015)
  8. Antoine, X.; Lorin, E.; Sater, J.; Fillion-Gourdeau, F.; Bandrauk, A. D.: Absorbing boundary conditions for relativistic quantum mechanics equations (2014)
  9. Dion, C. M.; Hashemloo, A.; Rahali, G.: Program for quantum wave-packet dynamics with time-dependent potentials (2014)
  10. Fillion-Gourdeau, François; Lorin, Emmanuel; Bandrauk, André D.: A split-step numerical method for the time-dependent Dirac equation in 3-D axisymmetric geometry (2014)
  11. Hammer, René; Pötz, Walter; Arnold, Anton: Single-cone real-space finite difference scheme for the time-dependent Dirac equation (2014)
  12. Blumenthal, Frederick; Bauke, Heiko: A stability analysis of a real space split operator method for the Klein-Gordon equation (2012)
  13. Fillion-Gourdeau, François; Lorin, Emmanuel; Bandrauk, André D.: Numerical solution of the time-dependent Dirac equation in coordinate space without fermion-doubling (2012)
  14. Bauke, Heiko; Keitel, Christoph H.: Accelerating the Fourier split operator method via graphics processing units (2011)
  15. Lorin, E.; Bandrauk, A.: A simple and accurate mixed (P^0-Q^1) solver for the Maxwell-Dirac equations (2011)
  16. Ruf, Matthias; Bauke, Heiko; Keitel, Christoph H.: A real space split operator method for the Klein-Gordon equation (2009)
  17. Mocken, Guido R.; Keitel, Christoph H.: FFT-split-operator code for solving the Dirac equation in (2+1) dimensions (2008)