Solving Dirac equations on a 3D lattice with inverse Hamiltonian and spectral methods

Date
2017
Journal Title
Journal ISSN
Volume Title
Publisher
American Physical Society
Abstract
A new method to solve the Dirac equation on a 3D lattice is proposed, in which the variational collapse problem is avoided by the inverse Hamiltonian method and the fermion doubling problem is avoided by performing spatial derivatives in momentum space with the help of the discrete Fourier transform, i.e., the spectral method. This method is demonstrated in solving the Dirac equation for a given spherical potential in a 3D lattice space. In comparison with the results obtained by the shooting method, the differences in single-particle energy are smaller than 10ֿ⁻⁴ MeV, and the densities are almost identical, which demonstrates the high accuracy of the present method. The results obtained by applying this method without any modification to solve the Dirac equations for an axial-deformed, nonaxial-deformed, and octupole-deformed potential are provided and discussed
Description
CITATION: Ren, Z. X., Zhang, S. Q. & Meng, J. 2017. Solving Dirac equations on a 3D lattice with inverse Hamiltonian and spectral methods. Physical Review C, 95(2):1-8, doi:10.1103/PhysRevC.95.024313.
The original publication is available at https://journals.aps.org/prc
Keywords
Spectral methods, Hamiltonian method, Spectral method, Dirac equation, Fourier transformations, Lattices
Citation
Ren, Z. X., Zhang, S. Q. & Meng, J. 2017. Solving Dirac equations on a 3D lattice with inverse Hamiltonian and spectral methods. Physical Review C, 95(2):1-8, doi:10.1103/PhysRevC.95.024313