Single-cone real-space finite difference scheme for the time-dependent Dirac equation

DOI10.1016/j.jcp.2014.01.028zbMath1349.65301arXiv1309.3452OpenAlexW2143076561MaRDI QIDQ348960

Walter Pötz, Anton Arnold, René Hammer

Publication date: 5 December 2016

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1309.3452

zbMATH Keywords

Dirac equationstaggered gridleap-frogfermion doublingFDTDKlein step

Mathematics Subject Classification ID

Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06)

Related Items (15)

Real-space finite difference scheme for the von Neumann equation with the Dirac Hamiltonian ⋮ Conservative second-order accurate finite-difference scheme for the coupled Maxwell-Dirac equations ⋮ Perfectly matched layers for Schrödinger-type equations with nontrivial energy-momentum dispersion ⋮ Finite difference time domain methods for the Dirac equation coupled with the Chern-Simons gauge field ⋮ Single-cone finite difference scheme for the \((2+1)\)D Dirac von Neumann equation ⋮ A conservative fourth-order real space method for the (2+1)D Dirac equation ⋮ Numerical Methods for the Nonlinear Dirac Equation in the Massless Nonrelativistic Regime ⋮ Low-regularity integrators for nonlinear Dirac equations ⋮ The Landau-Zener Transition and the Surface Hopping Method for the 2D Dirac Equation for Graphene ⋮ Numerical methods and comparison for the Dirac equation in the nonrelativistic limit regime ⋮ Absorbing layers for the Dirac equation ⋮ A uniformly accurate (UA) multiscale time integrator pseudospectral method for the nonlinear Dirac equation in the nonrelativistic limit regime ⋮ A Uniformly Accurate Multiscale Time Integrator Pseudospectral Method for the Dirac Equation in the Nonrelativistic Limit Regime ⋮ Uniformly Accurate Nested Picard Iterative Integrators for the Dirac Equation in the Nonrelativistic Limit Regime ⋮ Error estimates of finite difference methods for the Dirac equation in the massless and nonrelativistic regime

Uses Software

• Dirac++

Cites Work

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• Staggered grid leap-frog scheme for the \((2+1)D\) Dirac equation
• Numerical methods for nonlinear Dirac equation
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• Numerical solution of the time-dependent Dirac equation in coordinate space without fermion-doubling
• FFT-split-operator code for solving the Dirac equation in \(2+1\) dimensions
• Quantum field theory techniques in graphical enumeration
• A perfectly matched layer for the absorption of electromagnetic waves
• Analysis of a leap-frog pseudospectral scheme for the Schrödinger equation
• The reservoir technique: a way to make Godunov-type schemes zero or very low diffuse. Application to Colella-Glaz solver
• Numerical solution of initial boundary value problems involving maxwell's equations in isotropic media
• Quantum Field Theory

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