A dispersion and norm preserving finite difference scheme with transparent boundary conditions for the Dirac equation in \((1+1)\)D
From MaRDI portal
Publication:348392
DOI10.1016/j.jcp.2013.09.022zbMath1349.81085arXiv1302.5587OpenAlexW2015593049MaRDI QIDQ348392
Anton Arnold, Walter Pötz, 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/1302.5587
Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06)
Related Items (31)
Error Estimate of a New Conservative Finite Difference Scheme for the Klein-Gordon-Dirac System ⋮ Error estimates of numerical methods for the nonlinear Dirac equation in the nonrelativistic limit regime ⋮ Error analysis of a time fourth-order exponential wave integrator Fourier pseudo-spectral method for the nonlinear Dirac equation ⋮ Single-cone real-space finite difference scheme for the time-dependent Dirac equation ⋮ Convergence analysis of a symmetric exponential integrator Fourier pseudo-spectral scheme for the Klein-Gordon-Dirac equation ⋮ Energy conserving discontinuous Galerkin method with scalar auxiliary variable technique for the nonlinear Dirac equation ⋮ Real-space finite difference scheme for the von Neumann equation with the Dirac Hamiltonian ⋮ Convergence analysis of two conservative finite difference Fourier pseudo-spectral schemes for Klein-Gordon-Dirac system ⋮ Time-dependent Dirac equation with physics-informed neural networks: computation and properties ⋮ Transparent boundary conditions for the nonlocal nonlinear Schrödinger equation: a model for reflectionless propagation of PT-symmetric solitons ⋮ Error bounds of fourth‐order compact finite difference methods for the Dirac equation in the massless and nonrelativistic regime ⋮ Structure‐preserving exponential wave integrator methods and the long‐time convergence analysis for the Klein‐Gordon‐Dirac equation with the small coupling constant ⋮ Optimal error estimates of a time-splitting Fourier pseudo-spectral scheme for the Klein-Gordon-Dirac equation ⋮ Stability analysis of the numerical method of characteristics applied to a class of energy-preserving hyperbolic systems. I: Periodic boundary conditions ⋮ 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 study of solitary wave stability in cubic nonlinear Dirac equations in 1D ⋮ Transparent boundary conditions for higher-order finite-difference schemes of the Schrödinger equation in (1+1)D ⋮ A simple pseudospectral method for the computation of the time-dependent Dirac equation with perfectly matched layers ⋮ Optimal point-wise error estimate of two conservative fourth-order compact finite difference schemes for the nonlinear Dirac equation ⋮ Computational performance of simple and efficient sequential and parallel Dirac equation solvers ⋮ Analysis of a conservative fourth-order compact finite difference scheme for the Klein-Gordon-Dirac equation ⋮ Numerical methods and comparison for the Dirac equation in the nonrelativistic limit regime ⋮ Absorbing layers for the Dirac equation ⋮ A Uniformly Accurate Multiscale Time Integrator Pseudospectral Method for the Dirac Equation in the Nonrelativistic Limit Regime ⋮ Energy-preserving exponential integrator Fourier pseudo-spectral schemes for the nonlinear Dirac equation ⋮ Transparent boundary conditions for the sine-Gordon equation: modeling the reflectionless propagation of kink solitons on a line ⋮ Uniform Error Bounds of Time-Splitting Methods for the Nonlinear Dirac Equation in the Nonrelativistic Regime without Magnetic Potential ⋮ Pseudospectral computational methods for the time-dependent Dirac equation in static curved spaces ⋮ Transparent boundary conditions for the Bogoliubov-de Gennes equation in \((1+1)\)D
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Staggered grid leap-frog scheme for the \((2+1)D\) Dirac equation
- Numerical methods for nonlinear Dirac equation
- Numerical solution of the time-dependent Dirac equation in coordinate space without fermion-doubling
- The numerical study of a nonlinear one-dimensional Dirac equation
- An efficient adaptive mesh redistribution method for a nonlinear Dirac equation
- Split-step spectral schemes for nonlinear Dirac systems
- Linearized Crank-Nicolson scheme for nonlinear Dirac equations
- Quantum dynamics of relativistic electrons
- Discretely nonreflecting boundary conditions for linear hyperbolic systems
- Analysis of a leap-frog pseudospectral scheme for the Schrödinger equation
- Higher-order accurate Runge-Kutta discontinuous Galerkin methods for a nonlinear Dirac model
- Multi-symplectic Runge-Kutta methods for nonlinear Dirac equations
- Discrete transparent boundary conditions for the Schrödinger equation: fast calculation, approximation, and stability
- MATHEMATICAL CONCEPTS OF OPEN QUANTUM BOUNDARY CONDITIONS
- Geometric numerical integration illustrated by the Störmer–Verlet method
- Weak Ill-Posedness of Spatial Discretizations of Absorbing Boundary Conditions for Schrödinger-Type Equations
- Fast Convolution for Nonreflecting Boundary Conditions
- Scattering theory for mesoscopic quantum systems with non-trivial spatial asymptotics in one dimension
- Optical lattice quantum simulator for quantum electrodynamics in strong external fields: spontaneous pair creation and the Sauter–Schwinger effect
- Nonsymmetric Difference Equations
- Discrete transparent boundary conditions for transient kp‐Schrödinger equations with application to quantum heterostructures
- Implementation of transparent boundaries for numerical solution of the Schröder equation.
This page was built for publication: A dispersion and norm preserving finite difference scheme with transparent boundary conditions for the Dirac equation in \((1+1)\)D