Nonlinear Dirac Equation on Graphs with Localized Nonlinearities: Bound States and Nonrelativistic Limit [PDF]
SIAM Journal on Mathematical Analysis, 2018 In this paper we study the nonlinear Dirac (NLD) equation on noncompact metric graphs with localized Kerr nonlinearities, in the case of Kirchhoff-type conditions at the vertices.
William Borrelli +2 more
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A fourth-order compact time-splitting Fourier pseudospectral method for the Dirac equation [PDF]
Research in the Mathematical Sciences, 2017 We propose a new fourth-order compact time-splitting ($$S_\mathrm{4c}$$S4c) Fourier pseudospectral method for the Dirac equation by splitting the Dirac equation into two parts together with using the double commutator between them to integrate the Dirac ...
W. Bao, Jia Yin
semanticscholar +1 more source
International Journal of Theoretical Physics, 2002 Tensor, matrix and quaternion formulations of Dirac-K hler equation for massive and massless fields are considered. The equation matrices obtained are simple linear combinations of matrix elements in the 16-dimensional space. The projection matrix-dyads defining all the 16 independent equation solutions are found.
openaire +2 more sources
Solusi Persamaan Dirac untuk Fermion dengan Model Potensial Penghalang Medan Elektromagnetik
Jurnal Fisika Flux, 2020 The solution of the Dirac equation in the presence of the electromagnetic field on the one-dimensional barrier potential is studied. The energy spectrum and the eigenfunction of the Dirac equation obtained by solving the Dirac equation and we introduced ...
Arista Romadani, Erika Rani
doaj +1 more source
Numerical Methods and Comparison for the Dirac Equation in the Nonrelativistic Limit Regime [PDF]
Journal of Scientific Computing, 2015 We analyze rigorously error estimates and compare numerically spatial/temporal resolution of various numerical methods for the discretization of the Dirac equation in the nonrelativistic limit regime, involving a small dimensionless parameter ...
W. Bao +3 more
semanticscholar +1 more source
Algorithm for the solution of the Dirac equation on digital quantum computers [PDF]
, 2016 A quantum algorithm that solves the time-dependent Dirac equation on a digital quantum computer is developed and analyzed. The time evolution is performed by an operator-splitting decomposition technique that allows for a mapping of the Dirac operator to
F. Fillion-Gourdeau +2 more
semanticscholar +1 more source
A Uniformly Accurate Multiscale Time Integrator Pseudospectral Method for the Dirac Equation in the Nonrelativistic Limit Regime [PDF]
SIAM Journal on Numerical Analysis, 2015 We propose and rigourously analyze a multiscale time integrator Fourier pseudospectral (MTI-FP) method for the Dirac equation with a dimensionless parameter $\varepsilon\in(0,1]$ which is inversely proportional to the speed of light.
W. Bao +3 more
semanticscholar +1 more source
The Cubic Dirac Equation: Small Initial Data in $${{H^{\frac{1}{2}}} (\mathbb{R}^{2}}$$H12(R2) [PDF]
, 2015 Global well-posedness and scattering for the cubic Dirac equation with small initial data in the critical space $${{H^{\frac{1}{2}}} (\mathbb{R}^{2}}$$H12(R2) is established. The proof is based on a sharp endpoint Strichartz estimate for the Klein–Gordon
I. Bejenaru, S. Herr
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On the Fractional Derivative of Dirac Delta Function and Its Application
Advances in Mathematical Physics, 2020 The Dirac delta function and its integer-order derivative are widely used to solve integer-order differential/integral equation and integer-order system in related fields. On the other hand, the fractional-order system gets more and more attention.
Zaiyong Feng, Linghua Ye, Yi Zhang
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