The Experts below are selected from a list of 36606 Experts worldwide ranked by ideXlab platform
V. M. Shabaev - One of the best experts on this subject based on the ideXlab platform.
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dual kinetic balance approach to the Dirac Equation for axially symmetric systems application to static and time dependent fields
Physical Review A, 2014Co-Authors: Efim Rozenbaum, V. M. Shabaev, D A Glazov, Ksenia Sosnova, Dmitry A TelnovAbstract:The dual-kinetic-balance (DKB) technique was previously developed to eliminate spurious states in the finite-basis-set-based solution of the Dirac Equation in central fields. In the present paper, it is extended to the Dirac Equation for systems with axial symmetry. The efficiency of the method is demonstrated by the calculation of the energy spectra of hydrogenlike ions in the presence of static uniform electric or magnetic fields. In addition, the DKB basis set is implemented to solve the time-dependent Dirac Equation making use of the split-operator technique. The excitation and ionization probabilities for the hydrogenlike argon and tin ions exposed to laser pulses are evaluated.
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dual kinetic balance approach to basis set expansions for the Dirac Equation
Physical Review Letters, 2004Co-Authors: V. M. Shabaev, G. Plunien, I I Tupitsyn, G SoffAbstract:A new approach to finite basis sets for the Dirac Equation is developed. It does not involve spurious states and improves the convergence properties of basis-set calculations. Efficiency of the method is demonstrated for finite basis sets constructed from $B$ splines by calculating the one-loop self-energy correction for a hydrogenlike ion.
Dmitry A Telnov - One of the best experts on this subject based on the ideXlab platform.
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dual kinetic balance approach to the Dirac Equation for axially symmetric systems application to static and time dependent fields
Physical Review A, 2014Co-Authors: Efim Rozenbaum, V. M. Shabaev, D A Glazov, Ksenia Sosnova, Dmitry A TelnovAbstract:The dual-kinetic-balance (DKB) technique was previously developed to eliminate spurious states in the finite-basis-set-based solution of the Dirac Equation in central fields. In the present paper, it is extended to the Dirac Equation for systems with axial symmetry. The efficiency of the method is demonstrated by the calculation of the energy spectra of hydrogenlike ions in the presence of static uniform electric or magnetic fields. In addition, the DKB basis set is implemented to solve the time-dependent Dirac Equation making use of the split-operator technique. The excitation and ionization probabilities for the hydrogenlike argon and tin ions exposed to laser pulses are evaluated.
Jia Yin - One of the best experts on this subject based on the ideXlab platform.
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a fourth order compact time splitting fourier pseudospectral method for the Dirac Equation
Research in the Mathematical Sciences, 2019Co-Authors: Weizhu Bao, Jia YinAbstract:We propose a new fourth-order compact time-splitting ( $$S_\mathrm{4c}$$ ) 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 Equation at each time interval. The method is explicit, fourth-order in time and spectral order in space. It is unconditionally stable and conserves the total probability in the discretized level. It is called a compact time-splitting method since, at each time step, the number of substeps in $$S_\mathrm{4c}$$ is much less than those of the standard fourth-order splitting method and the fourth-order partitioned Runge–Kutta splitting method. Another advantage of $$S_\mathrm{4c}$$ is that it avoids to use negative time steps in integrating subproblems at each time interval. Comparison between $$S_\mathrm{4c}$$ and many other existing time-splitting methods for the Dirac Equation is carried out in terms of accuracy and efficiency as well as longtime behavior. Numerical results demonstrate the advantage in terms of efficiency and accuracy of the proposed $$S_\mathrm{4c}$$ . Finally, we report the spatial/temporal resolutions of $$S_\mathrm{4c}$$ for the Dirac Equation in different parameter regimes including the nonrelativistic limit regime, the semiclassical limit regime, and the simultaneously nonrelativistic and massless limit regime.
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a fourth order compact time splitting fourier pseudospectral method for the Dirac Equation
arXiv: Numerical Analysis, 2017Co-Authors: Weizhu Bao, Jia YinAbstract:We propose a new fourth-order compact time-splitting ($S_\text{4c}$) 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 Equation at each time interval. The method is explicit, fourth-order in time and spectral order in space. It is unconditional stable and conserves the total density in the discretized level. It is called a compact time-splitting method since, at each time step, the number of sub-steps in $S_\text{4c}$ is much less than those of the standard fourth-order splitting method and the fourth-order partitioned Runge-Kutta splitting method. Comparison among $S_\text{4c}$ and many other existing time-splitting methods for the Dirac Equation are carried out in terms of accuracy and efficiency as well as long time behavior. Numerical results demonstrate the advantage in terms of efficiency and accuracy of the proposed $S_\text{4c}$. Finally we report the spatial/temporal resolutions of $S_\text{4c}$ for the Dirac Equation in different parameter regimes including the nonrelativistic limit regime, the semiclassical limit regime, and the simultaneously nonrelativisic and massless limit regime.
Yin Jia - One of the best experts on this subject based on the ideXlab platform.
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A fourth-order compact time-splitting method for the Dirac Equation with time-dependent potentials
'Elsevier BV', 2021Co-Authors: Yin JiaAbstract:In this paper, we present an approach to deal with the dynamics of the Dirac Equation with time-dependent electromagnetic potentials using the fourth-order compact time-splitting method ($S_\text{4c}$). To this purpose, the time-ordering technique for time-dependent Hamiltonians is introduced, so that the influence of the time-dependence could be limited to certain steps which are easy to treat. Actually, in the case of the Dirac Equation, it turns out that only those steps involving potentials need to be amended, and the scheme remains efficient, accurate, as well as easy to implement. Numerical examples in 1D and 2D are given to validate the scheme.Comment: 24pages, 8 figure
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Super-resolution of time-splitting methods for the Dirac Equation in the nonrelativistic regime
2020Co-Authors: Bao Weizhu, Cai Yongyong, Yin JiaAbstract:We establish error bounds of the Lie-Trotter splitting ($S_1$) and Strang splitting ($S_2$) for the Dirac Equation in the nonrelativistic limit regime in the absence of external magnetic potentials, with a small parameter $0
Efim Rozenbaum - One of the best experts on this subject based on the ideXlab platform.
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dual kinetic balance approach to the Dirac Equation for axially symmetric systems application to static and time dependent fields
Physical Review A, 2014Co-Authors: Efim Rozenbaum, V. M. Shabaev, D A Glazov, Ksenia Sosnova, Dmitry A TelnovAbstract:The dual-kinetic-balance (DKB) technique was previously developed to eliminate spurious states in the finite-basis-set-based solution of the Dirac Equation in central fields. In the present paper, it is extended to the Dirac Equation for systems with axial symmetry. The efficiency of the method is demonstrated by the calculation of the energy spectra of hydrogenlike ions in the presence of static uniform electric or magnetic fields. In addition, the DKB basis set is implemented to solve the time-dependent Dirac Equation making use of the split-operator technique. The excitation and ionization probabilities for the hydrogenlike argon and tin ions exposed to laser pulses are evaluated.
