Convergence of a three-dimensional quantum lattice Boltzmann scheme towards solutions of the Dirac equation
Convergence of a three-dimensional quantum lattice Boltzmann scheme towards solutions of the Dirac equation
复制标题
三维量子晶格玻尔兹曼格式对狄拉克方程解的收敛
DOI：
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发表时间：
2011
期刊：
影响因子：
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通讯作者：
P. Dellar
中科院分区：
文献类型：
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作者：
D. Lapitski;P. Dellar
研究了狄拉克方程的三维量子晶格玻尔兹曼方案的收敛性。这些格式被构造为基于算子分裂的狄拉克方程的离散化，以分离沿三个坐标轴的流沿着，但它们的输出以前只与薛定谔方程的解进行了比较。薛定谔方程是狄拉克方程的非相对论极限，描述了与康普顿频率相比变化缓慢的解。我们证明了一阶收敛到一个独立的数值方法的基础上快速傅立叶变换和矩阵幂的狄拉克方程的解决方案。
We investigate the convergence properties of a three-dimensional quantum lattice Boltzmann scheme for the Dirac equation. These schemes were constructed as discretizations of the Dirac equation based on operator splitting to separate the streaming along the three coordinate axes, but their output has previously only been compared against solutions of the Schrödinger equation. The Schrödinger equation arises as the non-relativistic limit of the Dirac equation, describing solutions that vary slowly compared with the Compton frequency. We demonstrate first-order convergence towards solutions of the Dirac equation obtained by an independent numerical method based on fast Fourier transforms and matrix exponentiation.