Semi-spectral method for the Wigner equation
Semi-spectral method for the Wigner equation
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DOI：
10.1016/j.jcp.2015.11.023
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发表时间：
2015-06
期刊：
影响因子：
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通讯作者：
O. Furtmaier;S. Succi;M. Mendoza
中科院分区：
文献类型：
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作者：
O. Furtmaier;S. Succi;M. Mendoza
我们提出了一种数值方法来解决无自旋，非相对论性粒子的量子系统中的维格纳方程。该方法使用的谱分解成L2（RD）的动量空间的基函数，以获得一阶对流反应方程组的系统。由此产生的方程求解分裂的反应和平流步骤，以便允许从量子力学和计算流体动力学的数值技术相结合，通过确定的斜厄米反应矩阵作为一个发电机的酉旋转。该方法是有效的粒子的情况下，受到一个一维（一个）谐波和莫尔斯潜在的平流部分使用有限差分。由此，我们验证了二阶收敛性，并观察到维格纳函数演化的非经典行为。
We propose a numerical method to solve the Wigner equation in quantum systems of spinless, non-relativistic particles. The method uses a spectral decomposition into L 2 (R d) basis functions in momentum-space to obtain a system of first-order advection–reaction equations. The resulting equations are solved by splitting the reaction and advection steps so as to allow the combination of numerical techniques from quantum mechanics and computational fluid dynamics by identifying the skew-hermitian reaction matrix as a generator of unitary rotations. The method is validated for the case of particles subject to a one-dimensional (an-) harmonic and Morse potential using finite-differences for the advection part. Thereby, we verify the second order of convergence and observe non-classical behavior in the evolution of the Wigner function.