二维环面上朗道能级的数值计算
Landau levels on the 2D torus: a numerical approach
摘要：
本文提出了一种数值方法，可以计算在横向磁场和任意保守力共同作用下，约束在二维平面圆环上的粒子的Schroedinger算符谱。该方法采用快速傅立叶变换来准确地表示动量变量，并考虑到所需的存在的磁场的扭曲的边界条件。即使使用粗网格也能达到12位数的精度。朗道能级是在均匀场满足狄拉克条件的情况下再现的。当磁场具有周期与整数磁荷相等的正弦分量时，在单朗道能级内形成新的精细能级结构。
英文摘要：
A numerical method is presented which allows to compute the spectrum of the Schroedinger operator for a particle constrained on a two dimensional flat torus under the combined action of a transverse magnetic field and any conservative force. The method employs a fast Fourier transform to accurately represent the momentum variables and takes into account the twisted boundary conditions required by the presence of the magnetic field. An accuracy of twelve digits is attained even with coarse grids. Landau levels are reproduced in the case of a uniform field satisfying Dirac's condition. A new fine structure of levels within the single Landau level is formed when the field has a sinusoidal component with period commensurable to the integer magnetic charge.
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