论文标题
零绝对涡度平面库特流动作为垂直磁场下量子能状态的流体动力表示
Zero absolute vorticity plane Couette flow as an hydrodynamic representation of quantum energy states under perpendicular magnetic field
论文作者
论文摘要
在这里，我们将Schrödinger方程的Madelung转化扩展到类似流体的形式，以包括外部电磁场对带电粒子的影响。然后，玛德隆流体的涡度朝与施加的磁场相反的方向，并且在大小上等于回旋体角频率。当粒子运动局限于垂直于强加的磁场的平面时，等效流动动力学是在准2D旋转框架中获得的零绝对涡度，其中回旋频率在旋转框架中与科里奥利斯频率的作用相等。我们展示了整数量子大厅效应中的Landau水平和扩展模式如何映射到如此零的绝对涡流状平面COUETTE流动中，后者在磁力和量子（BOHM）电势和电力之间表现出地球样的平衡。
Here we extend the Madelung transformation of the Schrödinger equation into a fluid-like form to include the influence of an external electromagnetic field on a charged particle. The vorticity of the Madelung fluid is then in the opposite direction to the imposed magnetic field and equal in magnitude to the cyclotron angular frequency. When the particle motion is confined to a plane, perpendicular to an imposed magnetic field, the equivalent flow dynamics is that of zero absolute vorticity obtained in a quasi 2D rotating frame, where the cyclotron frequency plays a role equivalent to that of the Coriolis frequency in a rotating frame. We show how the Landau levels and the extended modes in the integer quantum Hall effect are all mapped into such zero absolute vorticity-like plane Couette flows, where the latter exhibit a geostrophic-like balance between the magnetic force and the gradients of the quantum (Bohm) potential and the electric force.
