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A simple model for the quantum hydrodynamic simulation of electron transport in quantum confined structures in the presence of vortices

机译：存在涡旋时电子在量子约束结构中传输的量子流体动力学模拟的简单模型

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We have previously shown that the flow in open quantum dots may be described in terms of meandering open orbits which separate regions of trapped flows around vortices. Furthermore the topology of the flow follows from a simple geometrical construction in which the classical ballistic trajectories are first computed and then all crossings are replaced by hyperbolic flow separation and for which all trapped flows form quantised closed orbits. In the present paper we extend this picture to a computational methodology for developing quantum hydrodynamic descriptions of flows in the presence of quantised vortices by extension from classical hydrodynamics. For coherent transport we again encounter the Bohm quantum potential but the singularity structure is predetermined by applying a fictitious repulsion which prevents trajectories and hence streamlines crossing. This leads to vortex producing terms in the hydrodynamic equations. The discussion is completed by including the effects of non-hermitian potentials into the Hamiltonian in order to simulate dissipation and phase breaking flows.
机译：先前我们已经表明，开放量子点中的流动可以用曲折的开放轨道来描述，该曲折的开放轨道将围绕涡旋的捕获流动的区域分开。此外，流动的拓扑结构来自简单的几何构造，在该几何构造中，首先计算了经典弹道，然后用双曲线流动分离代替了所有交叉，并且所有被困的流动都形成了量化的闭合轨道。在本文中，我们将这幅图扩展到一种计算方法，该方法可通过对经典流体力学的扩展来发展在存在量化涡流的情况下对流体进行量子流体力学描述。对于相干传输，我们再次遇到了Bohm量子势，但是奇异性结构是通过应用虚拟斥力来预先确定的，该斥力防止了轨迹的发生并因此阻止了流线的交叉。这导致在流体动力学方程中产生涡旋项。通过将非厄米特电位的影响包括在哈密顿量中以模拟耗散和相中断流来完成讨论。

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