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arXiv 1002.2317cond-mat.mes-hallcond-mat.mtrl-sci
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电流存在下受约束带电粒子量子理论中反常相互作用的消失

Absence of anomalous interactions in the quantum theory of constrained charged particles in presence of electrical currents

Carmine Ortix, Jeroen van den Brink

摘要:

在合成低维纳米结构的实验中,载流子被限制在弯曲表面上,这一实验进展促进了对弯曲二维流形上的量子力学理论的兴趣。最近有人断言,受约束的带电粒子耦合到A_3M中的一个线性项,其中A_3是电磁矢势的横截分量,M是表面平均曲率,从而使得在存在场的情况下降维过程是不可行的。在这里,我们解决这个明显的悖论,提供了一个一致的一般框架的薄壁量子化过程。我们还表明,运动运动方程的可分离性不危及特定的选择施加在波函数的横向波动的约束,这使得薄壁量子化过程是有根据的。它可以不受限制地应用。

英文摘要:

The experimental progress in synthesizing low-dimensional nanostructures where carriers are confined to bent surfaces has boosted the interest in the theory of quantum mechanics on curved two-dimensional manifolds. It was recently asserted that constrained electrically charged particles couple to a term linear in A_3 M, where A_3 is the transversal component of the electromagnetic vector potential and M the surface mean curvature, thereby making a dimensional reduction procedure impracticable in the presence of fields. Here we resolve this apparent paradox by providing a consistent general framework of the thin-wall quantization procedure. We also show that the separability of the equation of motions is not endangered by the particular choice of the constraint imposed on the transversal fluctuations of the wavefunction, which renders the thin-wall quantization procedure well-founded. It can be applied without restrictions.

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