论文标题
重新查看重力对量子厅效应的影响
A fresh look at the influence of gravity on the quantum Hall effect
论文作者
论文摘要
我们研究重力场内的量子厅效应。首先，我们回顾地球引力场对量子大厅效应的影响。将地球的重力域沿垂直方向均匀，我们计算受影响的量化霍尔电阻率。然后，我们研究重力场如何在垂直于运动平面的恒定和均匀的磁场存在下，在两个巨大半球之间移动的粒子水平。我们发现，去除了Landau水平的熟悉的退化，后者之间的间距取决于半球的质量密度和重力常数$ G $。我们使用此结果表明，夹在两个大半球之间的薄导体中的量子霍尔效应应与施加的磁场的霍尔电阻率略有不同。然后，我们认为，重力诱导的电场的众所周知的问题可能会被认为是阻碍重力的影响，实际上具有有益的作用，因为它会放大后者。我们最终讨论是否有可能使用量子厅效应来探测重力的反向定律。
We study the quantum Hall effect inside a gravitational field. First, we review the influence of the gravitational field of the Earth on the quantum Hall effect. Taking the gravitational field of the Earth to be uniform along the vertical direction, we compute the affected quantized Hall resistivity. Then, we investigate how the gravitational field modifies the Landau levels of a particle moving between two massive hemispheres in the presence of a constant and uniform magnetic field perpendicular to the plane of motion. We find that the familiar degeneracy of the Landau levels is removed and the spacing between the latter becomes dependent on the mass density of the hemispheres and on the gravitational constant $G$. We use this result to show that the quantum Hall effect in a thin conductor, sandwiched between two massive hemispheres, should yield a slightly different variation of the Hall resistivity with the applied magnetic field. We then argue that the well-known problem of the gravitationally induced electric field, that might a priori be thought to hinder the effect of gravity, has actually a beneficial role as it amplifies the latter. We finally discuss whether there is a possibility of using the quantum Hall effect to probe the inverse-square law of gravity.
