直抛物通道中的磁输运
Magnetic transport in a straight parabolic channel
摘要：
研究了二维带电粒子在均匀磁场作用下，受势扰动$W$的影响，被限制在一个直的抛物势通道中的运动。如果$W$是有界的，并且沿通道是周期性的，则微扰变元产生谱底部的绝对连续性。我们表明，它可以有任何有限数量的开放的差距提供的限制潜力是足够强。然而，如果$W$只依赖于周期变量，我们证明了托马斯的论点，整个频谱是绝对连续的，不管的扰动的大小。另一方面，如果$W$很小，并且在纵向上满足弱的局域化条件，我们用Brackre方法证明了一部分绝对连续谱是持续存在的。
英文摘要：
We study a charged two-dimensional particle confined to a straight parabolic-potential channel and exposed to a homogeneous magnetic field under influence of a potential perturbation $W$. If $W$ is bounded and periodic along the channel, a perturbative argument yields the absolute continuity of the bottom of the spectrum. We show it can have any finite number of open gaps provided the confining potential is sufficiently strong. However, if $W$ depends on the periodic variable only, we prove by Thomas argument that the whole spectrum is absolutely continuous, irrespectively of the size of the perturbation. On the other hand, if $W$ is small and satisfies a weak localization condition in the the longitudinal direction, we prove by Mourre method that a part of the absolutely continuous spectrum persists.
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