随机波纹边界制导系统局部化的对偶性质：Anderson型与熵
Dual nature of localization in guiding systems with randomly corrugated boundaries: Anderson-type versus entropic
摘要：
本文发展了一个有限段具有随机粗糙边界的多模长量子线电导的统一理论。它使人们能够考虑到所有机制的波散射，既涉及到边界粗糙度和接触之间的导线粗糙部分和引线在相同的技术框架。导线的粗糙部分被示出作为一个模式特定的随机调制的有效势垒，其高度基本上是由粗糙度斜率。屏障的平均高度指定传导通道的数量。在相对小的粗糙度振幅下，如果粗糙度足够尖锐，则该数字可以取任意小的值。当粗糙度增加时产生的通道截止可以被视为一种局部化，其与无序无关，而是熵的起源。屏障的波动部分导致两种根本不同类型的导波散射，即，模间和模内散射。模间散射被证明是在大多数情况下非常强大的，除了在（a）非常光滑的凹凸不平的情况下，（b）过小的长度的波纹段，和（c）凹凸不平的尖锐到足以只有一个导电通道留在电线。在强模间散射下，一组新的导电通道发展，其具有受个体随机势影响的解耦扩展模的形式。鉴于这一事实，只有两个传输制度是可实现的随机波纹多模线，具体地说，弹道和本地化制度，后者的一维随机系统的特点。因此，两种本地化的随机波纹边界的类波导系统中共存，具体地说，熵本地化和一维安德森局域化。
英文摘要：
A unified theory for the conductance of a long multimode quantum wire whose finite segment has randomly rough boundaries is developed. It enables one to take account of all mechanisms of wave scattering, both related to boundary roughness and to contacts between the wire rough section and the leads within the same technical frameworks. The rough part of the conducting wire is shown to act as a mode-specific randomly modulated effective potential barrier whose height is governed essentially by the asperity slope. The mean height of the barrier specifies the number of conducting channels. Under relatively small asperity amplitude this number can take on arbitrary small values if the asperities are sufficiently sharp. The channel cut-off that arises when the asperity sharpness increases can be regarded as a kind of localization, which is not related to the disorder but rather is of entropic origin. The fluctuating part of the barrier results in two fundamentally different types of guided wave scattering, viz., inter- and intramode scattering. The intermode scattering is shown to be for the most part very strong except in the cases of (a) extremely smooth asperities, (b) excessively small length of the corrugated segment, and (c) the asperities sharp enough for only one conducting channel to remain in the wire. Under strong intermode scattering, a new set of conducting channels develops, which have the form of decoupled extended modes subject to individual random potentials. In view of this fact, two transport regimes only are realizable in randomly corrugated multimode wires, specifically, the ballistic and the localized regime, the latter characteristic of one-dimensional random systems. Two kinds of localization are thus shown to coexist in waveguide-like systems with randomly corrugated boundaries, specifically, the entropic localization and the one-dimensional Anderson localization.
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