Landauer-Büttiker和无源电导
Landauer-Büttiker and Thouless conductance
摘要：
在独立电子近似下，流经连接到两个电子库的有限样本S的平均（能量/电荷/熵）电流可以通过散射理论参数计算，这导致了着名的Landauer-Büttiker公式。另一个众所周知的公式是由Elderless根据比例论证提出的。无量纲公式将样品的电导与通过周期性并置S获得的无限晶体的光谱带的宽度联系起来。在这种精神下，我们通过将Landauer-Büttiker公式扩展到一种设置来定义Landauer-Büttiker晶体电流，其中样品S被单位晶胞为S的周期性结构所取代。我们认为，这些晶体电流是密切相关的电流。例如，晶体热流的边界在无反射热流的上方，并且当储层和样品之间的耦合是无反射的时，该边界饱和。我们的分析导致了严格的推导，从量子统计力学的第一原理的无偏公式。
英文摘要：
In the independent electron approximation, the average (energy/charge/entropy) current flowing through a finite sample S connected to two electronic reservoirs can be computed by scattering theoretic arguments which lead to the famous Landauer-Büttiker formula. Another well known formula has been proposed by Thouless on the basis of a scaling argument. The Thouless formula relates the conductance of the sample to the width of the spectral bands of the infinite crystal obtained by periodic juxtaposition of S. In this spirit, we define Landauer-Büttiker crystalline currents by extending the Landauer-Büttiker formula to a setup where the sample S is replaced by a periodic structure whose unit cell is S. We argue that these crystalline currents are closely related to the Thouless currents. For example, the crystalline heat current is bounded above by the Thouless heat current, and this bound saturates iff the coupling between the reservoirs and the sample is reflectionless. Our analysis leads to a rigorous derivation of the Thouless formula from the first principles of quantum statistical mechanics.
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