论文标题
Fermi颗粒的传导模型在有限晶格上的传导模型的电流的渐近特性
Asymptotic property of current for a conduction model of Fermi particles on finite lattice
论文作者
论文摘要
在本文中，我们在有限样品上引入了费米颗粒的传导模型，并研究了大型样本量的固定电流的渐近行为。在我们的模型中，样品由一维有限晶格描述，在该晶格上，两端注入的费米颗粒在各种电势和噪声下移动。我们获得了一个简单的电流公式。该公式具有广泛的适用性，用于研究各种潜力。当缺乏噪声时，它提供了电流的渐近行为，以转移矩阵的形式。特别是，对于动态定义的潜在案例，获得了相关传输矩阵的电流衰减与Lyapunov指数之间的关系。例如，这表明当前的当前衰减为Anderson模型呈指数衰减。另一方面，当噪声存在但势不存在时，获得电流的明确形式，对于大样本尺寸N，它将缩放为1/N。此外，我们为更高维系统提供了扩展。对于三维情况，这表明电流的横截面成比例增加，并且与样品长度的相反。
In this paper, we introduce a conduction model of Fermi particles on a finite sample, and investigate the asymptotic behavior of stationary current for large sample size. In our model a sample is described by a one-dimensional finite lattice on which Fermi particles injected at both ends move under various potentials and noise from the environment. We obtain a simple current formula. The formula has broad applicability and is used to study various potentials. When the noise is absent, it provides the asymptotic behavior of the current in terms of a transfer matrix. In particular, for dynamically defined potential cases, a relation between exponential decay of the current and the Lyapunov exponent of a relevant transfer matrix is obtained. For example, it is shown that the current decays exponentially for the Anderson model. On the other hand, when the noise exists but the potential does not, an explicit form of the current is obtained, which scales as 1/N for large sample size N. Moreover, we provide an extension to higher dimensional systems. For a three-dimensional case, it is shown that the current increases in proportion to cross section and decreases in inverse proportion to the length of the sample.
