We consider the problem of electron transport across a quasi-one-dimensional disordered multiply scattering medium and study the statistical properties of the electron density inside the system. In the physical setup that we contemplate, electrons of a given energy feed the disordered conductor from one end. The physical quantity that is mainly considered is the logarithm of the electron density, $ln\mathcal{W}\left(x\right)$, since its statistical properties exhibit a self-averaging behavior. We also describe a gedanken experiment as a possible setup to measure the electron density. We study analytically and through computer simulations the ballistc, diffusive, and localized regimes. We generally find a good agreement between the two approaches. The extension of the techniques that were used in the past to find information outside the sample is done in terms of the scattering properties of the two segments that form the entire conductor on each side of the observation point. The problem is of interest in various other branches of physics, such as electrodynamics and elasticity.

中文翻译：

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准一维无序导体内的电子传输和电子密度

我们考虑了电子在准一维无序多重散射介质中的传输问题，并研究了系统内部电子密度的统计特性。在我们设想的物理设置中，给定能量的电子从一端向无序导体供电。主要考虑的物理量是电子密度的对数，$ln\mathcal{w\; ^}（X）$，因为它的统计特性显示出自平均行为。我们还将gedanken实验描述为一种测量电子密度的可能设置。我们通过计算机模拟进行分析研究，并研究弹道，扩散和局部状态。我们通常会在两种方法之间找到很好的协议。过去用于在样品外部查找信息的技术的扩展是根据形成观察点两侧的整个导体的两个部分的散射特性来完成的。该问题在物理的其他各个分支中都引起关注，例如电动力学和弹性。