arXiv subjects

Miztli Yepez

Publications and source records attributed to Miztli Yepez.

3 recordsLinked to original sources

arXiv2023

ELECTRON TRANSPORT AND ELECTRON DENSITY INSIDE ONE-DIMENSIONAL DISORDERED CONDUCTORS: An Analysis of the Electronic-Levels Contribution

We consider the problem of electron transport along a one-dimensional disordered multiple-scattering conductor, and study the electron density for all the electronic levels. A model is proposed for the reduced density matrix of the system placed between two reservoirs at different chemical potentials, and the statistical-mechanical expectation value of the electron density is evaluated. An ensemble average is computed over disordered configurations. We compare its predictions with computer simulations. We find that the contribution of low-lying levels is very different from that of the high-lying ones studied in the past. Going down in energy, the wave function penetrates ever less inside the sample. For high-lying levels, this is interpreted in terms of localization from disorder. For low-lying levels, this interpretation gradually gives way to an understanding in terms of the increasing reflection produced by each scatterer, which is seen by the electron as a higher and higher -- and hence impenetrable -- potential barrier. Indeed, the local-density-of-states, LDOS, is gradually depleted in the interior of the system, since the wave function is ever smaller inside. The problem studied here is also of interest in electromagnetic, thermal, and acoustic transport in disordered systems.

cond-mat.dis-nn↗

arXiv2017

Single-Parameter Scaling and Maximum Entropy inside Disordered One-Dimensional Systems: Theory and Experiment

The single-parameter scaling hypothesis relating the average and variance of the logarithm of the conductance is a pillar of the theory of electronic transport. We use a maximum-entropy ansatz to explore the logarithm of the energy density, $\ln {\cal W}(x)$, at a depth $x$ into a random one-dimensional system. Single-parameter scaling would be the special case in which $x=L$ (the system length). We find the result, confirmed in microwave measurements and computer simulations, that the average of $\ln {\cal W}(x)$ is independent of $L$ and equal to $-x/\ell$, with $\ell$ the mean free path. At the beginning of the sample, ${\rm var}[\ln {\cal W}(x)]$ rises linearly with $x$ and is also independent of $L$, with a sublinear increase near the sample output. At $x=L$ we find a correction to the value of ${\rm var}[\ln T]$ predicted by single-parameter scaling.

cond-mat.dis-nn↗

arXiv2015

Wave Transport in One-Dimensional Disordered Systems with Finite-Size Scatterers

We study the problem of wave transport in a one-dimensional disordered system, where the scatterers of the chain are $n$ barriers and wells with statistically independent intensities and with a spatial extension $ł_c$ which may contain an arbitrary number $δ/2π$ of wavelengths, where $δ= k l_c$. We analyze the average Landauer resistance and transmission coefficient of the chain as a function of $n$ and the phase parameter $δ$. For weak scatterers, we find: i) a regime, to be called I, associated with an exponential behavior of the resistance with $n$, ii) a regime, to be called II, for $δ$ in the vicinity of $π$, where the system is almost transparent and less localized, and iii) right in the middle of regime II, for $δ$ very close to $π$, the formation of a band gap, which becomes ever more conspicuous as $n$ increases. In regime II, both the average Landauer resistance and the transmission coefficient show an oscillatory behavior with $n$ and $δ$. These characteristics of the system are found analytically, some of them exactly and some others approximately. The agreement between theory and simulations is excellent, which suggests a strong motivation for the experimental study of these systems. We also present a qualitative discussion of the results.

cond-mat.dis-nn↗