Consistency of the Thomas-Fermi Potential from First Principles for Condensed Matter Systems

We proposed a formally exact, first-principles probabilistic method to assess the validity of the Thomas-Fermi approximation in condensed matter systems where electron dynamics is constrained to the Fermi surface. Our method, which relies on accurate solutions of the radial Schr\"odinger equation, yields the probability density function for momentum transfer. This allows for the computation of expectation values to be compared with unity. We applied this method to three {\it n}-type direct-gap III-V model semiconductors (GaAs, InAs, InSb) and found that the Thomas-Fermi approximation is certainly valid at high electron densities. In these cases, the probability density function exhibits the same profile, irrespective of the material under scrutiny. Furthermore, we show that this approximation can lead to serious errors in the computation of observables when applied to GaAs at zero temperature for most electron densities under scrutiny.Comment: 7 pages, 4 figures, typo corrected in Fig.1. This is the version of the article before peer review or editing, as submitted by an author to Electronic Structure (IOP Publishing Ltd). Preliminary results were presented at GW goes large-scale (GW-XL) Workshop in Helsinki and at International Workshop on Recent Developments in Electronic Structure (ES21), New Yor

Machine Learning S-Wave Scattering Phase Shifts Bypassing the Radial Schr\"odinger Equation

We present a machine learning model resting on convolutional neural network (CNN) capable to yield accurate scattering phase shifts in s-wave caused by different three-dimensional spherically symmetric potentials at fixed collision energy thereby bypassing the radial Schr\"odinger equation. We obtain good performance even in the presence of potential instances supporting bound states

The Role of bilinguals in the Bayesian naming game

We study the basic naming game model and the recently introduced Bayesian naming game model, in which the name learning processes are described more realistically within a Bayesian learning framework. We focus on the dynamics of the bilinguals population and show that in the Bayesian model the number of bilinguals is always lower with respect to the basic naming game model. We provide some analytical estimates of the upper bound for the number of bilinguals in both models and validate the estimate through extensive numerical simulations.Comment: 8 pages, 6 figure

The role of electron-electron scattering in spin transport for a GaAs semiconductor in the nondegenerate regime

We study the spin relaxation time in n-type GaAs. We focus on the role of the electron-electron scattering

Spin Relaxation in GaAs: Importance of Electron-Electron Interactions

We study spin relaxation in n-type bulk GaAs, due to the Dyakonov–Perel mechanism, using ensemble Monte Carlo methods. Our results confirm that spin relaxation time increases with the electronic density in the regime of moderate electronic concentrations and high temperature. We show that the electron-electron scattering in the non-degenerate regime significantly slows down spin relaxation. This result supports predictions by Glazov and Ivchenko. Most importantly, our findings highlight the importance of many-body interactions for spin dynamics: we show that only by properly taking into account electron-electron interactions within the simulations, results for the spin relaxation time—with respect to both electron density and temperature—will reach good quantitative agreement with corresponding experimental data. Our calculations contain no fitting parameters