One-dimensional p-wave superconductor toy-model for Majorana fermions in multiband semiconductor nanowires

Majorana fermions are particles identical to their antiparticles proposed theoretically in 1937 by Ettore Majorana as real solutions of the Dirac equation. Alexei Kitaev suggested that Majorana particles should emerge in condensed matter systems as zero mode excitations in one-dimensional p-wave superconductors, with possible applications in quantum computation due to their non-abelian statistics. The search for Majorana zero modes in condensed matter systems led to one of the first realistic models based in a semiconductor nanowire with high spin-orbit coupling, induced superconducting s-wave pairing and Zeeman splitting. Soon, it was realized that size-quantization effects should generate subbands in these systems that could even allow the emergence of more than one Majorana mode at each edge, resulting in a zero bias peak on the differential conductance with a different shape from the predicted by simplified theoretical models. In this work, we provide a connection between a finite-size nanowire with two occupied subbands and a 2-band Kitaev chain and discuss the advantage of an one-dimensional model to understand the phenomenology of the system, including the presence of a hidden chiral symmetry and its similarity with a spinfull Kitaev chain under a magnetic field.Comment: 4 pages, 2 figures. IEEE Transactions on Applied Superconductivity accepted versio

Who benefits from reducing the cost of formality? Quantile regression discontinuity analysis

This paper studies the effects of increasing formality via tax reduction and simplification schemes on micro-firm performance. It uses the 1997 Brazilian SIMPLES program. We develop a simple theoretical model to show that SIMPLES has an impact only on a segment of the micro-firm population, for which the effect of formality on firm performance can be identified, and that can be analyzed along the single dimensional quantiles of the conditional firm revenues. To estimate the effect of formality, we use an econometric approach that compares eligible and non-eligible firms, born before and after SIMPLES in a local interval about the introduction of SIMPLES. We use an estimator that combines both quantile regression and the regression discontinuity identification strategy. The empirical results corroborate the positive effect of formality on microfirms' performance and produce a clear characterization of who benefits from these programs

Influencer: The Science of Leading Change. By Joseph Grenny, Kerry Patterson, David Maxfield, Ron McMillan, & Al Switzler

INFLUENCER: THE SCIENCE OF LEADING CHANGE. By Joseph Grenny, Kerry Patterson, David Maxfield, Ron McMillan, & Al Switzler. New York, NY: McGraw-Hill Education (2013). Paperback, 299 pages. The five authors demonstrated that true leadership has primarily to do with change. Being able to change personally and helping others to change are at the heart of true leadership. It was clear that anyone with the desire to influence others toward positive change is able to accomplish this. The key is in following the three main ideas undauntedly and consistently—focus and measure, find vital behaviors, and engage all six sources of influence—as closely as possible; in this you are almost always guaranteed success in influencing others to change

Approximate high energy alpha-particle nucleus collision model

Alpha particle-nucleus collision model for nucleon energy and angular distribution prediction and residual nuclei cross section