Dinámica de sistemas desordenados y vórtices

Abstract

Dynamical simulations are powerful tools for the study of many physical systems. From condensed matter physics we exploit these techniques to expand our comprehension of the time response of many materials. In this work we use these techniques to study the dynamics of vortices driven by an external current through a two-dimensional Josephson Junction Array. Specifically, we try to find the maximum velocity for the stability the vortices can reach depending on the system parameters and what happens beyond the point of instability. We found velocity profiles in function of the Josephson Junction Array parameters. We discover that discrete velocity jumps take place because of the generation of cascades of vortex-antivortex pairs. Also, we show a phase diagram that characterizes the different dynamic regimes we can find for a moving vortex through a Josephson Junction Array. In this work, we study the dynamics of disordered electron systems. Our first objective was the interactive case. In this case, we study Efros-Shklovskii’s law, which takes place when the Coulomb interaction governs, and the activated regime, which takes place when the interaction is approximately logarithmic. During the development of this work, we realize that it was convenient first to look into the non-interactive case and to investigate Mott’s three-dimensional law. We carry out the most advanced simulations for the electrical conductivity of three-dimensional disordered non-interacting systems at low temperatures through the Monte Carlo method. We obtain the most reliable values for the characteristic temperatures. We find slight differences from Mott’s original law. We also take finite size and microscopical measurements that inform us regarding the conductivity structure. We perform random resistor network simulations that allow us to go to lower temperatures. We can deduce Mott’s law from a new theoretical model based on percolation theory, which allows us to go to beyond leading order. We simulate conductivity in the non-interactive two-dimensional case, the interactive three-dimensional case, and the two-dimensional activated regime. We suggest the best parameters we can currently obtain from simulations in each of these three cases.