Nonlinear effects in low-dimensional systems: graphene membrane and electron transport in semiconductor superlattices

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This PhD dissertation deals with two different topics: Mechanics of graphene from a statistical mechanics approach, where internal interactions and effects due to temperature are considered. And electron dynamics and chaos in semiconductor superlattices, where we aim at enhancing the chaotic behavior, with its applicability to random number generation in mind. It is not our purpose to bridge these two different topics. But we do believe that with the rise of nanotechnology and the ever-increasing interdisciplinary of science, studies where different topics are approached and discussed are highly desirable. Nanotechnology already rules our life. However, it is still surprising how much progress has been achieved without a fully understanding of the physics governing these structures. In particular, out-of-equilibrium behavior and non-linear responses are present in every nanostructure, but, sometimes, it is possible to avoid their effects at large time scales or small interactions. However, the increasing demand of better and/or new performances makes them sometimes unavoidable, or even, desirable. Micro-metric samples of graphene or semiconductor superlattices cannot be studied taking into account every microscopic interaction, which makes it necessary to use mesoscopic models with a certain range of validity. Throughout this work, we have tried to improve our understanding of the topics stated above, using mesoscopic physical models and techniques from statistical mechanics and dynamical systems. We hope that the obtained results will help the scientific community to gain insight into these fascinating topics and will motivate new research in this direction.
Mención Internacional en el título de doctor
Física del estado sólido, Física estadística, Nanotecnología, Semiconductores, Películas delgadas, Graphene, Semiconductor superlattices, Nonlinear electron transport
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