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Description
The goal of this project is to describe the hydrodynamic properties of electrons inside certain recently discovered materials, usually called topological semimetals. What is peculiar about the flow of electrons inside these materials, is the fact that exotic quantum effects allows to transport electrons inside a wire made of this material without loosing energy. The understanding of such properties will settle the ground for the design of more efficient devices to store energy, and might serve for the construction of quantum computers. The origin of such exotic properties relies on certain similarities of the mathematical models describing the physical properties of the electrons inside the material and the ones describing the interaction of highly energetic particles. In some sense, learning about the properties of such materials will provide us not only with important technological advances, but will help us acquire a deeper understanding of the fundamental laws of physics responsible for the structure of our universe. Based on the similarities to the relativistic subatomic particles, we propose in this project to apply these techniques in the description of those apparently disconnected systems, like electrons inside a material. Within these tools we will use the holographic principle which relates black holes with the dynamics of quantum particles in hydrodynamic regime. The holographic principle, usually called gauge/gravity duality, surprisingly relates the dynamics of the events horizon of a black hole with the theories of fluid dynamics. In other words, black holes behaves as a fluid. In particular, holography becomes a useful tool when the interaction between particles is so strong, that all the standard computational techniques fail. Finally, with this project we expect to predict the existence of new electronic transport properties in topological materials, and settle the ground for important technological advances in electronics.