Features of Rashba-coupled Fermi gases, master equations and memory effects
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The first part of this thesis studies interactions in Rashba-coupled Fermi gases. The main objective of this part of the thesis consists of proposing a model to describe dilute Fermi gases. Recent theoretical works propose to use Rashba spin-orbit-coupled systems by means to enhance superconductivity, topologically protected insulators, or quantum computing. The richness and potential of Rashba-coupled Fermi systems has been proved with currently ongoing experiments with cold atoms and synthetic gauge fields, which allow to simulate neutral particles using laser fields. In this part of the thesis, we conclude that it is possible to describe dilute Rashba-coupled Fermi gases with a model that has meaningful predictive power. In the second part of the thesis we analyse the validity of the master equation approach to describe open quantum systems. Using a Jaynes-Cummings Hamiltonian we show that under certain circumstances, the master equation approach does not fully describe the effect of the environment onto the system, hence additional tools are needed.