Green's Function Approach to Quantum Dynamics in Two-Dimensional Electron Gases at High Magnetic Fields

We develop a Green's function framework based on a coherent-state basis in order to study the electronic dynamics in two-dimensional electron gases under high perpendicular magnetic fields. This formalism allows us to analytically incorporate the effect of an arbitrary smooth potential energy and compute microscopic observables under the form of local functionals, which can then be analyzed for different temperature regimes. In the first part of this talk, we show that the framework can be extended to incorporate the effect of spin-orbit interaction of the Rashba type. In the second part, we will give a hint of how we can start the generalization of the Green's function formalism to include the effect of strong electron-electron interactions. To that purpose, the notion of bicomplex numbers is introduced and we prove that in this way we can incorporate a new type of topological (electronic) correlations by means of a non-Euclidean metric.