  In this thesis, we study two different aspects of many-particle physics. In
the first part, we study the Bose-Einstein condensation of microcavity
exciton-polaritons in different artificial lattices. Bose-Einstein condensation
is a quantum phase transition, which allows the system to macroscopically
occupy its ground state and develop coherence spontaneously. Often studied in
microcavities, which are optical cavities that trap light at specific
wavelengths, exciton-polaritons are a kind of quasiparticle arising from the
strong coupling between quantum well excitons and cavity photons. By
periodically aligning cavity pillars in different patterns, one can achieve
different artificial lattice structures. With this setup, we apply the
driven-dissipative Gross-Pitaevskii equations to investigate the different
consequences of the condensation by changing the pumping schemes and the design
of the trapping potentials. Topics include multivalley condensation, phase
selection and intermittency of exciton-polariton condensation, flat band
condensation, and exciton-polariton topological insulators. In the second part
of this thesis, we focus on the electron-scattering properties of a hybrid
Bose-Fermi system. We consider a system consisting of a spatially separated
two-dimensional electron gas layer and an exciton gas layer that interacts via
Coulomb forces. We study the temperature dependence of the system's resistivity
with this interlayer electron-exciton interaction and compare the results with
the electron-phonon interaction.
