İki-boyutlu seçilmiş sistemlerde çok-parçacık etkileri

In this thesis we study many-body effects in three distinct two-dimensionalsystems. The two dimensional electron gas is a model system yielding to basicanalytical and computational theoretical ideas of many-body physics and at thesame time allows faithful experimental realizations. In connection to the recentlyobserved metal-insulator transition in this system, the spin susceptibility is arelevant observable. The behavior of the spin polarization in a parallel magneticfield is studied using a parametrized ground-state energy expression from accuratequantum Monte Carlo simulations and compared with approximate theories. Thecritical field to fully polarize the system is calculated. A qualitative differencefor the ferromagnetic transition is found for an interval of density values. Next,we consider exciton condensation in an electron-hole bilayer system with densityimbalance. Electrons and holes attracting via Coulomb interaction pair up toform spatially separated excitons and condense at low temperatures. Using meanfieldtheory we establish the phase diagram at zero temperature for differentelectron and hole densities by comparing the energy of the normal phase withthat of the condensed phase. In the last chapter, the two-dimensional Bose-Fermiatomic gas mixture which is composed of a condensed boson component and aspin polarized Fermi component at zero temperature is studied. Confinementin the third direction affects the density profiles and can induce collapse of themixture and spatial separation of components.