BERKANE Amina Enc/ MEDJEDEL Soheyb2025-02-242025-02-242025-02-19https://repository.univ-msila.dz/handle/123456789/46135This thesis conducts a comprehensive analysis of some important fundamental equilibrium properties of a harmonically confined two-dimensional electron gas subjected to a uniform perpendicular magnetic field. Using single-particle wave functions and Bloch density matrix method, we obtain exact analytical expressions for various local and integral properties, including particle density, current distribution, microscopic magnetization, total magnetic moment, and the integrated persistent current. We provide a direct deduction of the total persistent current from the orbital microscopic magnetization, emphasizing their inherent connection. Numerical investigation, concentrating on strong magnetic field regimes, uncovers well-defined compressible and incompressible regions within the particle density profile. We unravel the underlying structure of the counter-propagating equilibrium currents in high-field regimes, induced by the oscillatory behavior of microscopic magnetization, which we derive in exact analytical form in real physical space. Moreover, an examination of changes in the energy spectrum reveals intricate influences on these properties, resulting in quantum oscillation patterns at high magnetic fields.enOrbital microscopic magnetizationPersistent electric currentOrbital magnetism Particle densityTwo-dimensional electron gasQuantum oscillationThesis