The Thermodynamic Property For A Two-dimension Electron Gas In The Presence Of An Anisotropic Harmonic Oscillator Potential And A Constant Magnetic Field

The thermodynamic property for a two-dimension electron gas in the presence of theanisotropic harmonic oscillator potential and a constant magnetic field is studied in thisthesis.we consider the system of an electron moving in the anisotropic two-dimension chargedharmonic oscillator in the presence of a constant external magnetic field. First, we obtainthe exact expression of the propagator in the model by using the path integral method.Then applying this result to the Einstein model, we obtain the partition function of thesystem and calculate some thermodynamics physical quantities. Second, We investigatethe specific heat due to anisotropy and the magnetic field interaction for a quasi-two-dimensional Boltzmann gas in an elliptical parabolic quantum dot, and we discuss in detailefects caused by spin Zeeman interaction, varying temperature, anisotropy and magneticfield strength. Third, we mainly calculate the expression of the propagator of a electronwith an anisotropic harmonic oscillator potential in a constant magnetic field and a time-dependent electric field, Various special cases appearing in the literature can be obtainedby properly setting the values of the parameters in this results.