Collective Dynamics Of The Electron Gas In Quantum Wells

In recent years, with the remarkable developments in nanotechnology, the low-dimensional quantum system has been widely used in laser, photoelectric device andquantum computer. There has been great interesting in studying the collective dynamicsof the particles in low dimensional quantum system (quantum well, quantum wires, quan-tum dots). However, the work focus on the collective dynamics of electron gas withoutexchange-correlation efect in an harmonic quantum well by far. Therefore, this papermainly studied the collective dynamics of electron gas with exchange-correlation efect inanharmonic quantum wells. The results of this paper have some guiding significance todeep-seated understanding the performance of the quantum-well-laser and the optoelec-tronic devices. The main contents and conclusions are as follows:Firstly, the concept of low-dimensional quantum system, the structures and applica-tions of quantum wells, and the exchange-correlation efect and quantum efect of electrongas in quantum wells are briefly introduced.Secondly, the collective dynamics of the electron gas in quantum wells are detailedlystudied in the following two chapters. In chapter II, within a quantum hydrodynamicmodel and using a variational method, the collective dynamics of the electron gas with theexchange-correlation efect in an anharmonic quantum well are studied both analyticallyand numerically. The two collective excitation modes, i.e. the dipole mode and thebreather mode, are obtained analytically. The frequency shift induced by the exchange-correlation, and the periodic collapse revival of the collective dynamics of the electrongas originating from nonlinear coupling between the two modes, are discussed. We foundthat the anharmonicity and the exchange-correlation efect are coupled, and the frequencyshift and the collapse revival of the collective excitations depend strongly on the numberof particles, the anharmonicity, and the quantum and exchange-correlation efects. Inchapter III, energy band structure and the current density of electron gas with exchange-correlation efect in the quantum wells are discussed. We can found that the energy bandcan show a swallowtail structure at the boundary of the first Brillouin zone only whenthe system with exchange-correlation efect and the average electron density smaller thana critical value, and the graphic of the current density show that electron gas tunnellingappeared in the quantum wells. Especially, the energy band structures are closely relatedto the current density of the system.Finally, we summarize the main results and give an outlook of the future in this field.