Study On The Quantum Fluctuation Properties Of The Charge And The Current In Nanometer Circuit With Source

With the development of the microelectronics, the nanotechnology and the nano-electronics, the trend in the miniaturization of circuits and devices towards atomic scale dimension becomes strong and definite. When the propagation scale of the system reaches the coherence length of the electron, quantum effects, such as the Coulumb blockade, the universal conductance fluctuations and the quantum fluctuations of current, would be found. Quantum fluctuations of current in the nanometer circuit has become the important question in the field of the quantum optics.In this thesis, based on the fact that the charge is quantized in a nanometer circuit, quantum fluctuations of the current in nanometer circuit with source is investigated by all quantum theories. Namely, starting from the classical motion equation of the nanometer circuit, the Schr?dinger equation of the circuit is achieved by the method of the canonical quantization, and then the equation is transformed into the standard Mathieu equation. Finally, the energy spectrum and the quantum fluctuation of the current in the system are calculated. The circuits are devised into the dissipative circuit and the non-dissipative circuit based on the fact that if there is dissipation in the circuit. The energy spectrum and the quantum fluctuations of the current in the dissipative non-coupled nanometer circuit of two meshes with source and the dissipative coupled nanometer circuit of two meshes with source are calculated for the dissipative circuit; for the non-dissipative circuit, the general method to deal with the quantum fluctuations of the current in the non-dissipative coupled nanometer circuit of any meshes with source is achieved by using the theory of quadratic form and the all quantum theories.