The Quantization And The Quantum Effects Of The Mesoscopic Circuits

This thesis is mainly about the basic mesoscopic circuits and those in which the superconducting Josephson junctions are included. Their quantization and quantum effects have been explored. To explore the quantization methods and to find the quantum fluctuation of the physical quantities are to provide guidance, to lower the noise and the resource degradation to enhance the efficiency. The main contents are as follows:1. The quantization and the quantum fluctuation of the passive mesoscopic LC circuit are investigated. We choose the flux as the generalized coordinate to calculate the Lagrangian function. Using the Dirac’s quantization method, the Hamiltonian operator and the quantum fluctuation are obtained.2. The quantization and the quantum fluctuation of the mesoscopic LC circuit with the time-varying sourse are investigated. We choose the flux as the generalized coordinate to calculate the Lagrangian function. Using the Dirac’ quantization method, the Hamiltonian operator and the coherent state’s corresponding quantum fluctuation are obtained.3. The quantization and the quantum fluctuation of the passive capacitance coupled mesoscopic LC circuit are investigated. Using the Dirac’ quantization method, the Hamiltonian operator are obtained, then it is diagonosed via a unitary operator and the corresponding quantum fluctuation is analyzed.4. The energy level transition’s selection rules of the mesoscopic capacitance coupling LC circuit with the time-varying sourse are studied. Using the Dirac’ quantization method, the Hamiltonian operator are obtained.Then utilizing the IEO method, we have given the sistem’s energy level transition’s selection rules under the external field’s effect.5. The quantization and the quantum fluctuation of the passive inductance coupling mesoscopic LC circuit are given. Using the Dirac’ quantization method, the Hamiltonian operator are obtained. Considering the low energy level on two sides of the LC circuit,we utilize the two-state approximation and base on the direct product of the two particles’ state to write out the matrix form of the Hamiltonian operator. Then we give the eigenvalues, the eigenvectors and the corresponding fluctuation.6. The J-C model’s application in the Josephson junction mesoscopic circuit is studied. The system’s Hamiltonian is given and quantized. After the two-state approximation, based on the J-C model, the matrix form and the eigenvalues, the eigenvectors are given. At last, we have studied the interaction’s impact on the uncoupled system’s energy degeneracy in the case of resonance.