Quantum Effects In Mesoscopic Circuits

With the rapid development in the nanotecchnoology and microelectronics, the electronic device in integrated circuits has reached to a mesoscopic scale, the quantum effects in the circuits become more and more important. A quantum theory to the mesoscopic circuits is demanded eagerly in the experiment and manufacture. Comparing with the quantization of a harmony, the quantum effects in the fundamental mesoscopic circuits are studied. However, the charge in the circuits is discrete, this fact is seldom considered. A whole quantum theory about the mesoscopic circuits should consider the discreteness of the charge. In recent years, the whole quantum theory and its application in mesoscopic circuits is setting up.In the framework of a whole quantum theory, the quantum effects in mesoscopic circuits is studied.Based on the fundamental fact that the charge takes discreteness value in the mesoscopic circuits, The quantization of a RLC mesoscopic circuit and RLC mesoscopic circuit with a source are performed respectively, With a unitary transformation, the finite-differenced Schrodinger equation becomes the standard Mathieu equation, then the energy spectrum and the wave functions of the system are obtained. Using the WKBJ method, the average of currents and square of the current are calculated, the results show the existence of the current fluctuation, which cause the noise in the circuits.The quantization of mesoscopic circuits is not only consists of the circuits but also the charge, Coulomb blocked effect is a significant certification. The whole quantum theory for mesoscopic circuits successfully explained this important phenomenon in experiment. The application of whole quantum theory to mesoscopic circuits can give the energy spectrum and the wave functions of the system. Furthermore the current fluctuation could be calculated, which is the main quantum noise in mesoscopic circuits. The deep researching works would be benefit to the control of quantum noise and design of mesoscopic circuits.