Quantum Effects In Mesoscopic Circuits

With the rapid development in microelectronics and nanotechnology, the electronic components in integrated circuits have reached to a mesoscopic scale, and the quantum effects in the circuits become more and more important. A quantum theory to 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 have been studied recently. However, the charge in the circuits is discrete, this character is seldom considered. A profound quantum theory about the mesoscopic circuits should consider the discreteness of the charge. In the framework of an improved quantum theory, the quantum effects in mesoscopic circuits are studied. The methods to deal with resistance phase, source phase, couple phase are proposed and applied to a mesoscopic device.The nonlear characters of mesoscopic circuits are firstly studied.Based on the discrete character of charge, the finite-differenced Schr?dinger equation of mesoscopic RLC circuit is achieved. The couple phase in the Schr?dinger equation could be eliminated with a unitary translation, and then the finite-differenced Schr?dinger equation becomes a standard Mathieu equation in p? -representation. Using the WKBJ method, Schr?dinger equation is solved, the stable energy spectrum and wave functions of the system are obtained, the average of currents and square of the current are calculated.With an appropriate formation of Hamilton, the quantization of a transient RLC mesoscopic circuit with source is performed, not only the transient finite-differenced Schr?dinger equation is achieved, but also the resistance phase problem in the equation is skillfully solved. With a unitary transformation, the finite-differenced Schr?dinger equation becomes a standard Mathieu equation in p? -representation. Using the WKBJ method, the energy spectrum and the wave functions of the system are obtained, the average of currents and square of the current are calculated.The Lagrange and Hamilton of the mesoscopic inductance and capacity coupling circuit are achieved. The couple phase in the Schr?dinger equation could be eliminated with a translation, and then the circuit is quantilazed with the finite-differenced Schr?dinger equation divided into two harmony equations. The Coulomb blockade effect, which is caused by the discreteness of electric charges, is studied. With the WKBJ method, Schr?dinger equations are solved, the currents quantum fluctuations and relationship of the two circuits are studied.The open electron resonator is a mesoscopic device that has attracted considerable attention due to its remarkable behavior-conductance oscillations. Based on anequivalent Hamilton of the device, the open electron resonator system is quantizated with the methods proposed by us. With a presentation transformation, the Schr?dinger equation becomes a standard Mathieu equation, and then the basal quantum character such as energy spectrum and wave functions of the system are obtained. Using WKBJ method, the average of currents and square of the current are calculated.In the case of the discreteness of the charge in mesoscopic circuits, the finite-differenced Schr?dinger equation is a Mathieu function in p? -representation, Mathieu equation is a typical nonlinear equation, and its stability character would be a new subject for the mesoscopic circuits. We firstly studied the stability of the open electron resonator and RLC circuits with a source, the stability and instability regions are discussed in a second approximate.The application of improved 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 a ubiquitous quantum noise in mesoscopic circuits. The deep researching works about these basal quantum characters would be benefit to the control of quantum noise and design of mesoscopic circuits.