Analysis Of Mesoscopic Circuit With Path Integrals

In general, the mesoscopic system means a physical world which is realized between microcosmic and macroscopic physics. The macrossopic and microcosmic system can be interpreted effectively. At the mesoscopic level, though the system contains a large number of particles, but the average properies which obey the laws of classical statistical mechanics is affected by quantum fluctuations. This situates the mesoscopic systems at the interface of statistical mechanics and quantum mechanics.When the components in circuits are miniaturized to a mesoscopic scale, the quantum effects in the circuits must be taken in account. The open electron resonator is a mescoscopic device that has attracted considerable attention due to its conductance periodcal fluction with gate voltage. Using the path integrals, the open electron resonator is studied. With this approach, the quantum wavefunction are obtained. The quantun fluctuations of charge and current as well as the uncertainty ralation are given. For the mesoscopic RLC coupling circuits, the couple phase in the Hamilton could be eliminated by a unitary transformation. Then the couple system is equivalent to two indepent harmonic osillator. By using the path integrals, the quantun fluctuations of charge and current are obtained.If the diode is included in the mesoscopic circuits, the system acquires a nonlinear characteristic. Based on the discrete character of charge, the finite differenced Schrodinger equation of the system is obtained. In momentum representation, the Schrodinger equation becomes a four order difference equation. With the extended perturbative method, the energy spectrum and wave functions are obtained. As an application, the fluctuation of current in the ground state is calculated.