Quantum Effect in a Diode Included Nonlinear Inductance-Capacitance Mesoscopic Circuit

The mesoscopic nonlinear inductance-capacitance circuit is a typical anharmonie oscillator, due to diodes included in the circuit. In this paper, using the advanced quantum theory of mesoseopie circuits, which based on the fundamental fact that the electric charge takes discrete value, the diode included mesoscopic circuit is firstly studied. Schrodinger equation of the system is a four-order difference equation in p rep asentation. Using the extended perturbative method, the detail energy spectrum and wave functions axe obtained and verified, as an application of the results, the current quantum fluctuation in the ground state is calculated. Diode is a basis component in a circuit, its quantization would popularize the quantum theory of mesoscopie circuits. The methods to solve the high order difference equation are helpful to the application of mesoscopic quantum theory.