有源LC介观电路的量子效应

Quantum Effect in the Mesoscopic LC Circuits with a Source

在电荷不连续的前提下,利用介观电路的量子化方法,得到了有源介观LC电路的有限差分薛定谔方程.通过么正变换,系统的薛定谔方程转化为标准的马丢(Mathieu)方程的形式,在WKBJ近似下,计算了系统的能谱和电流的量子涨落.

Based on the fundamental fact that the electric charge takes discrete value, the finite-differenced Schroedinger equation of the mesoscopic LC circuit with a source is achieved. With a unitary transformation, the Schroedinger equation becomes the standard Mathieu equation. 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 results show the existence of the current fluctuation, which cause the noise in the circuits.