介观电容耦合电路中的库仑阻塞和量子涨落

The Coulomb Blockade and Quantum Fluctuations of Mesoscopic Capacity Coupling Circuits

在电荷取分立值这一基本事实基础上,对介观电容介观电路进行了量子化,得到了该电路的有限差分形式的薛定谔方程。介观电路的量子效应不仅来源于电路的量子化,还来源于电荷的量子化,只有在考虑了电荷的量子化性质之后才有可能讨论介观电路中的库仑阻塞效应。经过幺正变换,薛定谔方程变为两个标准的马丢方程,利用WKBJ近似方法,讨论了介观电容耦合电路中电流在基态中的量子涨落,这是介观电路中量子噪声的主要来源。

Using the quantum theory for a mesoscopic circuit based on the discreteness of electric charges, the finite-differenced Schrodinger equation of the non-dissipative mesoscopic capacity coupling circuit are achieved. The quantum effect not only comes from the quanumnization of circuit but also that of charge. Only after the properties of charge quanumnization is considered can the Coulomb blockade effect of a mesoscopic circuit be discussed. The Schrodinger equation can be divided into two Mathieu equations in p-representation. With the WKBJ method, the currents quantum fluctuations in the ground states of the two circuits are calculated. And the fluctuations are the main noise sources of quantum in the mesoscopic circuit.