海森堡对应原理在含时介观耦合电路中的应用

Application of Heisenberg correspondence principle in the mesoscopic time-dependent coupled circuits

对于一般形式的含时电容和电感耦合电路,利用Heisenberg对应原理研究了体系的量子经典对应关系以及量子涨落。通过海森堡绘景中的波函数和运动方程的精确解,在大量子数极限下由量子解得到了经典解。对矩阵元中初始相位求平均得到了体系中电荷和磁通量的量子涨落。当电路中的电感随时间指数增加,而电容指数减小时,电路中的电荷和电流的量子涨落也随时间指数减小;当两个分回路中的电容和电感不随时间变化且相等时,发现耦合电容趋于减小电流的量子涨落,而耦合电感趋于减小电荷的量子涨落。

For the general time-dependent inductance-capacitance coupled circuits, quantum- classical correspondence and the quantum fluctuations are studied by using the Heisenberg correspondence principle. Through the wave functions and exact solution of equations of motion in Heisenberg picture, the classical solution is derived from quantum solution in the limit of large quantum numbers carrying out the average over the initial phase in the matrix elements, quantum fluctuations of the charges and magnetic fluxes are obtained. When the inductances in the circuit increase and the capacitances decrease exponentially with time, quantum fluctuations of the charge and current decrease exponentially with time; When the inductances and capacitances in the two component circuits are equal to each other and time-independent, it is found that the coupling capacitance tends to reduce the quantum fluctuations of the electric current and the coupling inductance tends to reduce the charge quantum fluctuations.