分回路中有电阻时电感耦合电路的量子涨落

Quantum Fluctuations in a Damped Inductive Coupled Electric Circuit

根据电阻产生的物理机制,即电子与声子的相互作用对两分回路中均有电阻的电感耦合电路进行了量子化,给出了分回路及耦合部分的量子涨落和电路中的参数与环境温度的关系.电感耦合可以降低电流的量子涨落,但是使电荷的电子涨落增大.与无耗散的电路类似,电源影响电荷和电流的大小,但不影响电荷和电流的电子涨落.以往从电荷的经典运动方程出发,通过变量代换的正则量子化方法,相当于将这里高温极限的结果应用到了低温情况.

According to the physical mechanism of the generation of resistance or the interaction of electrons with phonons, the inductivecoupled electric circuit was quantized when there exist resistances in the component circuits. Relations of the quantum fluctuations in the component circuits and the coupling part with the parameters of the coupled circuit and the environmental temperature were given. Inductance coupling can reduce the quantum fluctuations of the electric currents, but will increase the quantum fluctuations of the electric charges. Similar to the electric circuit without resistance, electric sources affect the amount of the electric charge and current, but do not affect their quantum fluctuations. The former canonical quantization method, which starts from the classical equation of the electric charge and makes some transformations, this corresponds to applying the result of high temperature limit to the lower temperature case.