中文摘要：

针对LC电路的实际情况提出了双耗散介观LC并联电路模型,并利用经典电路的基尔霍夫定律和阻尼谐振子的量子化方法对电路进行量子化。在电路模型量子化的基础上进一步讨论了双耗散LC介观并联电路在真空态下电感支路和电容支路中电流和电压的量子涨落,并分析耗散电阻RC和RL对两个支路中的量子涨落的影响。结果表明,两个支路的电流和电压的量子涨落不仅与LC电路的元件参数有关,而且受到耗散电阻的影响,它们都随时间按相同的指数规律衰减,但其系数在电流涨落中相同,在电压涨落中不同。当两个支路的耗散电阻相同时,即RC=RL,两个支路的电流涨落和电压涨落都相同。

英文摘要：

A mesoscopic parallel LC circuit model with double dissipative branch circuits is put forward according to the actual situation of the circuit.It is quantized with the theory of the classical circuit and the quantization method of damped harmonic oscillator.Then the quantum fluctuations of the voltage and the current of the circuit in vacuum state and the quantum fluctuations affected by the dissipative resistances are discussed.The results show that the quantum fluctuations of the voltage and the current of both branches are not only related with the parameters of the LC circuit components,but also affected by the dissipative resistances.They decay with the same exponential with time.The coefficients of the quantum fluctuations of the current are the same,while those of the voltage are different.When the two dissipative resistances are equal,the quantum fluctuations of the voltage and the current of both branches take on the same behavior respectively.