鉴于介观RLC电路中的电流要产生焦耳热,应考虑有限温度下的电路量子效应。 对于处在热环境中的平衡态,任何力学量的期望值可由系综平均表示。 在此基础上,利用有序算符内积分技术,首次求出介观RLC电路所对应的热真空态,最后,借助于 理论计算,储存在LC 元件与消耗在R元件上的系综平均能量可由热真空态的纯态期望值来代替。

Because the current of quantized mesoscopic RLC electric circuit can produce the Joule heat, quantum effects should be taken into account at finite temperature. In the equilibrium state of thermal environment, expected value of any mechanical quantity can be described by the ensemble average energy. Furthermore, using the technique of integration within ordered product(IWOP) of operator, the thermo-vacuum state was obtained in a quantized mesoscopic RLC electric circuit for the first time. Finally, by means of theoretical calculation, expected value of pure state at thermo-vacuum state was used to replace the ensemble average energy stored in the LC element and consumed in the R element.