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With the development of nanoelectronics, the trend of miniaturization of circuits and devices is becoming more and more intense. When the electron transport scale reaches the scale of twice inelastic collision of electrons, the quantum effects of devices and circuits must be considered. At present, the research on the quantum effect of circuits and devices has become one of the hot issues in mesoscopic physics research. For the quantum fluctuation of the current and the voltage across the inductor in the thermal vacuum state, we can obtain the mean value and the square mean value of the current and voltage in the inductance branch. Therefore, we can obtain the quantum fluctuation of the current and the voltage across the inductor. In order to obtain the quantum fluctuation of the current fluctuation of the voltage fluctuation in the 2.3-capacitance branch, we can immediately obtain the current flowing through the capacitor and the voltage across the capacitor. Quantum fluctuations are the fluctuation products. We get the vacuum fluctuations of the capacitance branch to the vacuum fluctuation product. The quantum fluctuation of the current and voltage of each branch is related to the parameters of the circuit device and the temperature. In this paper, starting from the classical equation of motion, the parallel LC circuit is quantized, and on this basis, the quantum fluctuations of the currents and voltages of the branches in the thermal vacuum state are studied. The results show that there are quantum fluctuations in each branch of the LC parallel circuit in the hot vacuum state. The quantum fluctuation of current and voltage of each branch is not only related to the parameters of the circuit device, but also related to the temperature. As the temperature T increases, the quantum fluctuation increases. The actual circuit always operates at a finite temperature, so it is very important to study the quantum effect of the LC circuit at a finite temperature. From the discussion of this paper, we can see that properly adjusting the parameters of the device can control the quantum noise of the circuit. This has certain guiding significance for the design and application of the mesoscopic circuit.
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