The evolution of quantum state with time in the mesoscopic RLC parallel circuit is studied. The results indicate that the system will evolve from the vacuum state to the squeezing state for RLC circuit.
According to the LR invariant theory, the mesoscopic RLC circuit driven by a alternating current source was discussed. The mutual coupling of electron wave functions between the two plates of capacitor and the resistance of the circuit were taken into account. In our conclusion, the quantum states which dominate the dynamic property of the system and the time evolution operator of the mesoscopic circuit were obtained. The wave function of the mesoscopic RLC system will evolve from an arbitrary initial state to a generalized squeezed state.
The quantum fluctuations of the voltage and the current in each branch of the quantized generalized mesoscopic RLC parallel circuit in squeezed vacuum state were studied.The factors affecting the fluctuations in each branch were also analyzed.The results show that the quantum fluctuations in each branch of the circuit in squeezed vacuum state are related to the factors which are the elements of the circuit,the parameters of the squeezed vacuum state and the time.All the quantum fluctuations of the voltage and the current in each branch of the circuit decay with time exponentially.The decay rates are related to the elements of the circuit only,not to the parameters of the squeezed vacuum state.The amplitude of the fluctuations at the initial stage depends on the elements of the circuit and the parameters of the squeezed vacuum state.