Abstract
The quantization of mesoscopic complicated RLC circuits involving inductance coupling is proposed. The time evolution is investigated by employing multiple unitary transformations. The quantum fluctuations of charge and current of each loop are calculated in vacuum state and evolving state. It is shown that the quantum fluctuations of charge and current in evolving state are independent of sources and only rely on inherent parameters of the circuit. And the uncertainty relations do not satisfy the uncertainty principle, except when the resistances become zero.
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