Quantum fluctuations of mesoscopic RLC circuit with sources and time-dependant resistances

Abstract

We discuss the quantization of two mesoscopic coupled RLC circuits with sources and a time-dependent resistances. We use unitary transformations to decouple the system and calculate the charge-current fluctuations for each loop. An adequate time-dependent form of resistances is used to simplify the quantum evolution of the system. We find that the charge-current fluctuations verify the Heisenberg principle and decrease when the time elapses.