Quantum fluctuations in capacitive coupled electric circuits at finite temperature

Using the thermal field dynamics, the quantum fluctuations in the capacitive coupled electric circuits at finite temperature are calculated. At zero temperature, the eigenstates of the capacitive coupled electric circuit are the displaced Fock states. At finite temperature, the states become the thermal displaced Fock states. The results show that in the coupling part of the circuit, the capacitance coupling reduces the quantum fluctuation of the electric charge and increases that of the electric current.