Studies On The Quantum Properties Of Mesoscopic Electric Circuit

Firstly, considering the charge's quantum character, this paper demonstrated the single electron tunnel process through a niesoscopic capacitor and studied the coulomb blockade effects in a niesoscopic electric circuit. Then we mainly investigated the single electron tunnel process and the coulomb blockade phenomenon in the mutual inductance circuit.Secondly, based on the existing quantum theories, we more studied the quantum character of the mesoscopic capacitor, i.e. the weak coupling effects. Because of the space between the two electrodes of a capacitor is very small (it's about several nm), then a weak coupling can be produced through the proximity effect of the normal metal electrons of the two electrodes of a mesoscopic capacitor. We think about the coupling effects of it, and bring forward the coupling energy that it is the function of the phase difference as the charge tunneling through the niesoscopic capacitor. Then we find that the energy of the system comprise not only the electromagnetic energy, but also the capacitor's coupling energy. The results show that: At absolute zero temperature the niesoscopic circuit system will evolve into squeezed state from the first quantum state with the influence of the coupling effects of the capacitor. We also calculated the quantum fluctuation of both charge and flux in the time evolved quantum state, and studied the quantum characters of tunneling current in the mesoscopic circuit.Thirdly, we studied the quantum effects of the mesoscopic RLC circuit from the original vacuum state due to the dissipative and the capacitor's weak coupling effects and investigated the infection of the quantum effects in the thermal Kerr state of mesoscopic LC circuit owing to the thermal effect of the environment.Finally, considering the effect of the non-linear components in mesoscopic circuit. We investigated the quantum effects of the mesoscopic LC circuit with a non-linear diode.