The Generalized Hellmann-Feynman Theorem Approach to Quantum Effects of Mesoscopic Complicated Coupling Circuit at Finite Temperature

Abstract

By employing the generalized Hellmann-Feynman theorem, the quantization of mesoscopic complicated coupling circuit is proposed. The ensemble average energy, the energy fluctuation and the energy distribution are investigated at finite temperature. It is shown that the generalized Hellmann-Feynman theorem plays the key role in quantizing a mesoscopic complicated coupling circuit at finite temperature, and when the temperature is lower than the specific temperature, the value of \((\vartriangle {\hat {H}})^{2}\) is almost zero and the values of \( _{e} \) and \((\vartriangle \hat {{H}})^{2}\)are basically constant, but while the temperature rises to the specific temperature, both of them move upward rapidly. The energy fluctuation of the system becomes larger when the coupling inductance is larger or the coupling capacitance is smaller.