Quantum Lc-circuit satisfying the Schrodinger-Fisher-Kolmogorov equation and quantization of Dc-Pumped Josephson parametric amplifier

摘要

In this study, we have discussed the quantization of the electric LC-circuit based on the generalized Heisenberg's uncertainty relation. The new electric system is governed by the Schrodinger-Fisher-Kolmogorov equation where its Lagrangian and Hamiltonian structures are obtained. As an application, we have analyzed the DC-pumped Josephson parametric amplifier. Several new properties were analyzed and discussed accordingly.