Number-phase quantization of a mesoscopic RLC circuit

With the help of the time-dependent Lagrangian for a damped harmonic oscillator, the quantization of mesoscopic RLC circuit in the context of a number-phase quantization scheme is realized and the corresponding Hamiltonian operator is obtained. Then the evolution of the charge number and phase difference across the capacity are obtained. It is shown that the number-phase analysis is useful to tackle the quantization of some mesoscopic circuits and dynamical equations of the corresponding operators.

交流源作用下介观串联RLC电路系统量子态随时间的演化

介观串联RLC电路系统在交流电压源的作用下,同时介观电容器极板间电子波函数的耦合作用和电路的耗散也考虑进来,由拉格朗日函数推导出系统的含时哈密顿量,根据量子不变量理论,系统的量子态将随时间演化到压缩态。分析结果表明,介观电路系统由任意的初态演化到一般的压缩态。