The nonlinear capacitor that obeys of a cubic polynomial voltage–charge relation (usually a power series in charge) is introduced. The quantum theory for a mesoscopic electric circuit with charge discreteness is investigated, and the Hamiltonian of a quantum mesoscopic electrical circuit comprised by a linear inductor, a linear resistor and a nonlinear capacitor under the influence of a time-dependent external source is expressed. Using the numerical solution approaches, a good analytic approximate solution for the quantum cubic Duffing equation is found. Based on this, the persistent current is obtained antically. The energy spectrum of such nonlinear electrical circuit has been found. The dependency of the persistent current and spectral property equations to linear and nonlinear parameters is discussed by the numerical simulations method, and the quantum dynamical behavior of these parameters is studied.

中文翻译：

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由线性电感器、线性电阻器和非线性电容器组成的介观驱动 RLC 电路的量子动力学

介绍了服从三次多项式电压-电荷关系的非线性电容器（通常是充电的幂级数）。研究了具有电荷离散性的介观电路的量子理论，表达了由线性电感器、线性电阻器和非线性电容器组成的量子介观电路在时变外源作用下的哈密顿量。使用数值求解方法，找到了量子三次 Duffing 方程的良好解析近似解。在此基础上，仿古获得持续电流。已经发现了这种非线性电路的能谱。通过数值模拟方法讨论了持续电流和光谱特性方程对线性和非线性参数的依赖性，