Use The Theory Of Generalized Linear Quantum Transformation Solving Quantum Effects In Mesosopic RLC Circuit

At present, the electronic components in integrated circuits has approached to the atomicmagnitude and reached to a mesoscopic scale, therefore quantum effects in circuits anddevices need to be considered. Since Louisell achieve quantization of mesoscopic circuit byanalogizing to quantization of classical harmonic oscillator[1], the quantum effects ofmesoscopic circuits under different circumstances have been studied with quantum methodsand substantial progress has been made[2-34], but it still has a certain distance to establish ageneral theory of mesoscopic circuit. The generalized linear quantum transformation theory isused to study the mesoscopic circuit, this method is simple and convenient and generallyapplicable.Mesoscopic RLC circuit with a source and mesoscopic inductance coupling circuit withalternating current power are studied; in the first system, analogizing Peng Huan Wu’smethod[35],regularization transform is used for quantization of the system, the expectationsand quantum fluctuations of current and voltage across components are given, thecharacteristic that the resistance inducing quantum noise approaching zero is discussed; in thesecond system, generalized linear quantum transformation theory is used to decouple thesystem, then the expectations and quantum fluctuations of charge and current are calculated.Generalized linear quantum transformation theory is applied to dissipation circuits andcoupling circuits, and it has no requirements to power supply or initial state, therefore it canbe extended to general mesoscopic RLC circuit and become a general theory, which is worthyfor in-depth study. The results provide a certain reference value on the application of themesoscopic circuit system, and have some practical guiding significance to designing tinycircuits and driving down the influence of quantum noise.