Application Of The Quantum Invariant Method In The Mesoscopic Circuit

With the development of technology, the size of the macro circuits become smaller and smaller. The size achieve the mesoscopic scale, we call them the mesoscopic circuit. Mesoscopic circuit show the quantum mechanical effects. When design microcircuit, we have to take into account of the quantum mechanics effect of mesoscopic circuit. The practice urgent requirements the development of the theory, so studying the quantum mechanical effects of the mesoscopic circuit and establishing the mesoscopic circuit theory of quantum mechanics are very urgent. For time-dependent microscopic system, path integral method and the quantum invariant method are two main methods. To more complex mesoscopic circuit, path integral method is difficult to calculate the propagator and wave function. Quantum invariant method has some relative advantage.In this paper, on the basis of the mesoscopic time-dependent L(t)C circuit, by using the quantum invariant method and introducing external power related with parameters and the auxiliary equation, we calculate the mesoscopic including source L(t)C circuit of quantum invariant operator. By unitary transformation, we got the wave function and the phase factor of the system. By defining the phase factors associated with resistance, we realized the quantization of the Mesoscopic time-dependent R(t)L(t)C circuit. For mesoscopic including source R(t)L(t)C circuit, by introducing foreign related parameters and the auxiliary equation, defining the phase factors associated with resistance, we got the quantum invariant operator of the system and solved the system under arbitrary exogenous wave function and the phase factor of general representation.In this paper, applicating the result, we solved the mesoscopic inverse square potential L(t)C circuit, found that the quantum invariant operator is same with the mesoscopic time-dependent L(t)C circuit, even accordanced with the previous results. Then we got the wave function of mesoscopic ac source R(t)L(t)C circuit system, and calculated the quantum coherent states and quantum fluctuation of system, found that the quantum invariant operator and wave function were same with the mesoscopic source containing R(t)L(t)C circuit.The results of the theory and method in this paper have certain guiding significance to design microscopic circuit and preparate and regulate quantum state.