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Applied Physics Research

Evolution of Quantum State in the Mesoscopic LC Circuit Driven by a Time Dependent Source

Xiaojian Xia

Published Jan 31, 2012• 3 citations
Publisher

Abstract

We obtained the exact solution of time evolution by applying the Wei-Norman method.The quasi-probability distribution function of phase space is used to investigate the quantum state of the mesoscopic LC circuit in coherent state. The results show that the function of the system is the two dimensional motional gauss wave-packet. The centre charge and flux of the wave-packet vary with cosine and sine wave.

DOI
10.5539/apr.v4n1p241

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We obtained the exact solution of time evolution by applying the Wei-Norman method.The quasi-probability distribution function of phase space is used to investigate the quantum state of the mesoscopic LC circuit in coherent state. The results show that the function of the system is the two dimensional motional gauss wave-packet. The centre charge and flux of the wave-packet vary with cosine and sine wave.
The exact solution of time evolution operator is obtained by applying the gauge transform of algebra dynamic.Such an operator describes the quantum state of time depen- dence of mesoscopic LC circuit containing voltage source.The coherence of quantum state of mesoscopic LC circuit is taken into account.The result showed that the probability of charge stored in capacitor is a motional Gauss wave-packet.The relation between centre charge of wave-packet and voltage source is given.The special example in which the circuit is driven by single rectangle pulse is investigated.
The authors took the LC circuit as an example to discuss the relationship between the time evolution formula for the charge mean value in mesoscopic circuit and the Kirchoffs law,put forward the equation satisfying the wave function of coherent state,the wave function of coherent state of LC circuit and the quasi-classical wave function satisfying the Schrdinger equation,the current intensity,the quantum fluctuation and the quantum phase,and discussed the motion characteristics of wave packet.
The exact solution of time evolution operator was obtained by applying the gauge transform of algebra dynamic. Such an operator describes the quantum state of time dependence of mesoscopic LC circuit containing voltage source. The zero-state response in mesoscopic LC circuit was researched, and the charge and current zero-state response of the import signal were also acquired. The result showed that the system of mesoscopic LC circuit has linear time invariant feature, and the response in mesoscopic LC circuit is the same as in the macroscopic LC circuit.