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College Physics

Time evolution of mesoscopic LC circuit under an alternating source

Zou Dan

Published Jan 1, 2006• 1 citation
OpenAlex

Abstract

The dynamical evolution of mesoscopic LC[WTBZ] circuit with alternating source is discussed by quantum invariant theory.The time evolution operator of the quantum state is obtained.Analytical results indicate that the system will evolve from initial state to squeezed state when the coupling effects from electron wavefunctions between mesoscopic capacitor plates are taking into account.

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Chinese Journal of Quantum Electronics•Jan 1, 2005•0 citations
The dynamical evolution of mesoscopic LC[WTBZ] circuit with alternating source is discussed by quantum invariant theory.The time evolution operator of the quantum state is obtained.Analytical results indicate that the system will evolve from initial state to squeezed state when the coupling effects from electron wavefunctions between mesoscopic capacitor plates are taking into account.
According to the LR invariant theory, the mesoscopic RLC circuit driven by a alternating current source was discussed. The mutual coupling of electron wave functions between the two plates of capacitor and the resistance of the circuit were taken into account. In our conclusion, the quantum states which dominate the dynamic property of the system and the time evolution operator of the mesoscopic circuit were obtained. The wave function of the mesoscopic RLC system will evolve from an arbitrary initial state to a generalized squeezed state.
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.
In this paper, we examine a mesoscopic LC circuit with alternating source and solve its time-dependent Schrödinger equation by selecting a proper Hermitian invariant operator. We study LR geometric phase in mesoscopic circuit system. Our results indicate that LR geometric phase is present at all times. In the evolution of the circuit system, it is a geometric phase factor accumulated by the wavefunction of external source's interaction with circuit system after nonadiabatic and noncyclic evolution. Its property lies in that it depends on the evolution path of the system wavefunction in the parameter space.
This paper studied the time evolution of quantum state in a mesoscopic LC circuit with the coupling energy caused by mesoscopic capacitor acting as a tunnel junction. It indicates that the state of the junction evolves into the quantum superposition of two coherent states and, in the state, nonclassical squeezing properties of the circuit appear. It also indicates that the dynamic behavior of the current shows collapse and revival phenomenon. The research in the paper will be helpful to miniaturize integrate circuits and electric components. It will be also important for the utilization of mesoscopic circuits to evolve the quantum states, which work as information carriers.