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International Journal of Modern Physics B

GEOMETRIC PHASE IN A MESOSCOPIC LC CIRCUIT WITH ALTERNATING SOURCE

Yinghua Ji, Juju Hu, Qing Liu, Zou Dan

Published Dec 27, 2006• 0 citations
Publisher

Abstract

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.

DOI
10.1142/s0217979206035862

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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.
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 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.