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Acta Physica Sinica

Time evolution of mesoscopic RLC circuit driven by an alternating current source

Qing Liu, Zou Dan, Ji Ying-Hua, (1)江西师范大学物理与通信电子学院,南昌 330022; (2)江西师范大学物理与通信电子学院,南昌 330022;井冈山学院物理系,吉安 343009

Published Jan 1, 2006• 2 citations
Publisher

Abstract

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.

DOI
10.7498/aps.55.1596

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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.
The dynamical problem of a mesoscopic RLC circuit with a source ruled by a time-dependent Hermitian Hamiltonian is exactly solved by algebraic method. The dynamical variations of the charge and current in a mesoscopic RLC circuit with a dc or ac source are studied in detail. In particluar, we have shown that squeezed coherent states of light field can be generated in a mesoscopic RLC circuit driven by an external source, although their quantum statistical properties are not dependent of the external source.
The exact solution of time evolution operator was obtained by applying the gauge transform of algebra dynamics.Such an operator describes the quantum state of time dependence of mesoscopic RLC circuit containing voltage source.The charge and current zero-state response of the import voltage signal in mesoscopic RLC circuit were acquired.The result shows that the system of mesoscopic RLC circuit has linear time invariant feature,and the response in mesoscopic RLC circuit is the same as that,in the macroscopic RLC circuit.