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Advances in engineering research/Advances in Engineering Research

Exact Wave functions of Time-dependent Mesoscopic LC Circuit with an External Power Source

Zhanyuan Yan, LI Chun-qiang, Gao-qing Meng, MA Jin-ying

Published Jan 1, 2015• 0 citations
Publisher

Abstract

Quantization of the mesoscopic circuit with an external power source has been studied in this paper.The exact quantum invariant and wave function of the time-dependent mesoscopic LC circuit with an external power source, has been obtained via the field invariant method.The auxiliary functions in the quantum invariant operator and wave function corresponds to the external power source in the Hamiltonian of the mesoscopic circuit.

DOI
10.2991/ipemec-15.2015.52

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Quantization of the mesoscopic circuit with an external power source has been studied in this paper.The exact quantum invariant and wave function of the time-dependent mesoscopic LC circuit with an external power source, has been obtained via the field invariant method.The auxiliary functions in the quantum invariant operator and wave function corresponds to the external power source in the Hamiltonian of the mesoscopic circuit.
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When a time-dependent harmonic system is further driven by an external source, it presents significant challenges to obtaining analytical solutions for the system. This paper applies the Lewis-Riesenfeld invariant method to a mesoscopic time-dependent dissipative inductor-capacitor (RLC) circuit with an external source. By constructing quantum invariant Hermitian operators and introducing auxiliary equations that can describe the effects of external sources and resistance, we analytically solve the Schrödinger equation of the system. Taking an alternating current (AC) voltage source as an example, we derive the generalized coherent states of a mesoscopic time-dependent RLC circuit with an external source, calculate the quantum fluctuations of charge and current, and obtain their corresponding uncertainty relations. The results indicate that the time-dependent inductance and resistance disrupt the minimum uncertainty relation of the Glauble coherent states in driven time-dependent mesoscopic RLC circuits. This research contributes to the establishment of a quantum theory for mesoscopic circuits.
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.
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.