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Chinese Journal of Quantum Electronics

Complete solution of zero-state response in mesoscopic RLC circuit

Zhou Xiao-fang

Published Jan 1, 2008• 0 citations
OpenAlex

Abstract

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.

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The complete solution of zero-state response in mesoscopic LC circuit

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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.
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 was obtained by applying the gauge transform of algebra dynamic.Such an operator describes the quantum state of time dependence of capacitance coupled mesoscopic circuit containing voltage source.The charge and current zero-state response of the import voltage signal in capacitance coupled mesoscopic circuit were introduced.The result shows that the system of capacitance coupled mesoscopic circuit has linear time invariant feature,and the response in mesoscopic circuit is the same as in the macroscopic 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.
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.
In this paper, we present a comprehensive quantum description of a mesoscopic RLC circuit with time-dependent resistance, inductance and capacitance. Based on the dynamical invariant method and using quadratic invariants, we derive exact nonstationary quantum states for this circuit and write them in terms of solutions of the Milne–Pinney equation. Afterwards, we use quadratic invariants to construct coherent states for this quantized system and employ them to investigate quantum properties of the RLC circuit. In particular, we show that the product of the quantum fluctuations of the charge and the magnetic flux does not satisfy the minimum uncertainty relation.