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Gongneng cailiao yu qijian xuebao

RESPONSES OF A MESOSCOPIC RLC CIRCUIT TO dc-AND ac-SOURCE

Lei Xiaolin

Published Jan 1, 1999• 0 citations
OpenAlex

Abstract

A time-dependent Hermitian Hamiltonian with SU(1,1)H(3) algebraic structure is constructed to describe a mesoscopic RLC circuit with a source by quantizing the relevant classical equation of motion. Quantum dynamical problem corresponding to such a system is exactly solved by evolution operator method. The response features of the mesoscopic RLC circuit to a dc and an ac source are then discussed in detail.

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A time-dependent Hermitian Hamiltonian with SU(1,1)H(3) algebraic structure is constructed to describe a mesoscopic RLC circuit with a source by quantizing the relevant classical equation of motion. Quantum dynamical problem corresponding to such a system is exactly solved by evolution operator method. The response features of the mesoscopic RLC circuit to a dc and an ac source are then discussed in detail.
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.
In this paper, mesoscopic RLC circuit with source is studied with Feynman's path integral method. Resistance and source in the circuits make the quantization process rather complicated. To solve the problem, fluctuation analysis method is proposed to calculate the path integral propagator. Furthermore, the wave function and quantum fluctuation of the system are obtained, and time evolution characters of the system are discussed. The methods used in the paper would be helpful to the application of mesoscopic quantum theory.
With the help of the time-dependent Lagrangian for a damped harmonic oscillator, the quantization of mesoscopic RLC circuit in the context of a number-phase quantization scheme is realized and the corresponding Hamiltonian operator is obtained. Then the evolution of the charge number and phase difference across the capacity are obtained. It is shown that the number-phase analysis is useful to tackle the quantization of some mesoscopic circuits and dynamical equations of the corresponding operators.