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International Journal of Modern Physics B

EVOLUTION OF QUANTUM FLUCTUATIONS OF A OVER-DAMPED MESOSCOPIC CIRCUIT AT FINITE TEMPERATURE

Juju Hu, Qiang Ke, Yinghua Ji

Published Dec 20, 2007• 0 citations
Publisher

Abstract

Time evolution of quantum fluctuations is investigated for an over-damped mesoscopic circuit with the help of the quantum characteristic function. It is found that, for an initial squeezed state, the quantum fluctuations of charge and current evolve with time by hyperbolic functions, and relate not only with the circuit parameters, but also the squeezing parameter. It is also found that with other conditions invariant to reducing the quantum fluctuations of charge and current, we should reduce the squeezing amplitude parameter. The research will be helpful in miniaturizing integrated circuits and electric components. It will also be significant for the further study of quantum information.

DOI
10.1142/s0217979207038307

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Time evolution of quantum fluctuations is investigated for an over-damped mesoscopic circuit with the help of the quantum characteristic function. It is found that, for an initial squeezed state, the quantum fluctuations of charge and current evolve with time by hyperbolic functions, and relate not only with the circuit parameters, but also the squeezing parameter. It is also found that with other conditions invariant to reducing the quantum fluctuations of charge and current, we should reduce the squeezing amplitude parameter. The research will be helpful in miniaturizing integrated circuits and electric components. It will also be significant for the further study of quantum information.
Using the path integral method we derive quantum wave function and quantum fluctuations of charge and current in the mesoscopic RLC circuit. We find that the quantum fluctuation of charge decreases with time, oppositely, the quantum fluctuation of current increases with time monotonously. Therefore there is a squeezing effect in the circuit. If some more charge devices are used in the mesoscopic-damped circuit, the quantum noise can be reduced. We also find that uncertainty relation of charge and current periodically varies with the period π/2 in the under-damped case.
Using the path integral method we derive quantum wave function and quantum fluctuations of charge andcurrent in the mesoscopic RLC circuit. We find that the quantum fluctuation of charge decreases with time, oppositely,the quantum fluctuation of current increases with time monotonously. Therefore there is a squeezing effect in the circuit.If some more charge devices are used in the mesoscopic-damped circuit, the quantum noise can be reduced. We also findthat uncertainty relation of charge and current periodically varies with the period π/2 in the under-damped case.
When the inelastic coherence length of the charge carrier reaches the Fermi wavelength,quantum effects in electronic devices and circuit should be taken into account.Due to the existence of finite environmental temperature and damped resistance,practical circuits are always working in damped thermal states at finite temperature.With the rapid development of nanotechnology and microeletronics,the quantum effects of mesoscopic circuit have become an active problem now.In this paper,mesoscopic series-parallel connection RLC circuit was quantized by the method of damped harmonic oscillator quantization.Quantum fluctuatioins of the current and voltage of each branch were studied by thermo-field dynamics(TFD) theory in thermal vacuum state,thermal coherent state and thermal squeezed state.The results show that the quantum fluctuations of the current and voltage of each branch are related to not only parameters of the circuit,but also squeezed coeficients,squeezed angle and envionmental temperature.Because of the existence of current Joule heat,environmental temperature and damped resistances,the fluctuations increase with the increasing of temperature and decay with time.The study of these quantum fluctuation is significant for the design of miniature circuits and the reduction of quantum noise.