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Chinese Physics B

Quantum fluctuation in excited states of mesoscopic LC circuits at finite temperature

Ji‐Suo Wang, Fan Hong‐Yi, Meng Xiang-Guo

Published Mar 1, 2010• 12 citations
Publisher

Abstract

We discuss quantum fluctuation in excited states (named thermo number states) of mesoscopic LC circuits at a finite temperature. By introducing the coherent thermo state into the thermo field dynamics pioneered by Umezawa and using the natural representation of thermo squeezing operator we can concisely derive the fluctuation. The result shows that the noise becomes larger when either temperature or the excitation number increases.

DOI
10.1088/1674-1056/19/3/034206

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We discuss quantum fluctuation in excited states (named thermo number states) of mesoscopic LC circuits at a finite temperature. By introducing the coherent thermo state into the thermo field dynamics pioneered by Umezawa and using the natural representation of thermo squeezing operator we can concisely derive the fluctuation. The result shows that the noise becomes larger when either temperature or the excitation number increases.
The time evolution of a quantum state of mesoscopic LC circuit are studied in detail by using thermo-field dynamics (TFD) at a finite temperature. The result indicates that the quantum state of a mesoscopic LC circuit evolves from the thermal vacuum state to coherence state and go on by the action of an external impulse functional signal on the circuit; the thermal squeezing properties of charge and flux appear in the circuit under some conditions; and furthermore, the typical quantum squeezing effect may occur when certain conditions and particular temperature are meet.
At a definite temperature,a mesoscopic circuit isn't in a determinate quantum state,but in the mixed state.Using the quantum canonic ensemble theory,the quantum fluctuations of charge and circuit of a mesoscopic LC circuit in the mixed state were studied. It is shown that the quantum fluctuations of a mesoscopic LC circuit depend on not only the circuit component parameters,but also the temperature.The higher the temperature,the more quantum noise the mesoscopic LC exhibits.This method is more easily understood and applied than the TFD method.As the mesoscopic circuit is always at finite temperatures,the result is useful for controlling the quantum fluctuations of mesoscopic circuit.
By extending the thermal field dynamics to the time dependent system, quantum fluctuations of the time dependent mesoscopic LC electric circuit at finite temperature were studied. While the up going temperature will increase the quantum fluctuations, time changes of the physical quantities such as the inductance and capacitance can suppress the quantum fluctuations. The electric source will not affect the quantum fluctuations, but will contribute to the averages of the charge and magnetic flux. It was also found that if there is a source, the averages will depend on the temperature; if there is no source, the averages will be zero and so temperature independent.