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Chinese Journal of Quantum Electronics

Quantum Fluctuations of Mesoscopic Capacitance Coupled Circuit With Mutual Inductance

Shou Zhang

Published Jan 1, 2004• 0 citations
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Abstract

The quantum fluctuations of charges and currents of mesoscopic capacitance coupled circuit with mutual inductance are studied by using canonical transformation and unitary transformation. The results show that when the components of the circuit are given, especially when the value of L1 = L2 is very small, with the increasing of coupling extent, the quantum fluctuations of charges in one loop of circuit decrease obviously, while those charge of the other loop increase obviously.

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The quantum fluctuations of charges and currents of mesoscopic capacitance coupled circuit with mutual inductance are studied by using canonical transformation and unitary transformation. The results show that when the components of the circuit are given, especially when the value of L1 = L2 is very small, with the increasing of coupling extent, the quantum fluctuations of charges in one loop of circuit decrease obviously, while those charge of the other loop increase obviously.
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The quantum effect of mesoscopic inductance-capacitance coupled circuit with mutual inductance was investigated by canonical transformation and unitary transformation. The mesoscopic inductance-capacitance coupled circuit was compared with several coupling circuits. It is found that it is convenient to control the quantum fluctuations and squeezed effect by adjusting mutual inductance coupling coefficient in mutual inductance circuit with coupling capacitance. Uncertainty relations of charges and conjugate currents are related to canonical transformation parameter φ and uncertainty relations parameter ξ. When ξ→1 or φ→nπ/2, (n = 0,1,2,…), the uncertainty relations approach minimum value h/2.
A mesoscopic double resonance circuit with mutual inductance and capacitance-inductance coupling was quantized using canonical quantization method.The Hamiltonian of the system was diagonalized by unitary transformation to obtain the eigenenergy spectra of the circuit.The quantum fluctuations of the charge and current in the two loops of the circuit were studied under squeezed vacuum excitation state,squeezed vacuum state and vacuum state,respectively.The results show that quantum fluctuations are dependent not only on circuit parameters,quantum number of excitation,squeezed coefficients and squeezed angle,but also on mutual inductance coefficient,capacitance and inductance.
Starting from Kirchhoff's equation for each mesoscopic coupled circuit, we investigated the quantum fluctuations of a dissipative mesoscopic capacitance–resistance–inductance coupled circuit using canonical transformation and unitary transformation. It is shown that the quantum fluctuations of charges and currents are not only related to the parameters of components in the self-circuit and coupled part, but also influenced by the parameters of other circuit. The uncertainty relations of the charges and currents are analyzed briefly.
Mesoscopic double resonance mutual inductance and capacitance coupling circuit is quantized by the method of harmonic oscillator quantization linear transformation.The energy spectra of this circuit are given.The quantum fluctuations of the charge and current of each loop are researched by the method of thermo-field dynamics(TFD) in thermal excited state,thermal squeezed vacuum state,thermal vacuum state and vacuum state.It is show that,the quantum fluctuations of the charge and current are related to not only circuit inherent parameter and coupled magnitude,but also quantum number of excitation,squeezed coefficients,squeezed angle,environmental temperature.And,the quantum fluctuations increase with the increase of temperature.