Quantum fluctuations of mesoscopic RLC circuit involving complicated coupling in thermal squeezed state

2007 ◽  
Vol 396 (1-2) ◽  
pp. 199-206 ◽  
Author(s):  
Xing-Lei Xu ◽  
Hong-Qi Li ◽  
Ji-Suo Wang
Keyword(s):  
Quantum Fluctuations ◽  
Squeezed State ◽  
Rlc Circuit ◽  
Mesoscopic Rlc Circuit

THE QUANTUM FLUCTUATIONS OF MESOSCOPIC DAMPED MUTUAL INDUCTANCE COUPLED DOUBLE RESONANCE RLC CIRCUIT AT FINITE TEMPERATURE

2007 ◽  
Vol 21 (27) ◽  
pp. 4725-4738 ◽  
Author(s):  
XING-LEI XU ◽  
HONG-QI LI ◽  
SHI-MIN XU ◽  
JI-SUO WANG
Keyword(s):  
Environmental Temperature ◽  
Energy Levels ◽  
Double Resonance ◽  
Quantum Fluctuations ◽  
Vacuum State ◽  
Mutual Inductance ◽  
Squeezed State ◽  
Thermal Vacuum ◽  
Thermo Field Dynamics ◽  
Rlc Circuit

Mesoscopic damped mutual inductance coupled double resonance RLC circuit is quantized by the method of damped harmonic oscillator quantization and linear transformation. The energy levels of this circuit are given. By thermo-field dynamics (TFD), the quantum fluctuations of the current and voltage of each loop are researched in the thermal vacuum state, thermal coherent state and thermal squeezed state. It is shown that the quantum fluctuations of the current and voltage are related not only to the circuit inherent parameter and coupled magnitude of mutual inductance, but also squeezed coefficients, squeezed angle, environmental temperature and damped resistance. Furthermore, because of environmental temperature and damped resistance, the quantum fluctuations increase with the increase of temperature and decay along with time.

Equivalent Analogy of Mesoscopic RLC Circuit and Its Thermal Effect

2010 ◽  
Vol 49 (8) ◽  
pp. 1768-1774
Author(s):  
Bao-Long Liang ◽  
Ji-Suo Wang ◽  
Shi-Xue Song ◽  
Xiang-Guo Meng
Keyword(s):  
Thermal Effect ◽  
Rlc Circuit ◽  
Mesoscopic Rlc Circuit

Linear invariants and the quantum dynamics of a nonstationary mesoscopic RLC circuit with a source

2014 ◽  
Vol 28 (27) ◽  
pp. 1450212 ◽  
Author(s):  
I. A. Pedrosa ◽  
J. L. Melo ◽  
E. Nogueira
Keyword(s):  
Quantum Dynamics ◽  
Power Source ◽  
Oscillation Circuit ◽  
Uncertainty Product ◽  
Rlc Circuit ◽  
External Power ◽  
Arbitrary Weight ◽  
Gaussian Packet ◽  
Mesoscopic Rlc Circuit ◽  
Linear Invariants

In this paper, we use Hermitian linear invariants and the Lewis and Riesenfeld invariant method to obtain the general solution of the Schrödinger equation for a mesoscopic RLC circuit with time-dependent resistance, inductance, capacitance and a power source and represent it in terms of an arbitrary weight function. In addition, we construct Gaussian wave packet solutions for this electromagnetic oscillation circuit and employ them to calculate the quantum fluctuations of the charge and the magnetic flux as well as the associated uncertainty product. We also show that the width of the Gaussian packet and the fluctuations do not depend on the external power.

FLUCTUATIONS AT FINITE TEMPERATURE AND THERMODYNAMICS OF MESOSCOPIC RLC CIRCUIT CALCULATED BY USING GENERALIZED THERMAL VACUUM STATE

2011 ◽  
Vol 25 (31) ◽  
pp. 2353-2361 ◽  
Author(s):  
HONG-CHUN YUAN ◽  
XUE-XIANG XU ◽  
XUE-FEN XU ◽  
HONG-YI FAN
Keyword(s):  
Thermal Field ◽  
Quantum Noise ◽  
Vacuum State ◽  
Nonzero Temperature ◽  
Thermal Vacuum ◽  
Partial Trace ◽  
Expectation Value ◽  
Rlc Circuit ◽  
Thermal Vacuum State ◽  
Mesoscopic Rlc Circuit

By using the partial trace method and the technique of integration within an ordered product of operators we obtain the explicit expression of the generalized thermal vacuum state (GTVS) for an RLC circuit instead of using the Takahashi–Umezawa approach. According to thermal field dynamics (TFD), namely, the expectation value of physical observables in this GTVS is equivalent to their ensemble average, based on GTVS we successfully derive the quantum fluctuations at nonzero temperature and the thermodynamical relations for the mesoscopic RLC circuit. Our results show that the higher the temperature is, the more quantum noise the RLC circuit exhibits.

FLUCTUATION OF MESOSCOPIC RLC CIRCUIT AT PHOTON-SUBTRACTED AND PHOTON-ADDED THERMO VACUUM STATES WITH FINITE TEMPERATURE

2011 ◽  
Vol 25 (01) ◽  
pp. 31-39 ◽  
Author(s):  
XUE-XIANG XU ◽  
LI-YUN HU ◽  
HONG-YI FAN
Keyword(s):  
Wigner Function ◽  
Finite Temperature ◽  
Uncertainty Relation ◽  
Quantum Fluctuation ◽  
Expectation Values ◽  
Rlc Circuit ◽  
Vacuum States ◽  
Mesoscopic Rlc Circuit

By using the Wigner function to evaluate expectation values of any symmetrically order of operator in a classical fashion, we study the quantum fluctuation and the uncertainty relation of mesoscopic RLC circuit at photon-subtracted and photon-added thermo vacuum states. It is found that the fluctuations and the uncertainty relation of both charge and current are linearly related to the photon-subtracted and photon-added number.

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