Quantum fluctuations of mesoscopic damped circuit involving capacitance-inductance coupling at a finite temperature

The quantization of mesoscopic damped circuit involving capacitance-inductance coupling is proposed by the method of thrice linear transformation and damped harmonic oscillator quantization. The quantum fluctuations of the charges and current of each loop are calculated by thermo-field dynamics (TFD) in thermal vacuum state, thermal coherent state and thermal squeezed state, respectively. It is shown that the quantum fluctuations of the charges and current not only depend on circuit inherent parameter and coupled magnitude, but also rely on squeezed coefficients, squeezed angle, environmental temperature and damped resistance. And, because of influence of environmental temperature and damped resistance, the quantum fluctuations increase with increasing temperature and decrease with prolonging time.