Based upon the quantization of a mesoscopic lossless transmission line, analysis is made for the quantum fluctuations of the current and current gradient of the line in the vacuum state and squeezed vacuum state, especialy for the difference between the quantum fluctuations of the transmission line and LC circuit.
By making use of thermo-field dynamics (TFD), the quantum fluctuations of current of the mesoscopic lossless transmission line in the vacuum state, the coherent states and the squeezed states with thermal noise have been studied. Thus the dependence of the fluctuations on temperature in these states at finite temperature can be seen. It is shown that the quantum fluctuations depend on not only the parameters of the transmission line but also the environmental temperature T. The higher the temperature, the more quantum noise the line exhibits.
Starting with the Lagrange of circuit system and using number-phase quantization scheme,mesoscopic LC circuit is quantized and the Hamiltonian expressed by charge number operator and the phase-difference operator is obtained.The quantum fluctuations of both charge number and phase-difference are researched in both vacuum state and squeezed vacuum state.The results show that the quantum fluctuations only relate to the parameters of circuit system in vacuum state,but in the squeezed vacuum state,the quantum fluctuations relate to not only the parameters of circuit system,but also the squeezing parameter.