The Thermal Vacuum State For Mesoscopic Capacitance Coupling Circuit Quantum Fluctuations

Above all, we transpose the Hamiltonian with the Capacitance-coupled circuit into harmonic Hamiltonian by using the methods of canonical transformation and build the unitary operator by using the methods of unitary transformation, and then we utilize the theory of Thermal Field Dynamics (TFD) to investigate the quantum fluctuations of mesoscopic Capacitance-coupled circuit in thermal vacuum state , eventually the quantum fluctuation at a finite temperature are compared with that at absolute zero. It is shown that at a finite temperature, the fluctuations of electric charges and currents change with temperature. The higher the temperature, the more quantum noise the coupled circuit exhibits.