Abstract
By employing a two-mode integral-form projection operator in coordinate representation and IWOP technique, we investigate the quantum fluctuations and variances of the current in each loop for an inductance-coupled double L-C circuit. It is found that investigating the mesoscopic circuit with the help of such an operator and IWOP technique can bring us the following conveniences. Firstly, it is easier to eliminate the coupling term of Hamiltonian, which comes from two-mode coupled harmonic oscillator system. Secondly, the system’s ground state is generalized a two-mode squeezed state. Thus, the quantum fluctuations of the squeezed state and the variances of current in each loop are calculated, the charge-current uncertainty relation is revealed. Both the uncertainty relation and fluctuation of the current in each loop become larger when L0 is larger.
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