Abstract
For the first time we considered the quantum effects of mesoscopic non-linear series circuit with the coherent thermo state representation \(\left | \tau \right \rangle \). After introducing the representation \(\left |\tau \right \rangle \), we derived the expression of the density matrix ρ and find that \(\left | \rho \right \rangle _{T} \) presents Gauss type with the representation \(\left | \tau \right \rangle \). In addition, we derived the Wigner function and calculated the quantum fluctuation in the thermo vacuum state |0(β)〉. It is shown that the circuit has the zero current fluctuation because the diode has the reverse saturation current, and the temperature affects the Wigner function of the circuit in thermo vacuum state deeply.
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