Abstract
Finite temperature field(FTF) theory provides an elegant method for describing thermal and quantum noise in an electrical network. This method is applied to give fluctuation dissipation theorem results for the second moments representing noise in a dissipative LRC quantum oscillator. Classical dissipation is understood from a phase space analysis. Quantum dissipation can be studied with the aid of an effective Lagrangian obtained from considering a semi-infinite low-pass filter. This provides a frequency cut-off which yields finite second moments for both charge and current. The method has been extended to interacting oscillators, coupled by mutual inductance, to investigate a system which may be useful in the detection of vibrations induced by gravitational radiation.
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