Fluctuation Dissipation Theorem and Electrical Noise Revisited

The fluctuation dissipation theorem (FDT) is the basis for a microscopic description of the interaction between electromagnetic radiation and matter. By assuming the electromagnetic radiation in thermal equilibrium and the interaction in the linear-response regime, the theorem interrelates the macroscopic spontaneous fluctuations of an observable with the kinetic coefficients that are responsible for energy dissipation in the linear response to an applied perturbation. In the quantum form provided by Callen and Welton in their pioneering paper of 1951 for the case of conductors [H. B. Callen and T. A. Welton, Irreversibility and generalized noise, Phys. Rev. 83 (1951) 34], electrical noise in terms of the spectral density of voltage fluctuations, SV(ω), detected at the terminals of a conductor was related to the real part of its impedance, Re[Z(ω)], by the simple relation SV(ω)=2ℏωcothℏω2KBTRe[Z(ω)], where KB is the Boltzmann constant, T is the absolute temperature, ℏ is the reduced Planck constant and ω=...