Noise thermal impedance of a diffusive wire.

The current noise density S2 of a conductor in equilibrium, the Johnson noise, is determined by its temperature T: S2 = 4k(B)TG, with G the conductance. The sample's noise temperature T(N) = S2/(4k(B)G) generalizes T for a system out of equilibrium. We introduce the "noise thermal impedance" of a sample as the ratio deltaT(N)omega/deltaP(J)omega of the amplitude deltaT(N)omega of the oscillation of T(N) when heated by an oscillating power deltaP(J)omega at frequency omega. For a macroscopic sample, it is the usual thermal impedance. We show for a diffusive wire how this (complex) frequency-dependent quantity gives access to the electron-phonon interaction time in a long wire and to the diffusion time in a shorter one, and how its real part may also give access to the electron-electron inelastic time. These times are not simply accessible from the frequency dependence of S2 itself.