The noise thermal impedance of a diffusive wire

The current noise density $S_2$ of a conductor at equilibrium is determined by its temperature $T$: $S_2=4k_BTG$ with $G$ the conductance (Johnson noise). The noise temperature $T_N=S_2/ (4k_BG)$ generalizes $T$ for a system even out of equilibrium. We introduce the noise thermal impedance of a sample as the amplitude of the oscillation of $T_N$ when heated by an ac power. It is the usual thermal impedance for a macroscopic sample. 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 interaction time. We will also present experimental results in various limits.