Dephasing due to electron interactions in inhomogeneous systems

At sufficiently low temperatures, the dephasing time $\tau_\varphi$ of mesoscopic samples is governed by so-called Johnson-Nyquist (electronic) noise. We study the spatial dependence of the corresponding noise correlation function (NFC) in inhomogeneous systems. Using the fluctuation-dissipation theorem and the random-phase approximation, we derive a real-space integro-differential equation for the NCF and show that it reduces to a diffusion equation in the case of strong screening. In particular, using a method based on the spectral determinant, we evaluate the NCF for arbitrary networks of quasi-1D disordered wires with boundary conditions. As an application, we construct a realistic quantum dot model via a set of parallel wires connected at contacts to leads, and calculate the temperature dependence of $\tau_\varphi$ as well as the quantum corrections to the conductance. Furthermore, we analyze the observability of the elusive 0D regime (reached at $T < E_{\rm Thouless}$ with the characteristic $\tau_\varphi \propto T^{-2}$ behavior) in such systems, and discuss alternative scenarios of its observation.