Quantum decoherence of interacting electrons in arrays of quantum dots and diffusive conductors

We develop a new unified theoretical approach enabling us to non-perturbatively study the effect of electron-electron interactions on weak localization in arbitrary arrays of quantum dots. Our model embraces (i) weakly disordered conductors (ii) strongly disordered conductors and (iii) metallic quantum dots. In all these cases at $T \to 0$ the electron decoherence time is determined by the universal formula $\tau_{\varphi 0}\sim g\tau_D/\ln (E_C/\delta)$, where $g$, $\tau_D$, $E_C$ and $\delta$ are respectively dimensionless conductance, dwell time, charging energy and level spacing of a single dot. In the case (i) this formula yields $\tau_{\varphi 0}\propto D^3/\ln D$ ($D$ is the diffusion coefficient) and matches with our previous quasiclassical results [D.S. Golubev, A.D. Zaikin, Phys. Rev. Lett. 81 (1998) 1074], while in the cases (ii) and (iii) it illustrates new physics not explored earlier. A detailed comparison between our theory and numerous experiments provides an overwhelming evidence that zero temperature electron decoherence in disordered conductors is universally caused by electron-electron interactions rather than by magnetic impurities.