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We develop a new unified theoretical approach enabling us tonon-perturbatively study the effect of electron-electron interactions on weaklocalization in arbitrary arrays of quantum dots. Our model embraces (i) weaklydisordered conductors (ii) strongly disordered conductors and (iii) metallicquantum dots. In all these cases at $T \to 0$ the electron decoherence time isdetermined by the universal formula $\tau_{\varphi 0}\sim g\tau_D/\ln(E_C/\delta)$, where $g$, $\tau_D$, $E_C$ and $\delta$ are respectivelydimensionless conductance, dwell time, charging energy and level spacing of asingle dot. In the case (i) this formula yields $\tau_{\varphi 0}\proptoD^3/\ln D$ ($D$ is the diffusion coefficient) and matches with our previousquasiclassical results [D.S. Golubev, A.D. Zaikin, Phys. Rev. Lett. 81 (1998)1074], while in the cases (ii) and (iii) it illustrates new physics notexplored earlier. A detailed comparison between our theory and numerousexperiments provides an overwhelming evidence that zero temperature electrondecoherence in disordered conductors is universally caused by electron-electroninteractions rather than by magnetic impurities.

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