Interactions and Weak Localization: Perturbation Theory and Beyond

We establish an explicit correspondence between perturbative and nonperturbative results in the problem of quantum decoherence in disordered conductors. We demonstrate that the dephasing time $\tau_{\phi}$ cannot be unambiguously extracted from a perturbative calculation. We show that the effect of the electron-electron interaction on the magnetoconductance is described by the function $A_d(t)\exp (-f_d(t))$. The dephasing time is determined by $f_d(t)$, i.e. in order to evaluate $\tau_{\phi}$ it is sufficient to perform a nonperturbative analysis with an exponential accuracy. The effect of interaction on the pre-exponent $A_d(t)$ is important if one calculates the interaction-dependent part of the weak localization correction for strong magnetic fields. The zero temperature dephasing time drops out of this correction in the first order due to the exact cancellation of the linear in time $T$-independent contributions from the exponent and the pre-exponent. Nonlinear in time $T$-independent contributions do not cancel out already in the first order of the perturbation theory and yield an additional contribution to dephasing at all temperatures including T=0.