Golubev and Zaikin Reply: In their Comment [1], Aleiner, Altshuler, and Gershenson (AAG) stated that we [2] "found that 'zero-point fluctuations of electrons' contribute to the dephasing rate 1͞t w ." We made no such claims. Obviously, the eigenmodes of any quantum system preserve their coherence. On the other hand, single-particle properties of an interacting system-which are not directly expressed in terms of eigenmodes-can display a finite decoherence length L w even in the lowtemperature limit. An example is provided by a particle coupled to a harmonic oscillator bath [4], which we discuss explicitly below. This is also the case for the weak localization correction to the conductivity ds in the presence of interaction, where we found [2] L w to remain finite at T ! 0. AAG furthermore concluded that our procedure is "simply wrong" because "some contributions were lost." This is not the case, as demonstrated by the fact that our approach [2]-if analyzed perturbativelyreproduces the AAG result for ds (Ref.[2] of [1]) before disorder averaging. The main discrepancy between [1] and [2] is due to the golden rule approximation employed by AAG and not due to averaging over disorder.

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We investigate the breakdown of BCS superconductivity in {\em ultra}\/small metallic grains as a function of particle size (characterized by the mean spacing $d$ between discrete electronic eigenstates), and the parity ($P$ = even/odd) of the number of electrons on the island. Assuming equally spaced levels, we solve the parity-dependent BCS gap equation for the order parameter $\Delta_P (d,T)$. Both the $T=0$ critical level spacing $d_{c,P} $ and the critical temperature $T_{c,P} (d)$ at which $\Delta_P = 0$ are parity dependent, and both are so much smaller in the odd than the even case that these differences should be measurable in current experiments.Comment: 4 pages RevTeX, 1 encapsulated postscript figure, submitted to Physical Review Letter

We point out that the low temperature saturation of the electron phase decoherence time in a disordered conductor can be explained within the existing theory of weak localization provided the effect of quantum (high frequency) fluctuations is taken into account. Making use of the fluctuation-dissipation theorem we evaluate the quantum decoherence time, the crossover temperature below which thermal effects become unimportant, and the weak localization correction $\delta \sigma$ at T=0. For 1d systems the latter is found to be $\delta \sigma \propto 1/ \sqrt{N}$, where $N$ is the number of conducting channels.Comment: RevTeX, 3 page