Golubev and Zaikin Reply:

Abstract

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.

Control of Coulomb blockade in a mesoscopic Josephson junction using single electron tunneling

“…13 only. According to the P(E) theory, tunneling does not happen strictly at Q I ϭe, but is rather represented with a finite distribution, which is schematically shown in Fig.…”

Coulomb blockade and insulator-to-metal quantum phase transition

“…(4) are small in the parameter β/g 0 ≪ 1. Nevertheless, one cannot yet conclude that the system behavior is metallic at T = 0 because the Langevin equation analysis [4] does not fully account for the charge discreteness in our system. Specifically, this analysis does not include subtle nonperturbative effects which can be captured only by means of the instanton technique.…”

“…This Coulomb blockade of tunneling is a direct consequence of the electron charge discreteness, manifestations of which persist even for junctions with resistances well below the quantum resistance unit R Q = h/e 2 ≈ 25.8 kΩ. Recently it was argued [4] that the I − V curve of an arbitrary -albeit relatively short -coherent conductor in the presence of interactions can be expressed in the form…”

“…Within the approach [4] one can demonstrate that all corrections to eq. (4) are small in the parameter β/g 0 ≪ 1.…”

“…The result (3) is valid down to energies max(T, eV ) ∼ g 0 E C exp(−g 0 /2). At even lower T and eV energy relaxation effects turn out to be particularly important making the conductance saturate at a universal value [4] …”