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is anti-symmetric, and any loop contributes equally to both terms. Consequently, WL corrections are canceled, and they appear only if 〈 R$_{4t}$ 〉 ̸ = 0, e.g. in a quasi-1d dis- ordered structure [30] with a special probe arrangement. 

Similarly, the TRS-breaking does not affect the fluc- tuations of R$_{4t}$ as shown by Eq. (3), in contrast with Eq. (4) for R$_{2t}$ . Indeed, inverting time we must invert magnetic flux Φ and swap the current- with voltage- probes. The ensuing symmetry R$_{2t}$ (Φ) = R$_{2t}$ ( − Φ) gives ∂R$_{2t}$/∂ Φ = 0 at Φ = 0, but there is no such a restric- tion on R$_{4t}$ (Φ). Fluctuations of R$_{2t}$ (Φ) are analogous to a perturbation on a string with a free end, where the perturbation maximum corresponds to the maximum in R$_{2t}$ -fluctuations at Φ = 0. On the other hand, R$_{4t}$ (Φ) is analogous to an infinite string, so that zero field is as good as any other: neither TRS-breaking effects like WL in Eq. (2) or 2 /β -coefficient of Eq. (4), nor ”quenching” (diminished sensitivity to Φ at Φ = 0) appear for R$_{4t}$ in chaotic dots [28]. In addition, in contrast to the classi- cal four-terminal scheme [3], the properties of source and drain are never fully eliminated: a measurement affects the sample and so the mesoscopic fluctuations in R$_{4t}$ do depend on contacts. Importantly, in the experiment [18] the voltage probes are invasive. 

For the non-ideal contact coupling a tunneling limit for the voltage probes is often taken, tr Γ$_{v}$ ≪ 1; in the opposite limit, tr Γ$_{v}$ ≫ 1, UCF presents a complicated 6-th order polynomial of Γ$_{j}$ [20]. In contrast, for a fixed set { Γ$_{j}$ } the fluctuations of R$_{4t}$ given by Eq. (3) can be expressed only in terms of conductance tr Γ$_{j}$ and Fano factor F $_{j}$, the ratio of shot noise to current [31], of each QPC. The result of a separate averaging over mesoscopic contact j , tr Γ 2 $_{j}$/ tr $^{2}$Γ$_{j}$ → (1 − 〈F j 〉 ) / 〈 tr Γ$_{j}$ 〉 , is propor- tional to the QPC resistance with a numerical prefactor: it ranges from 1 for ballistic to 2/3 for a short diffusive wire, if disorder is increased; for a wide tunneling QPC it is equal to 1 if Γ$_{j}$ ≪ 1 are the same, and 1 / 2 for a dirty interface [32]. We observe that, generally, a poorer coupling increases fluctuations of R$_{4t}$ . 

Often conductors have more contacts then needed for a four-terminal measurement. A floating (unused) con- tact f does not to draw any current from the sample, but leads to decoherence [33], its coupling is related to the inelastic scattering time τ$_{in}$ = h/ Δtr Γ$_{f}$ [19]. Data are often interpreted as an addition of several fictitious dephasing channels to the real contacts. However, here it is important to distinguish between a floating probe and a contact used for transport measurements. Simi- larly to Ref. 19, we find that a floating probe decreases fluctuations of R$_{4t}$ by increasing the total coupling tr Γ of the dot to reservoirs. Due to the zero-dimensional ge- ometry of the dot, they are independent of the number of such probes, and only the total tr Γ$_{f}$ is relevant. The voltage probes used to define R$_{4t}$ and floating probes are not equivalent, an increase of the former decreases fluctuations stronger. Indeed, in two measurements with 

unequal probes used as voltage and floating ones and vice versa, the better the voltage probe conducts the smaller the fluctuations of R$_{4t}$ . Importantly, if the dephasing probe model is used, dephasing channels should be in- cluded not into the real, but into the floating probes. 

AC setup, ω ̸ = 0 . Now we generalize our dc re- sults to finite frequency ω to consider dynamics of resis- tances. The screened conductance g s ω in Eq. (6) becomes complex and depends not only on τ$_{d}$ [34], but also on τ$_{RC}$ = C$_{µ}$/ tr Γ. Here C$_{µ}$ is the electro-chemical capaci- tance, which relates the charge of the dot to the chem- ical potentials, it is defined by the Coulomb interaction strength, 1 /C$_{µ}$ ≡ 1 /C +Δ /ν$_{s}$ [25]. A frequency ∼ 1 /τ$_{RC}$ , when the capacitor and the contacts conduct similarly, is then a natural characteristic of a two-terminal mea- surement. The finite-frequency correlations and WL of conductance were considered only for ballistic QPCs at T, ω → 0. Quantum effects in ac transport depended only on ωτ$_{d}$ at low frequencies [21], but at higher ω they start to depend on ωτ$_{RC}$ as well. In contrast, for R$_{2t}$ our Eq. (2) shows that at any frequency the WL is indepen- dent of τ$_{RC}$ ; this is compatible with τ$_{RC}$ -dependent WL in conductance [21], because τ$_{RC}$ is eliminated by the matrix inversion. The reason is that WL only increases the return probability, but does not redistribute charge. Low-frequency conductance correlations can be gen- eralized to arbitrary frequencies ω, ω ′ using parameter z ≡ − iωτ$_{RC}$/ (1 − iωτ$_{RC}$ ) and z ′ introduced similarly, and considering ballistic QPCs with n$_{i}$ = N$_{i}$/N for sim- plicity. For β = 2 we find the correlations, 

<img src='content_image/393942.jpg'>

and for β = 1 the same r.h.s. with k ↔ l should be added. Results of Ref. [21] are reproduced by differen- tiation ∂$_{ω}$$_{(}$$_{ω}$ ′ ) of Eq. (7) at ω, ω ′ = 0. Using Eq. (7) we find that fluctuations of R$_{2t}$ in a dot with ballistic probes, N = N$_{1}$ + N$_{2}$ + N$_{f}$ , given by Eq. (4) manifestly depend on both τ$_{d}$ and τ$_{RC}$ . Only the four-probe scheme can show if ωτ$_{RC}$ is an intrinsic scale of the dot itself, or if it comes from the chosen two-terminal measurement scheme. In other words, does the frequency-scale 1 /τ$_{RC}$ survive in resistance statistics if the role of contacts is minimized? Equation (3) for R$_{4t}$ does not depend on τ$_{RC}$ , and we conclude that this scale is extrinsic and can be under- stood as a contact property. Since Gaussian R$_{4t}$ is fully characterized by Eqs. (1,3), we conclude that the quan- tum transport at arbitrary frequency ω is insensitive to screening only in the four-terminal scheme. 

Experimental relevance. Recently, Lerescu et al. [18] measured statistics of R$_{4t}$ in dc-biased ballistic dots and compared with numerical data for N$_{f}$ = 0. The rms R$_{4t}$ qualitatively agreed with the numerics, but was about 20 

