Full counting statistics

Josephson Junctions as Threshold Detectors for Full Counting Statistics... 

Summary. We discuss how threshold detectors can be used for a direct measurement of the full counting statistics (FCS) of current fluctuations and how to implement Josephson junctions in this respect. We propose a scheme to characterize the full counting statistics from the current dependence of the escape rate measured. We illustrate the scheme with explicit results for tunnel, diffusive and quasi-ballistic mesoscopic conductors. 

To conclude, we proved that Josephson junctions can be used as threshold detectors for non-Gaussian noise produced by coherent conductors. Our theoretical results facilitate a new type of electric noise measurement direct measurement of full counting statistics of the transferred charge. 

Figure 2 Variations of counting statistical error (2cr or 95% confidence) for nuclides of different half-lives using different measurement techniques. Four different scenarios are shown with details listed in legend, aimed to cover a typical range of conditions. The values of ionization efficiencies span a full range of values appropriate for elements difficult (Th) and easy (Ra) to ionize thermally, see text. All scenarios assume a sample with MORB-hke U concentration (50 ngg ), but with all daughter nuclides in secular equilibrium (for illustrative simplicity). Calculations assume (unrealistic) 100% yields for chemical purification of the nuclide of interest and 40% counting...

Figure 5 Examples of measured TOF spectra from liquid 6V, Hi, in a Nb can, at T 295 K. The error bars are due to counting statistics only. The full lines denote the fitted TOF spectra. For the scattering angle 0 = 65°, the C- and 7V6-recoil peaks overlap. For 0 = 132°, however, these two peaks are well resolved, thus facilitating a reliable determination of the C- and Nb-peak intensities.

Figure 7 Structure and TOF spectra of 1S0-C4E1 in D2O measured for scattering angles a - 9 = 144° and b - 6 = 51°. Small vertical bars one standard deviation error due to counting statistics. Full lines fitted theoretical TOF-spectra to the measured data, a - Note the separation of the joint C, O-peak from the Nb can-peak in the spectrum, which is necessary for data analysis (see text).

The full line in Fig. VI1-6 gives the statistically expected standard deviation. The experimental standard deviations are significantly higher than those calculated on statistical grounds. The difference can be attributed to a so-called "instrumental error", which can be obtained by subtracting the variance caused by counting statistics from the experimental one. At high count rates ca. 1.7 % is obtained for the instrumental error, which takes into account ... 

Since a vast number of photon counts may be rapidly accumulated, i.e. a full memory of 4096 measurements at 20 ysec per measurement is obtained in 82 msec, a statistical analysis of such data can, in principle, lead to separate characterization of the ordinary signal from latex particles and an extraordinary signal which may arise from dust particles as in the present instance or in general from a low population of any extraordinary particles. 

Again, Brookfield s (1989) statistics can help. We compare the progeny two at a time with their mother. They must be full or half siblings, depending upon whether or not they share a father. Counting bands reveals the following results ... 

---