Relations between cumulants in noncommutative probability

We express classical, free, Boolean and monotone cumulants in terms of each other, using combinatorics of heaps, pyramids, Tutte polynomials and permutations. We completely determine the coefficients of these formulas with the exception of the formula for classical cumulants in terms of monotone cumulants whose coefficients are only partially computed.Comment: 27 pages, 7 figures, AMS LaTe

Convergence of the Fourth Moment and Infinite Divisibility: Quantitative estimates

We give an estimate for the Kolmogorov distance between an infinitely divisible distribution (with mean zero and variance one) and the standard Gaussian distribution in terms of the difference between the fourth moment and 3. In a similar fashion we give an estimate for the Kolmogorov distance between a freely infinitely divisible distribution and the Semicircle distribution in terms of the difference between the fourth moment and 2.Comment: 12 page

Computation of current-voltage characteristics of weak links

Simplified model for current-voltage characteristics of weak links is suggested. It is based on approach which considers Andreev reflections as responsible for the dissipative current through the metallic Josephson junction. The model allows to calculate current-voltage characteristics of weak links (superconductor - normal metal - superconductor junctions, microbridges, superconducting nanowires) for different thicknesses of the normal layer at different temperatures. The current-voltage characteristics of tin microbridges at different temperatures were computed.Comment: 11 pages, 5 figure

Description of hysteretic current-voltage characteristics of SNS junctions

Simplified model for current-voltage characteristics of weak links is suggested. It is based on an approach considering the multiple Andreev reflection in metallic Josephson junction. The model allows to calculate current-voltage characteristics of the superconductor - normal metal - superconductor junctions with different thicknesses of normal layer at different temperatures. A hysteretic peculiarity of $V(I)$ dependence is described as result of the negative differential resistance. The current-voltage characteristic of high-$T_c$ composite YBCO +BaPbO${_3}$ were computed.Comment: 9 pages, 5 figures, submited to Supercond. Sci. Technol, replased Fig.5 for more correct comparison with experimen