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Authors develop new nonparametric methods for verification and monitoring for quantum randomness based on the ranged correlation function (RCF) and a sequence of the ranged amplitudes (SRA). We carried out RCF-analysis of different topology subsamples from raw data of the prototype of a quantum random number generator on homodyne detection. It is shown that in the real system there are weak local regression relations, for which it is possible to introduce a robust criterion of significance, and also precise SRA-identification of long samples statistics is made. The obtained results extend the traditional entropy methods of the useful randomness analysis and open the way for creation of new strict quality quantum standards and defense for physical random numbers generators.

Single-photon detectors based on avalanche photodiodes (SPAD) are key elements of many modern highly sensitive optical systems. One of the bottlenecks of such detectors is a afterpulsing effect which limits a detection rate and requires an optimal hold-off time. In this letter we propose a novel approach for statistical analysis of SPAD dark counts and we demonstrate its usefulness for the search of the experimental condition where the afterpulsing effect can be strongly eliminated. This approach exploits a sequence of ranked time intervals between the dark counts and does not contain a complex mathematical analysis of the experimental data. We show that the approach can be efficiently applied for a small number of the dark counts and it seems to be very beneficial for practical characterization of SPAD devices.

We suggest a new method of calculation of the equilibrium correlation functions of an arbitrary order for the interacting Fermi-gas model in the frame of the static fluctuation approximation (SFA) method. This method based only on the single and controllable approximation allows to obtain the so-called far-distance equations (FDEs). These equations connecting the quantum states of a Fermi particle with variables of the local field operator contains all necessary information related to calculation of the desired correlation functions and basic thermodynamic parameters of the many-body system considered. The basic expressions for the mean energy and heat capacity for electron gas at low temperatures in the limit of high density were obtained. All expressions are given in the units of r_s,where r_s determines the ratio of a mean distance between electrons to the Bohr radius a_0. In these expressions we calculated the terms of the order r_s and r_s^2, correspondingly. It was shown also that the SFA allows to find the terms related with high orders of the decomposition with respect to the parameter r_s., Comment: 22 pages, 5 figures

The energy spectrum of eigenvalues of the equal spin-spin interactions (ESSI) Hamiltonian has been found. The obtained spectrum is free from limitations imposed on number of spins and parameters of the ESSI Hamiltonian. This model can be used for consideration of spin dynamics of mesoscopic systems and molecules with large number of nuclei spins.