Related papers: From Quantum Systems to L-Functions: Pair Correlat…
The difference between two consecutive prime numbers is called the distance between the primes. We study the statistical properties of the distances and their increments (the difference between two consecutive distances) for a sequence…
By using ideas and strong results borrowed from the classical moment problem, we show how -under very general conditions- a discrete number of values of the spectral zeta function (associated generically with a non-decreasing sequence of…
We develop a free energy functional for an inhomogeneous system that contains both symmetry conserved and symmetry broken parts of the direct pair correlation function. These correlation functions are found by solving the Ornstein- Zernike…
The correlation effects in nuclei owing to which the nuclear wave functions are different from the Slater determinants are studied on the basis of the original theory. The calculated numbers of nucleons out of the nuclear Fermi-surface are…
We propose a novel statistical approach to the analysis of experimental data obtained in nucleus-nucleus collisions at high energies which borrows from methods developed within the context of Random Matrix Theory. It is applied to the…
The Giant Pairing Vibration, a two-nucleon collective mode originating from the second shell above the Fermi surface, has long been predicted and expected to be strongly populated in two-nucleon transfer reactions with cross sections…
The influence of short-range correlations on the momentum and energy distribution of nucleons in nuclei is evaluated assuming a realistic meson-exchange potential for the nucleon-nucleon interaction. Using the Green-function approach the…
For a grand canonical ensemble of classical point-like particles at equilibrium in continuous space we investigate the functional relationship between a stable and regular pair potential describing the interaction of the particles and the…
The distribution of the ratios of nearest neighbor level spacings has become a popular indicator of spectral fluctuations in complex quantum systems like interacting many-body localized and thermalization phases, quantum chaotic systems,…
In 1970, based on newly available empiric evidence, a remarkable monotonicity property for $| \zeta(z) |$ was conjectured by R. Spira. The $\zeta$-monotonicity property can be written as follows: $$ | \zeta (x_2 + y i ) | < | \zeta \left (…
The complex zeros of the Riemannn zeta-function are identical to the zeros of the Riemann xi-function, $\xi(s)$. Thus, if the Riemann Hypothesis is true for the zeta-function, it is true for $\xi(s)$. Since $\xi(s)$ is entire, the zeros of…
Particular families of special functions, conceived as purely mathematical devices between the end of XVIII and the beginning of XIX centuries, have played a crucial role in the development of many aspects of modern Physics. This is indeed…
We study distributions of differences of unscaled Riemann zeta zeros, $\gamma-\gamma^{'}$, at large distances. We show, that independently of the height, a subset of finite number of successive zeros knows the locations of lower level…
Results of a multipart work are outlined. Use is made therein of the conjunction of the Riemann hypothesis, RH, and hypotheses advanced by the author. Let z(n) be the nth nonreal zero of the Riemann zeta-function with positive imaginary…
The atomic nucleus is composed of two different kinds of fermions, protons and neutrons. If the protons and neutrons did not interact, the Pauli exclusion principle would force the majority fermions (usually neutrons) to have a higher…
The relation between nuclear saturation and NN-correlations is examined. Nucleons bound in a nucleus have a reduced effective mass due to the mean field. This results in off-energy-shell scatterings modifying the free-space NN-interaction…
Poissonian pair correlations have sparked interest within the mathematical community, because of their number theoretic properties, and their connections to quantum physics and probability theory, particularly uniformly distributed random…
A relationship between the Riemann zeta function and a density on integer sets is explored. Several properties of the examined density are derived.
In this paper, we empirically investigate correlations among four centrality measures, originated from the social science, of various complex networks. For each network, we compute the centrality measures, from which the partial correlation…
Based on the relationship that the interaction energy between any two subsystems is equal to their internal energy multiplied by the interaction coefficient, we have derived a series correlated expressions of statistical physical…