Related papers: From Quantum Systems to L-Functions: Pair Correlat…
The evolution of the pairing correlations from closed shell to middle shell nuclei is analyzed with a Finite Range Density Dependent interaction in the Sn isotopes. As theoretical approaches we use the Hartree-Fock-Bogoliubov, the…
Correlation functions and related statistics have been favorite measures of the distributions of extragalactic objects ever since people started analyzing the clustering of the galaxies in the 1930s. I review the evolving reasons for this…
Karlin and Altschul in their statistical analysis for multiple high-scoring segments in molecular sequences introduced a distribution function which gives the probability there are at least r distinct and consistently ordered segment pairs…
We study 1S0 pairing gaps in neutron and nuclear matter as well as in finite nuclei on the basis of microscopic two-nucleon interactions. Special attention is paid to the consistency of the pairing interaction and normal self-energy…
In this note we describe weight functions that exhibit a transitional behavior between weak and strong correlation with the Liouville function. We also describe a binary problem which may be considered as an interpolation between Chowla's…
The Riemann hypothesis, which states that the non-trivial zeros of the Riemann zeta function all lie on a certain line in the complex plane, is one of the most important unresolved problems in mathematics. Inspired by the P\'olya-Hilbert…
$\Theta$ function is defined based upon Kronecher symbol. In light of the principle of inclusion-exclusion, $\Theta$ function of sine function is used to denote the distribution of composites and primes. The structure of Goldbach Conjecture…
Physics is a fertile environment for trying to solve some number theory problems. In particular, several tentative of linking the zeros of the Riemann-zeta function with physical phenomena were reported. In this work, the Riemann operator…
This is a survey on weight enumerators, zeta functions and Riemann hypothesis for linear and algebraic-geometry codes.
It is well understood that the studies of correlations between produced particles, the effects of coherence and chaoticity, an estimation of particle emitting source size play an important role in high energy physics [1]. We mean the…
We argue that the freezing transition scenario, previously explored in the statistical mechanics of 1/f-noise random energy models, also determines the value distribution of the maximum of the modulus of the characteristic polynomials of…
This part offers a survey of models proposed to cope with the symmetry-breaking challenge. Among them are the two-component neutrinos, the neutrino twins, the universal Fermi interaction, etc. Moreover, the broken discrete symmetries in…
We present a remarkably simple and surprisingly natural interpretation of the values of zeta functions at negative integers and zero. Namely we are able to relate these values to areas related to partial sums of powers. We apply these…
The properties of a fictitious, fermionic, many-body system based on the complex zeros of the Riemann zeta function are studied. The imaginary part of the zeros are interpreted as mean-field single-particle energies, and one fills them up…
The pair correlation is a localized statistic for sequences in the unit interval. Pseudo-random behavior with respect to this statistic is called Poissonian behavior. The metric theory of pair correlations of sequences of the form $(a_n…
The large values of the singlet and triplet two-nucleon scattering lengths locate the nuclear system close to the unitary limit. This particular position strongly constrains the low-energy observables in the three-nucleon system as…
The dynamics of phase transitions plays a crucial r\^ole in the so-called interface between high energy particle physics and cosmology. Many of the interesting results generated during the last fifteen years or so rely on simplified…
Two-nucleon momentum distributions are calculated for the ground states of nuclei with mass number $A\leq 8$, using variational Monte Carlo wave functions derived from a realistic Hamiltonian with two- and three-nucleon potentials. The…
Expanding a double tetrahedron formation of equal spheres arranged in fcc structure correlation between the positions of the nucleons and quantum numbers has been detected. The number of protons in the structure is not simply consistent…
In this paper we will focus on the study of relationships that can exist between odd numbers and different traditional functions like the gamma function, Riemann zeta function or function of von Mangoldt. Number theory applies to this…