Related papers: Nuclei, Primes and the Random Matrix Connection
In this article, the notion of a mathematical model in science is attempted to be enlightened from several points of view. In particular, it is shown that mathematical models are introduced differently and used differently in different…
Pairing correlations in symmetric nuclear matter are studied within a relativistic mean-field approximation based on a field theory of nucleons coupled to neutral ($\sigma$ and $\omega$) and to charged ($\varrho$) mesons. The Hartree-Fock…
In what follows we first set the context for inverse scattering in nuclear physics with a brief account of inverse problems in general. We then turn to inverse scattering which involves the S-matrix, which connects the interaction potential…
Molecules containing short-lived, radioactive nuclei are uniquely positioned to enable a wide range of scientific discoveries in the areas of fundamental symmetries, astrophysics, nuclear structure, and chemistry. Recent advances in the…
The Facility for Rare Isotope Beams (FRIB) will be a world-leading laboratory for the study of nuclear structure, reactions and astrophysics. Experiments with intense beams of rare isotopes produced at FRIB will guide us toward a…
Since it was first applied to the study of nuclear interactions by Wigner and Dyson, almost 60 years ago, Random Matrix Theory (RMT) has developed into a field of its own within applied mathematics, and is now essential to many parts of…
Random matrix theory has played a major role in several areas of pure and applied mathematics, as well as statistics, physics, and computer science. This lecture aims to describe the intrinsic freeness phenomenon and how it provides new…
An accurate description of nuclear matter starting from free-space nuclear forces has been an elusive goal. The complexity of the system makes approximations inevitable, so the challenge is to find a consistent truncation scheme with…
Nuclear Physics has had its ups and downs. However in recent years, bucked up by some new and often puzzling data, it has become a potentially very rich field. We review some of these exciting developments in a few important sectors of…
The theory of random real numbers is exceedingly well-developed, and fascinating from many points of view. It is also quite challenging mathematically. The present notes are intended as no more than a gateway to the larger theory. They…
The status of relativistic nuclear many-body calculations of nuclear systems to be built up in terms of protons and neutrons is reviewed. In detail, relativistic effects on several aspects of nuclear matter such as the effective mass,…
Nuclear supersymmetry is reviewed and some of its applications and extensions are discussed, together with a proposal for new, more stringent and precise tests to probe the supersymmetry classification, in particular, correlations between…
Since the quantum field theory treats a system of particles, there must be a distribution which is associated with the system of particles. It means that a meaningful quantity is adjoined in the system of particles. It seems that these…
Nuclear astrophysics is a multi-disciplinary field with a huge demand for nuclear data. Among its various fields, stellar evolution and nucleosynthesis are clearly the most closely related to nuclear physics. The need for nuclear data for…
Among all nuclear ground-state properties, atomic masses are highly specific for each particular combination of N and Z and the data obtained apply to a variety of physics topics. One of the most crucial questions to be addressed in mass…
The apparent impossibility of extending non-relativistic quantum mechanics to a relativistic quantum theory is shown to be due to the insufficient structural richness of the field of complex numbers over which quantum mechanics is built. A…
We propose a novel approach to the analysis of experimental data obtained in relativistic nucleus-nucleus collisions which borrows from methods developed within the context of Random Matrix Theory. It is applied to the detection of…
A relativistic approach to describe nuclear and in general strongly interacting matter is introduced and discussed. Here, not only the nuclear forces but also the masses of the nucleons are generated through meson fields. Within this…
Standard concepts of nuclear physics explaining the systematics of ground state spins in nuclei by the presence of specific coherent terms in the nucleon-nucleon interaction were put in doubt by the observation that these systematics can be…
First we survey generating function methods for obtaining useful probability estimates about random matrices in the finite classical groups. Then we describe a probabilistic picture of conjugacy classes which is coherent and beautiful.…