Related papers: Nuclei, Primes and the Random Matrix Connection
The general nuclear contact matrices are defined, taking into consideration all partial waves and finite-range interactions, extending Tan's work for the zero range model. The properties of these matrices are discussed and the relations…
The problem of how mathematics and physics are related at a foundational level is of much interest. One approach is to work towards a coherent theory of physics and mathematics together. Here steps are taken in this direction by first…
This paper explores the interactions between knot theory and quantum computing. On one side, knot theory has been used to create models of quantum computing, and on the other, it is a source of computational problems. Knot theory is often…
Random matrices now play a role in many parts of computational mathematics. To advance these applications, it is desirable to have tools that are flexible, easy to use, and powerful. Over the last 25 years, researchers have developed a…
Motivation and perspective for an exciting new research direction interconnecting logic, spacetime theory, relativity--including such revolutionary areas as black hole physics, relativistic computers, new cosmology--are presented in this…
This series of introductory lectures consists of two parts. In the first part, I rapidly review the basic notions of quantum physics and many primitives of quantum information (i.e. notions that one must be somehow familiar with in the…
This book collects the lectures about graph theory and its applications which were given to students of mathematical departments of Moscow State University and Peking University. Graph theory is a very wide field with a lot of applications…
There is growing interest in nuclear physics applications of effective field theory. I give a brief account of some of the latest developments in this area. I also describe interplay between this new approach and the traditional nuclear…
Nuclear theory today aims for a comprehensive theoretical framework that can describe all nuclei. I discuss recent progress in this pursuit and the associated challenges as we move forward.
Quantum theory revolutionised physics by introducing a new fundamental constant and a new mathematical framework to describe the observed phenomena at the atomic scale. These new concepts run counter to our familiar notions of classical…
In this review we discuss the current status of research in nuclear physics which is being carried out in different centers in the World. For this purpose we supply a short account of the development in the area which evolved over the last…
The rotating nuclei represent one of most interesting subjects for theoretical and experimental studies. They open a new dimension of nuclear landscape, namely, spin direction. Contrary to the majority of nuclear systems, their properties…
In non-relativistic as well as in special relativistic quantum theory, {\em mass} and {\em charge} are {\em pure numbers} appearing in various (quantum) operators and admit {\em any values}, {\it ie}, values for these quantities are to be…
The symmetry energy describes how the energy of nuclear matter rises as one goes away from equal numbers of neutrons and protons. This is very important to describe neutron rich matter in astrophysics. This article reviews our knowledge of…
Neutron stars are rich laboratories of multiple branches of modern physics. These include gravitational physics, nuclear and particle physics, (quantum) electrodynamics, and plasma astrophysics. In this chapter, we present the pioneering…
The different facets of the $R$-matrix method are presented pedagogically in a general framework. Two variants have been developed over the years: $(i)$ The "calculable" $R$-matrix method is a calculational tool to derive scattering…
We introduce in this section an Algebraic and Combinatorial approach to the theory of Numbers. The approach rests on the observation that numbers can be identified with familiar combinatorial objects namely rooted trees, which we shall here…
Astrophysics is gaining increased attention from the particle and nuclear physics communities, as budget cuts, delays, and cancellations limit opportunities for breakthrough research at accelerator laboratories. Observations of cosmic rays…
Algebraic quantum field theory is an approach to relativistic quantum physics, notably the theory of elementary particles, which complements other modern developments in this field. It is particularly powerful for structural analysis but…
For the better part of a century the field of nuclear astrophysics has aimed to answer fundamental questions about nature, such as the origin of the elements and the behavior of high-density, low-temperature matter. Sustained and concerted…