Related papers: Open Problems in Applying Random-Matrix Theory to …
Reaction networks are a general formalism for describing collections of classical entities interacting in a random way. While reaction networks are mainly studied by chemists, they are equivalent to Petri nets, which are used for similar…
The problem of determining the effects of the surrounding plasma on nuclear reaction rates in stars is formulated ab initio, using the techniques of quantum statistical mechanics. We derive a result that expresses the complete effects of…
This work analyzes singular-value spectra of weight matrices in pretrained transformer models to understand how information is stored at both ends of the spectrum. Using Random Matrix Theory (RMT) as a zero information hypothesis, we…
This review focuses on nuclear reactions in astrophysics and, more specifically, on reactions with light ions (nucleons and alpha particles) proceeding via the strong interaction. It is intended to present the basic definitions essential…
We solve the quasiclassical problem of tunneling through an external potential barrier in a dense plasma, where the tunneling particles undergo simultaneous collisions with other particles in thermodynamic equilibrium. Under such conditions…
The interpretation of experimental results at RHIC and in the future also at LHC requires very reliable and realistic models. Considerable effort has been devoted to the development of such models during the past decade, many of them being…
The Nystr\"om method is a popular choice for finding a low-rank approximation to a symmetric positive semi-definite matrix. The method can fail when applied to symmetric indefinite matrices, for which the error can be unboundedly large. In…
The transition-matrix ($T$-matrix) approach provides a general formalism to study scattering problems in various areas of physics, including acoustics (scalar fields) and electromagnetics (vector fields), and is related to the theory of the…
The response function to an external prove is evaluated using the ring approximation in nuclear matter. Contrary to what it is usually assumed, it is shown that the summation of the ring series and the solution of the Dyson's equation are…
The unfolding problem in particle physics is to make inferences about the true particle spectrum based on smeared observations from a detector. This is an ill-posed inverse problem, where small changes in the smeared distribution can lead…
Radiation technologies have found wide application in power engineering, medicine, biology and other areas of human activities. However, theoretical calculations of nuclear reactions and, correspondingly, the interpretation of experimental…
Machine learning has recently emerged as a powerful tool for generating new molecular and material structures. The success of state-of-the-art models stems from their ability to incorporate physical symmetries, such as translation,…
R-matrix theory was originally developed to describe nuclear reactions. The framework was further extended to describe {\beta} decay to unbound states. However, at the time writing, no clear description of {\gamma} decays to unbound states…
Machine learning techniques applied to chemical reactions has a long history. The present contribution discusses applications ranging from small molecule reaction dynamics to platforms for reaction planning. ML-based techniques can be of…
A zone of reactions is determined and then exploited as a tool in studying the space-time structure of an interacting system formed in a collision of relativistic nuclei. The time dependence of the reaction rates integrated over spatial…
There exists an exact relationship between the quasi-exactly solvable problems of quantum mechanics and models of square and rectangular random complex matrices. This relationship enables one to reduce the problem of constructing…
One-nucleon transfer reactions, in particular (d,p) reactions, have played a central role in nuclear structure studies for many decades. Present theoretical descriptions of the underlying reaction mechanisms are insufficient for addressing…
We consider theoretically ionization of an atom by neutrino impact taking into account electromagnetic interactions predicted for massive neutrinos by theories beyond the Standard Model. The effects of atomic recoil in this process are…
Random matrix theory (RMT) is a powerful statistical tool to model spectral fluctuations. In addition, RMT provides efficient means to separate different scales in spectra. Recently RMT has found application in quantum chromodynamics (QCD).…
The optical properties of a fixed atom are well-known and investigated. For example, the extraordinarily large cross section of a single atom as seen by a resonant photon is essential for quantum optical applications. Mechanical effects…