Nuclei, Primes and the Random Matrix Connection

2009/09/20 by F.W.K. Firk, Frank W. K. Firk, Steven J. Miller · 1 voice · 3 citations
Mathematics · Physics and Astronomy · #Algebra over a field #Analytic Number Theory Research #Computer science #Connection (principal bundle) #Context (archaeology) #Geometry #Mathematical Dynamics and Fractals #Mathematics #Matrix (chemical analysis) #Number theory #Physics #Probability theory #Pure mathematics #Quantum chaos and dynamical systems #Quantum mechanics #Random matrix #Statistical physics #Statistics #Theoretical physics #math-ph #math.MP #math.NT #msc:11M26 #msc:15A52 #msc:82D99

paper · pdf · doi:10.3390/sym1010064

published as Symmetry 1 (2009), 64--105 · 54 pages, 11 images

openalex publication_date 2009/09/20 · arxiv created 2009/09/27 · arxiv published 2009/09/27 · arxiv updated 2009/09/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

In this article, we discuss the remarkable connection between two very different fields, number theory and nuclear physics. We describe the essential aspects of these fields, the quantities studied, and how insights in one have been fruitfully applied in the other. The exciting branch of modern mathematics, random matrix theory, provides the connection between the two fields. We assume no detailed knowledge of number theory, nuclear physics, or random matrix theory; all that is required is some familiarity with linear algebra and probability theory, as well as some results from complex analysis. Our goal is to provide the inquisitive reader with a sound overview of the subjects, placing them in their historical context in a way that is not traditionally given in the popular and technical surveys.

Citations

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Cited by

• A unitary test of the Ratios Conjecture
• Will a physicist prove the Riemann Hypothesis?
• Cause and cure of sloppiness in ordinary differential equation models

Discussions

• 0909.4914v1.pdf https://arxiv.org/pdf/0909.4914 [bsky, 0 points, 0 comments]

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