Plasmon Resonances in Nanoparticles, Their Applications to Magnetics and Relation to the Riemann Hypothesis

TL;DR

This paper reviews the mathematical modeling of plasmon resonances in nanoparticles, explores their applications in magnetics, and discusses a theoretical connection to the Riemann hypothesis, highlighting interdisciplinary significance.

Contribution

It provides a comprehensive mathematical framework for plasmon resonances and introduces a novel discussion linking eigenvalue problems to the Riemann hypothesis.

Findings

Mathematical treatment of plasmon resonances as eigenvalue problems

Potential applications of plasmon resonances in magnetic technologies

Discussion of a theoretical link to the Riemann hypothesis

Abstract

The review of the mathematical treatment of plasmon resonances as an eigenvalue problem for specific boundary integral equations is presented and general properties of plasmon spectrum are outlined. Promising applications of plasmon resonances to magnetics are described. Interesting relation of eigenvalue treatment of plasmon resonances to the Riemann hypothesis is discussed.