# Quantum integrable systems and concentration of plasmon resonance

@inproceedings{Ammari2021QuantumIS, title={Quantum integrable systems and concentration of plasmon resonance}, author={Habib M. Ammari and Yat Tin Chow and Hongyu Liu and Mahesh Sunkula}, year={2021} }

We are concerned with the quantitative mathematical understanding of surface plasmon resonance (SPR). SPR is the resonant oscillation of conducting electrons at the interface between negative and positive permittivity materials and forms the fundamental basis of many cutting-edge applications of metamaterials. It is recently found that the SPR concentrates due to curvature effect. In this paper, we derive sharper and more explicit characterisations of the SPR concentration at high-curvature… Expand

#### References

SHOWING 1-10 OF 78 REFERENCES

Ergodic properties of eigenfunctions

- Uspehi Mat. Nauk, 29
- 1974

Quantum ergodicity and localization of plasmon resonances

- Physics, Mathematics
- 2020

We are concerned with the geometric properties of the surface plasmon resonance (SPR). SPR is a non-radiative electromagnetic surface wave that propagates in a direction parallel to the negative… Expand

Surface Localization of Plasmons in Three Dimensions and Convexity

- Computer Science, Mathematics
- SIAM J. Appl. Math.
- 2021

It is proved that on smooth bounded domains of general shape the sequence of plasmons converges to zero off the boundary surface almost surely at the rate of $j^{-1/2}$ and that cloaking by anomalous localized resonance does not occur on three-dimensional strictly convex smooth domains. Expand

Mathematical analysis of plasmon resonances for curved nanorods

- Mathematics, Physics
- 2020

We investigate plasmon resonances for curved nanorods which present anisotropic geometries. We analyze quantitative properties of the plasmon resonance and its relationship to the metamaterial… Expand

Symplectic invariants of semitoric systems and the inverse problem for quantum systems

- Mathematics, Physics
- 2020

Simple semitoric systems were classified about ten years ago in terms of a collection of invariants, essentially given by a convex polygon with some marked points corresponding to focus-focus… Expand

Characterization of the essential spectrum of the Neumann–Poincaré operator in 2D domains with corner via Weyl sequences

- Mathematics
- Revista Matemática Iberoamericana
- 2019

The Neumann-Poincar\'e (NP) operator naturally appears in the context of metamaterials as it may be used to represent the solutions of elliptic transmission problems via potentiel theory. In… Expand

Localized sensitivity analysis at high-curvature boundary points of reconstructing inclusions in transmission problems

- Mathematics
- 2019

In this paper, we are concerned with the recovery of the geometric shapes of inhomogeneous inclusions from the associated far field data in electrostatics and acoustic scattering. We present a local… Expand

Spectral Properties of Neumann-Poincaré Operator and Anomalous Localized Resonance in Elasticity Beyond Quasi-Static Limit

- Mathematics, Physics
- 2019

This paper is concerned with the polariton resonances and their application for cloaking due to anomalous localized resonance (CALR) for the elastic system within the finite frequency regime beyond… Expand