An Approximate Method for Modeling Plasmons on Graphene with Time- and Space-dependent Properties
Abstract
This paper presents approximate computational methods for modeling surface plasmon propagation on a graphene sheet with time- and space-dependent material properties. Starting from Maxwell's equations, the evolution of current density under a spatially and temporally modulated Drude weight is formulated as a partial integro-differential equation (PIDE). Assuming small-amplitude perturbations of the Drude weight, a regular perturbation expansion is developed. The solvability and Fourier invertibility of the resulting order-by-order integral equations are established in appropriate Sobolev spaces. A numerical solver combining a Volterra integral equation formulation with the fast Fourier transform (FFT) is introduced, along with pointwise error estimates and computational complexity analysis. Additionally, an analytical transform-based solution using contour integration and Laplace inversion is derived for traveling-wave Drude weight modulations. Numerical simulations demonstrate diverse wave phenomena, including traveling, standing, and exponentially growing plasmonic current densities.
Related
- Seizure recruitment properties are dependent upon dynamotype: A modeling study
- Surface scalar plasmons on curved interfaces: a venue for analogue gravity
- Spectral Chebyshev wavelet method for state-dependent fractional integro-differential equations in adaptive tumor growth modeling
- Reliability Modeling using an Equilibrium-Based Xgamma Distribution: Properties, Estimation, and Applications
- Covariate-dependent Joint Modeling of Multivariate Ordinal Preferences and Its Connections with Comparison Models
BibTeX
@misc{rudge2026approximate,
title = {{An Approximate Method for Modeling Plasmons on Graphene with Time- and Space-dependent Properties}},
author = {Kaleigh Rudge and Fadil Santosa},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.38370},
eprint = {2609.38370},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.38370},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - An Approximate Method for Modeling Plasmons on Graphene with Time- and Space-dependent Properties
AU - Kaleigh Rudge
AU - Fadil Santosa
PY - 2026
DA - 2026/09/29
PB - arXiv
DO - 10.48550/arxiv.2609.38370
UR - https://arxiv.org/abs/2609.38370
AB - This paper presents approximate computational methods for modeling surface plasmon propagation on a graphene sheet with time- and space-dependent material properties. Starting from Maxwell's equations, the evolution of current density under a spatially and temporally modulated Drude weight is formulated as a partial integro-differential equation (PIDE). Assuming small-amplitude perturbations of the Drude weight, a regular perturbation expansion is developed. The solvability and Fourier invertibility of the resulting order-by-order integral equations are established in appropriate Sobolev spaces. A numerical solver combining a Volterra integral equation formulation with the fast Fourier transform (FFT) is introduced, along with pointwise error estimates and computational complexity analysis. Additionally, an analytical transform-based solution using contour integration and Laplace inversion is derived for traveling-wave Drude weight modulations. Numerical simulations demonstrate diverse wave phenomena, including traveling, standing, and exponentially growing plasmonic current densities.
ER -