Driven linear modes: Analytical solutions for finite discrete systems

TL;DR

This paper derives exact analytical solutions for driven linear modes in finite discrete systems, revealing their frequency-dependent localization and resonance behaviors within the system's dispersion relation.

Contribution

It provides the first closed-form analytical expressions for driven linear modes in finite discrete systems, including their localization and resonance characteristics.

Findings

Modes are extended within the linear frequency band.

Modes are localized or avoided at the system edges outside the band.

Resonant frequencies form the system's dispersion relation.

Abstract

We have obtained exact analytical expressions in closed form, for the linear modes excited in finite and discrete systems that are driven by a spatially homogeneous alternating field. Those modes are extended for frequencies within the linear frequency band while they are either end-localized or end-avoided for frequencies outside the linear frequency band. The analytical solutions are resonant at particular frequencies, which compose the frequency dispersion relation of the finite system.