Spectral analysis of quantum graphs and networks

Project funded by Swedish Research Council (Project grant), grant 2013-04973_VR. Participating organisations named by the source: Stockholm University. Funded amount: SEK 3,000,000, as stated by the source. Runs 2014-01-01 to 2017-12-31. Keywords: Naturvetenskap, Natural Sciences, Matematik, Mathematics, Matematisk analys, Mathematical Analysis. Source: OpenAIRE Graph, from the funder's project data (collected by OpenAIRE on 2025-12-04); national funding data, not CORDIS. Abstract given by the source: Quantum graphs and networks - differential operators on finite and infinite metric graphs - are used to describe spectral and transport properties of systems of completely different origin: from microwave cavities to water transport in narrow channels. The main goal of the current project is to provide a more systematic study of spectral properties of (finite) quantum graphs investigating behavior of eigenvalues under topological and geometric perturbations. Global spectral properties will be investigated by proving Kottos-Smilansky trace formula in the most general case and establishing new trace inequalities of Lieb-Thirring type. Obtained results will be applied to study transport and scattering properties of (infinite) quantum networks focusing on explicit conditions that guarantee self-adjointness and semiboundedness. Systematic studies of self-similar and periodic networks will form a basis for investigating quasicrystallic networks providing a natural transition to random quantum networks, which is a far-sighted goal of our studies.

Original source.

Source: OpenAIRE Graph: projects of national funders, OpenAIRE, from the project data of Swedish Research Council. Retrieved 2026-10-28. Licence: Creative Commons Attribution 4.0 (OpenAIRE Graph). Selected metadata, adapted presentation; the publisher's record is authoritative. No endorsement by the source is implied. Licence: Creative Commons Attribution 4.0 (CC BY 4.0).

AI-assisted summary: The project "Spectral analysis of quantum graphs and networks" was funded by the Swedish Research Council with SEK 3,000,000 from 2014 to 2017, involving Stockholm University. It aims to systematically study spectral properties of quantum graphs and their applications. Suggested technology pillar: simulation. Generated by AI from the public source text; it may contain errors and the original source is authoritative.