Inverse problems for quantum graphs

Project funded by Swedish Research Council (Project grant), grant 2008-05254_VR. Participating organisations named by the source: Stockholm University. Funded amount: SEK 1,940,000, as stated by the source. Runs 2009-01-01 to 2011-12-31. Keywords: Oklassificerat, Unclassified. 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: Under quantum graphs we understand differential operators on geometric graphs coupled by certain vertex matching conditions. Such operators appear in models from nano-electronics and are expected to be used in designing modern computers. From the mathematical point of view this area lies on the border between analysis and discrete mathematics often leading to an interesting interplay. Analytic studies show that these problems inherit typical properties of both ordinary and partial differential operators allowing to use corresponding specific methods. The current research program concerns different inverse problems for quantum graphs such as reconstruction of the metric graph, the potential or the vertex conditions from spectral or scattering data. The first two problems have been solved recently for graphs without cycles based on the matrix Titchmarsh-Weyl function. We propose to study all described inverse problems for arbitrary graphs (even allowing cycles) in the presence of a varying magnetic field. It is already shown by the main applicant that the knowledge of the spectral data for different values of the magnetic field allows one to reconstruct simplest graphs (with Euler characteristic zero). It is planned not only to develop algorithms to solve the inverse problems but also to study the relations between geometric characteristics of graphs and their spectral and transport properties as well. In particular characterization of planar graphs will be investigated.

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 "Inverse problems for quantum graphs" was funded by the Swedish Research Council with a grant of SEK 1,940,000, running from January 1, 2009, to December 31, 2011, involving Stockholm University. It focuses on inverse problems related to differential operators on geometric graphs. Suggested technology pillar: computing. Generated by AI from the public source text; it may contain errors and the original source is authoritative.