{"cited_by_count":1160954,"description":"This cluster of papers focuses on the spectral theory and properties of differential operators, particularly Schr\u00f6dinger operators, on various structures such as quantum graphs and thin manifolds. It explores topics such as localization, inverse spectral problems, Anderson localization, scattering theory, and Weyl\u2013Titchmarsh theory. The papers also delve into eigenvalue estimates and applications to quantum chaos and universal spectral statistics.","display_name":"Spectral Theory in Mathematical Physics","domain_id":"3","external_ids":{"openalex":"https://openalex.org/T11022","wikipedia":"https://en.wikipedia.org/wiki/Spectral_theory_of_differential_operators"},"field_id":"26","id":"T11022","keywords":[{"display_name":"spectral theory","id":"spectral-theory","score":0.5192,"url":"https://openalex.org/keywords/spectral-theory"},{"display_name":"Schr\u00f6dinger operators","id":"schrodinger-operators","score":0.7686,"url":"https://openalex.org/keywords/schrodinger-operators"},{"display_name":"eigenvalues","id":"eigenvalues","score":0.2198,"url":"https://openalex.org/keywords/eigenvalues"},{"display_name":"self-adjoint operators","id":"self-adjoint-operators","score":0.4675,"url":"https://openalex.org/keywords/self-adjoint-operators"},{"display_name":"eigenfunctions","id":"eigenfunctions","score":0.3039,"url":"https://openalex.org/keywords/eigenfunctions"},{"display_name":"scattering theory","id":"scattering-theory","score":0.3325,"url":"https://openalex.org/keywords/scattering-theory"},{"display_name":"Sturm-Liouville problems","id":"sturm-liouville-problems","score":0.5417,"url":"https://openalex.org/keywords/sturm-liouville-problems"},{"display_name":"Sturm-Liouville operators","id":"sturm-liouville-operators","score":0.8325,"url":"https://openalex.org/keywords/sturm-liouville-operators"},{"display_name":"inverse spectral problem","id":"inverse-spectral-problem","score":0.7547,"url":"https://openalex.org/keywords/inverse-spectral-problem"},{"display_name":"Anderson localization","id":"anderson-localization","score":0.2074,"url":"https://openalex.org/keywords/anderson-localization"},{"display_name":"eigenvalue asymptotics","id":"eigenvalue-asymptotics","score":0.7439,"url":"https://openalex.org/keywords/eigenvalue-asymptotics"},{"display_name":"Laplacian","id":"laplacian","score":0.2741,"url":"https://openalex.org/keywords/laplacian"},{"display_name":"discrete spectrum","id":"discrete-spectrum","score":0.4745,"url":"https://openalex.org/keywords/discrete-spectrum"},{"display_name":"essential spectrum","id":"essential-spectrum","score":0.5725,"url":"https://openalex.org/keywords/essential-spectrum"},{"display_name":"spectral gap","id":"spectral-gap","score":0.2136,"url":"https://openalex.org/keywords/spectral-gap"},{"display_name":"Dirac operator","id":"dirac-operator","score":0.2654,"url":"https://openalex.org/keywords/dirac-operator"},{"display_name":"spectrum","id":"spectrum","score":0.2057,"url":"https://openalex.org/keywords/spectrum"},{"display_name":"eigenvalue bounds","id":"eigenvalue-bounds","score":0.3079,"url":"https://openalex.org/keywords/eigenvalue-bounds"},{"display_name":"self-adjoint extensions","id":"self-adjoint-extensions","score":0.7559,"url":"https://openalex.org/keywords/self-adjoint-extensions"},{"display_name":"non-self-adjoint operators","id":"non-self-adjoint-operators","score":0.5414,"url":"https://openalex.org/keywords/non-self-adjoint-operators"},{"display_name":"eigenfunction expansion","id":"eigenfunction-expansion","score":0.2149,"url":"https://openalex.org/keywords/eigenfunction-expansion"},{"display_name":"singular potentials","id":"singular-potentials","score":0.4365,"url":"https://openalex.org/keywords/singular-potentials"},{"display_name":"spectral geometry","id":"spectral-geometry","score":0.3468,"url":"https://openalex.org/keywords/spectral-geometry"},{"display_name":"elliptic operators","id":"elliptic-operators","score":0.2189,"url":"https://openalex.org/keywords/elliptic-operators"},{"display_name":"absolutely continuous spectrum","id":"absolutely-continuous-spectrum","score":0.8569,"url":"https://openalex.org/keywords/absolutely-continuous-spectrum"}],"legacy_keywords":["Spectral Theory","Differential Operators","Quantum Graphs","Localization","Schr\u00f6dinger Operators","Inverse Spectral Problems","Anderson Localization","Scattering Theory","Weyl\u2013Titchmarsh Theory","Eigenvalue Estimates"],"openalex_id":"https://openalex.org/T11022","source_created_date":"2024-01-23T15:27:09","source_updated_date":"2026-10-17T03:02:00","subfield_id":"2610","url":"/topics/T11022","works_api_url":"https://api.openalex.org/works?filter=topics.id:T11022","works_count":102095,"label":"Spectral Theory in Mathematical Physics","provider":"openalex","revision":"e62a43caeb6b2530","taxonomy_revision":"f050b5d4780b1289","title":"Spectral Theory in Mathematical Physics","kind":"topic-directory","aeo_cohort":"topic-directory","catalogue_revision":"f050b5d4780b1289","numeric_address":"36240762249586929","address_version":"morton4x16-v1","coordinates":[3,26,2610,11022],"answer_status":"Directory metadata; local answer requires separate source review","truth_status":"Subject descriptor, not a factual answer or a demonstrated knowledge gap","reviewed_answer":null}