Spectral Theory in Mathematical Physics
Spectral Theory in Mathematical Physics is a research topic within Mathematical Physics. Science Explorer counts 23k research works in it since 1950. 14.4% of them reached the world's top 10% most cited for their field and year.
This cluster of papers focuses on the spectral theory and properties of differential operators, particularly Schrödinger 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–Titchmarsh theory. The papers also delve into eigenvalue estimates and applications to quantum chaos and universal spectral statistics.
- Spectral Theory
- Differential Operators
- Quantum Graphs
- Localization
- Schrödinger Operators
- Inverse Spectral Problems
- Anderson Localization
- Scattering Theory
- Weyl–Titchmarsh Theory
- Eigenvalue Estimates
- Research works
- 23k fractional, since 1950
- In the world top 10%
- 3.4k per year above
- Top-10% rate
- 14.4% share of its works in the world top 10%
- Growth, 2013–17 → 2018–22
- +2% the tick is no change
Which countries lead Spectral Theory in Mathematical Physics research?
By volume, China and the United States publish the most (515 and 325 works in 2022–2025).
By volume, 2022–2025
- 1 China 515 works
- 2 United States 325 works
- 3 Russia 310 works
- 4 France 159 works
- 5 Italy 146 works
- 6 Germany 136 works
- 7 India 102 works
- 8 Japan 96 works
- 9 Türkiye 76 works
- 10 United Kingdom 73 works
How concentrated that is
The same countries as shares of everything the list above accounts for. A node where two countries do two thirds of the work and one spread evenly across twelve read alike as a ranking and not at all alike here.
Shares of the rows listed above, not of the whole node.
Which institutions lead Spectral Theory in Mathematical Physics research?
By volume in 2022–2025, Lomonosov Moscow State University publishes the most Spectral Theory in Mathematical Physics research, followed by St Petersburg University and Centre National de la Recherche Scientifique.
By volume, 2022–2025
- 1 Lomonosov Moscow State UniversityRussia 32 works
- 2 St Petersburg UniversityRussia 31 works
- 3 Centre National de la Recherche ScientifiqueFrance 25 works
- 4 University of SfaxTunisia 23 works
- 5 Peoples' Friendship University of RussiaRussia 16 works
- 6 Steklov Mathematical InstituteRussia 15 works
- 7 Russian Academy of SciencesRussia 14 works
- 8 Samarkand State University named after Sharof RashidovUzbekistan 13 works
- 9 Stockholm UniversitySweden 13 works
- 10 Czech Technical University in PragueCzechia 12 works
Who are the leading researchers in Spectral Theory in Mathematical Physics?
The most-cited researchers publishing on Spectral Theory in Mathematical Physics include Guanrong Chen, Stephan Ramon Garcia and Terence Tao.
- 1 Guanrong Chen Hong Kong 5.4k citations
- 2 Stephan Ramon Garcia United States 4k citations
- 3 Terence Tao United States 3.1k citations
Ranked by citations received across their whole record, among researchers with at least three works on this topic.
Where is Spectral Theory in Mathematical Physics research done?
The largest centres of Spectral Theory in Mathematical Physics research in 2022–2025 are Moscow (Russia), Beijing (China), Saint Petersburg (Russia) and Paris (France). Among places with at least 20 works in it, it is an unusually large share of all research in Sfax.
Largest cities, 2022–2025
- 1 Moscow Russia 130 works
- 2 Beijing China 77 works
- 3 Saint Petersburg Russia 51 works
- 4 Paris France 46 works
- 5 Nanjing China 39 works
- 6 Baku Azerbaijan 28 works
- 7 London United Kingdom 27 works
- 8 Tokyo Japan 26 works
- 9 Shanghai China 26 works
- 10 Mexico City Mexico 26 works
Where it is the local speciality
- SfaxTN · 23.0 works21×
Location quotient: how much more of its research is in Spectral Theory in Mathematical Physics than the world average.
Where is the best place to study Spectral Theory in Mathematical Physics?
Among universities, judged by research, Lomonosov Moscow State University, Saratov State University and University of Sfax score highest, combining excellence, specialisation, size, growth and international reach. Research strength is one signal when choosing where to study; it does not measure teaching.
One dot per university in the table below. The upper left is the interesting corner: small places doing unusually strong work.
| # | University | Score | Top 10% | Specialisation | Works | Growth |
|---|---|---|---|---|---|---|
| 1 | Lomonosov Moscow State UniversityRussia | 65.8 | 6.6% | 13.2× | 32 | +63.8% |
| 2 | Saratov State UniversityRussia | 65.8 | 45.6% | 41.8× | 10 | +42.5% |
| 3 | University of SfaxTunisia | 61.6 | 9.6% | 31.8× | 23 | +52.3% |
| 4 | St Petersburg UniversityRussia | 60.4 | 4.6% | 22.9× | 31 | +87.5% |
| 5 | Peoples' Friendship University of RussiaRussia | 54.1 | 11.8% | 17.8× | 16 | +56.5% |
| 6 | Samarkand State University named after Sharof RashidovUzbekistan | 53.4 | 26.0% | 39.8× | 13 | -12.3% |
| 7 | Czech Technical University in PragueCzechia | 53.4 | 19.8% | 17.8× | 12 | +15.3% |
| 8 | Zhejiang Normal UniversityChina | 52.8 | 20.2% | 13.9× | 12 | +31.5% |
| 9 | Stockholm UniversitySweden | 50.3 | 6.2% | 13.7× | 12 | +43.9% |
| 10 | Central China Normal UniversityChina | 46.4 | 9.1% | 14.9× | 11 | +64.7% |
Universities only. Score blends excellence (30%), specialisation (25%), size (20%), growth (15%) and international reach (10%), 2015–2022; growth compares 2010–14 with 2015–19.
Is Spectral Theory in Mathematical Physics research growing?
Output in 2018–2022 was 2% higher than in 2013–2017, peaking in 2025. The fastest-growing topics are Spectral Theory in Mathematical Physics.
The same series as a ribbon — one cell per year, darker for more. The line above answers how much; this answers when.
Which topics inside it are moving
Growth and decline on one axis around a shared zero. Two lists side by side hide the thing that matters: whether the growth dwarfs the decline, or the other way round.