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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. 10.0% 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%
2.3k
per year above
Top-10% rate
10.0%
share of its works in the world top 10%
Growth, 2018-21 → 2022-25
+17%
the tick is no change
Largest producer
China
27% of the 10 largest, 2022-now
Spectral Theory in Mathematical Physics

Which countries lead Spectral Theory in Mathematical Physics research?

By volume, China and the United States publish the most (608 and 389 works in 2022-now).

By volume, 2022-now

  1. 1 China 608 works
  2. 2 United States 389 works
  3. 3 Russia 348 works
  4. 4 France 188 works
  5. 5 Italy 167 works
  6. 6 Germany 154 works
  7. 7 India 125 works
  8. 8 Japan 110 works
  9. 9 United Kingdom 87 works
  10. 10 Türkiye 84 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.

China: 26.9%United States: 17.2%Russia: 15.4%France: 8.3%6 others listed: 32.2%27%largest
China608 · 26.9%United States389 · 17.2%Russia348 · 15.4%France188 · 8.3%6 others listed727 · 32.2%

Shares of the rows listed above, not of the whole node.

Which institutions lead Spectral Theory in Mathematical Physics research?

By volume in 2022-now, Russian Academy of Sciences publishes the most Spectral Theory in Mathematical Physics research, followed by Centre National de la Recherche Scientifique and Lomonosov Moscow State University.

By volume, 2022-now

  1. 1 Russian Academy of SciencesRussia 101 works
  2. 2 Centre National de la Recherche ScientifiqueFrance 94 works
  3. 3 Lomonosov Moscow State UniversityRussia 36 works
  4. 4 St Petersburg UniversityRussia 33 works
  5. 5 University of SfaxTunisia 24 works
  6. 6 Peoples' Friendship University of RussiaRussia 17 works
  7. 7 Tsinghua UniversityChina 16 works
  8. 8 Samarkand State University named after Sharof RashidovUzbekistan 15 works
  9. 9 Ludwig-Maximilians-Universität MünchenGermany 14 works
  10. 10 Czech Technical University in PragueCzechia 14 works

Who are the leading researchers in Spectral Theory in Mathematical Physics?

The most-cited researchers publishing on Spectral Theory in Mathematical Physics include Florian Fischer, Kenji Watanabe and Takashi Taniguchi.

  1. 1 Florian Fischer Germany 257k citations
  2. 2 Kenji Watanabe Japan 237k citations
  3. 3 Takashi Taniguchi Japan 227k citations
  4. 4 Edward H. Witten United States 174k citations

Ranked by citations received across their whole record, among researchers with at least three works on this topic.

What are the most cited papers in Spectral Theory in Mathematical Physics?

The most cited paper in Spectral Theory in Mathematical Physics is "On the generators of quantum dynamical semigroups" (Göran Lindblad, 1976), with 7,738 citations. Next come "Unpaired Majorana fermions in quantum wires" (4,840) and "Minimax Methods in Critical Point Theory with Applications to Differential Equations" (4,190).

Most cited papers
#PaperReleasedCitations
1 On the generators of quantum dynamical semigroups Göran Lindblad · Communications in Mathematical Physics Jun 1976 7,738
2 Unpaired Majorana fermions in quantum wires A Yu Kitaev · Physics-Uspekhi Open access Oct 2001 4,840
3 Minimax Methods in Critical Point Theory with Applications to Differential Equations Paul H. Rabinowitz · Regional conference series in mathematics Conference paper Jul 1986 4,190
4 Separability of mixed states: necessary and sufficient conditions Michał Horodecki, Paweł Horodecki, Ryszard Horodecki · Physics Letters A Open access Nov 1996 3,678
5 The Kondo Problem of Heavy Fermions Alex C. Hewson, Piers Coleman · Physics Today Mar 1994 2,364
All 100 most cited papers, with filters and sorting

Where is Spectral Theory in Mathematical Physics research done?

The largest centres of Spectral Theory in Mathematical Physics research in 2022-now are Moscow (Russia), Beijing (China), Paris (France) and Saint Petersburg (Russia). Among places with at least 20 works in it, it is an unusually large share of all research in Sfax.

Largest cities, 2022-now

  1. 1 MoscowRussia 148 works
  2. 2 BeijingChina 89 works
  3. 3 ParisFrance 55 works
  4. 4 Saint PetersburgRussia 54 works
  5. 5 NanjingChina 44 works
  6. 6 ShanghaiChina 34 works
  7. 7 BakuAzerbaijan 31 works
  8. 8 LondonUnited Kingdom 31 works
  9. 9 WuhanChina 30 works
  10. 10 Mexico CityMexico 29 works

Where it is the local speciality

  1. SfaxTN · 24.5 works20×
← less than its size predicts1×more →

Location quotient: how much more of its research is in Spectral Theory in Mathematical Physics than the world average.

See Spectral Theory in Mathematical Physics on the map

Where is the best place to study Spectral Theory in Mathematical Physics?

Among universities, judged by research, Samarkand State University named after Sharof Rashidov, Zhejiang Normal 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.

0%20%40%mean 17.26%fractional works in this field (log) →share of work in the world top 10% →Samarkand State Univ…Zhejiang Normal Univ…Tsinghua UniversityUniversity of Sfax
above the meannear itbelow it

One dot per university in the first ten of the table below, at the default weights. The upper left is the interesting corner: small places doing unusually strong work.

Excellenceshare of its work in the world top 10%, 2022-now and all time averaged
40%
Specialisationhow much of its work is in this field, counted up to 10× the world share
10%
Sizeits output in this field, on a log scale
30%
Growthoutput growth, counted from -20% to +20%
10%
Internationalshare of its work with a co-author abroad
10%
Each slider sets a weight; the share it gets of the score is beside it.
#UniversityScoreTop 10%SpecialisationWorksGrowth
1Samarkand State University named after Sharof RashidovUzbekistan 69.024.1%44.5×15 +176.3%
2Zhejiang Normal UniversityChina 65.821.5%15.2×13 +209.4%
3University of SfaxTunisia 63.36.6%33.2×24 +107.9%
4Tsinghua UniversityChina 61.918.5%2.3×16 +163.5%
5Texas A&M UniversityUnited States 59.419.5%5.2×13 +118.2%
6Saratov State UniversityRussia 58.630.6%48.0×12 -49.1%
7University College LondonUnited Kingdom 58.021.1%1.9×9 +80.9%
8Lomonosov Moscow State UniversityRussia 57.53.9%14.4×36 -4.0%
9Czech Technical University in PragueCzechia 57.512.6%19.4×14 +69.4%
10Ludwig-Maximilians-Universität MünchenGermany 53.314.2%5.4×14 +1.7%

Universities only. The score blends excellence (40%), size (30%), specialisation (10%), growth (10%), international reach (10%), 2022-now; growth compares 2018-21 with 2022-25 and counts up to +20%, since a jump from a small base is mostly noise.

Every institution in Spectral Theory in Mathematical Physics, country by country

Is Spectral Theory in Mathematical Physics research growing?

Output in 2022-2025 was 17% higher than in 2018-2021, peaking in 2025. The fastest-growing topics are Spectral Theory in Mathematical Physics.

still counting19801990200020102020
grewheldshrank

The same series as a ribbon: one cell per year, darker for more. The line above answers how much; this answers when.

Its share of all research

Growing output can still be a shrinking share: all of science grows. This is Spectral Theory in Mathematical Physics as a percentage of every work published that year, 0.015% in 2024.

still counting0.020%0.040%0.060%Spectral Theory in Mathematical Physics0.015% in 202519801990200020102020

Fractional works of Spectral Theory in Mathematical Physics over all fractional works that year. How the balance of science has shifted.

How much of it reaches the world top 10%

Year by year.

still counting5%10%15%Spectral Theory in Mathematical Physics10.1% in 2025200020102020

Of each year's works in it, the share that reached the world's 10% most cited for their field and year. A field is the world for its own topics, so there is no other line to hold it against.

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.

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