CoChat
Sign Up
Cited by 2,551Quantum chaos and dynamical systemsQuantum and electron transport phenomenaSpectral Theory in Mathematical Physics

The DOI matches its Crossref record; 346 of the 347 references it cites were found in a registry or an index.

Random-matrix theory of quantum transport

Open access
Beenakker, C. W. J.·1997·Reviews of Modern Physics
DOI 10.1103/revmodphys.69.731
Open this paper in CoChat — free accountOpen PDF

Abstract

This is a review of the statistical properties of the scattering matrix of a mesoscopic system. Two geometries are contrasted: A quantum dot and a disordered wire. The quantum dot is a confined region with a chaotic classical dynamics, which is coupled to two electron reservoirs via point contacts. The disordered wire also connects two reservoirs, either directly or via a point contact or tunnel barrier. One of the two reservoirs may be in the superconducting state, in which case conduction involves Andreev reflection at the interface with the superconductor. In the case of the quantum dot, the distribution of the scattering matrix is given by either Dyson's circular ensemble for ballistic point contacts or the Poisson kernel for point contacts containing a tunnel barrier. In the case of the disordered wire, the distribution of the scattering matrix is obtained from the Dorokhov-Mello-Pereyra-Kumar equation, which is a one-dimensional scaling equation. The equivalence is discussed with the nonlinear $\ensuremath{\sigma}$ model, which is a supersymmetric field theory of localization. The distribution of scattering matrices is applied to a variety of physical phenomena, including universal conductance fluctuations, weak localization, Coulomb blockade, sub-Poissonian shot noise, reflectionless tunneling into a superconductor, and giant conductance oscillations in a Josephson junction.

Overview

Integrity signals

Registry

Crossref · 10.1103/revmodphys.69.731

Cites

346 of 346 references verified0 citation errors · 0 not checkable

Statistics

Recomputing p-values needs the paper’s full text.

Verification

Claims the paper makes

We couldn’t retrieve this paper’s full text, so its claims and self-check weren’t run. The registry and citation checks still apply.

Claims other papers make about this one

Each is checked against this paper’s own text: does it say what the citing paper says it does?

Citations

Cites

Flagged first, then by citations

Show all 347 references

1 of the 347 references couldn’t be matched to a known paper.

Research works printed but not linked: 37

  1. Altshuler, B. L., 1985, JETP Lett., 41, 648
  2. Altshuler, B. L., 1994, JETP Lett., 59, 857
  3. Altshuler, B. L., 1986, Sov. Phys. JETP, 64, 127
  4. Altshuler, B. L., 1987, Sov. Phys. JETP, 65, 343
  5. Andreev, A. F., 1964, Zh. Eksp. Teor. Fiz., 46, 1823
  6. Andreev, A. F., 1966, Sov. Phys. JETP, 24, 1019
  7. Büttiker, M., 1986, Phys. Rev. B, 57, 1761
  8. Dorokhov, O. N., 1982, JETP Lett., 36, 318
  9. Dorokhov, O. N., 1983, Sov. Phys. JETP, 58, 606
  10. Dorokhov, O. N., 1990, Sov. Phys. JETP, 71, 360
  11. Efetov, K. B., 1982, Sov. Phys. JETP, 56, 467
  12. Efetov, K. B., 1983, Sov. Phys. JETP, 58, 444
  13. Gazaryan, Yu. L., 1969, Sov. Phys. JETP, 29, 996
  14. Gertsenshtein, M. E., 1959, Teor. Veroyatn. Primen., 4, 424
  15. Golubov, A. A., 1995, JETP Lett., 61, 851
  16. Gor’kov, L. P., 1965, Zh. Eksp. Teor. Fiz., 48, 1407
  17. Gor’kov, L. P., 1979, JETP Lett., 30, 228
  18. Jalabert, R. A., 1995, J. Phys. I, 5, 287
  19. Keldysh, L. V., 1964, Zh. Eksp. Teor. Fiz., 47, 1515
  20. Khlus, V. A., 1987, Sov. Phys. JETP, 66, 1243
  21. Kulik, I. O., 1984, Sov. J. Low Temp. Phys., 10, 158
  22. Kulik, I. O., 1975, Sov. Phys. JETP, 41, 308
  23. Larkin, A. I., 1975, Sov. Phys. JETP, 41, 960
  24. Larkin, A. I., 1977, Sov. Phys. JETP, 46, 155
  25. Lesovik, G. B., 1989, JETP Lett., 49, 592
  26. Mel’nikov, V. I., 1981, Sov. Phys. Solid State, 23, 444
  27. Muzykantskiĭ, B. A., 1995, JETP Lett., 62, 76
  28. Nguyen, V. I., 1985, JETP Lett., 41, 42
  29. Sharvin, Yu. V., 1965, Zh. Eksp. Teor. Fiz., 48, 984
  30. Shekhter, R. I., 1973, Sov. Phys. JETP, 36, 747
  31. Shelankov, A. L., 1980, JETP Lett., 32, 111
  32. Shelankov, A. L., 1984, Sov. Phys. Solid State, 26, 981
  33. Spivak, B. Z., 1982, JETP Lett., 35, 412
  34. Steinbach, A. H., 1995, Bull. Am. Math. Soc., 40, 400
  35. Wigner, E. P., 1967, SIAM (Soc. Ind. Appl. Math.) Rev., 9, 1
  36. Zaĭtsev, A. V., 1980, Zh. Eksp. Teor. Fiz., 78, 221
  37. Zaĭtsev, A. V., 1984, Sov. Phys. JETP, 59, 1015

Cited by

Sorted by citations

See all 2,551

Related

Metadata

Authors
Beenakker, C. W. J.
Affiliations
Leiden University (NL)
Corresponding author
Beenakker, C. W. J.
ORCID
Beenakker, C. W. J.
Venue
Reviews of Modern Physics
Publisher
American Physical Society (APS)
Published
1997-07-01
Volume
69
Issue
3
Pages
731-808
ISSN
  • 0034-6861 (ISSN-L)
  • 1539-0756
DOI
10.1103/revmodphys.69.731
OpenAlex
W2092583264
Cited by
2,551
References
347
Citations by year
2026: 58 · 2025: 92 · 2024: 79 · 2023: 75 · 2022: 98 · 2021: 111 · 2020: 116 · 2019: 100 · 2018: 76 · 2017: 98 · 2016: 91 · 2015: 88 · 2014: 99 · 2013: 110 · 2012: 83
FWCI
68.17
Type
journal article
Language
en
Open access
Licence
link.aps.org/licenses/aps-default-license (vor)
Locations
  • Reviews of Modern Physics (publishedVersion)
  • arXiv (Cornell University) (submittedVersion)
  • Leiden Repository (Leiden University) (submittedVersion)
  • Data Archiving and Networked Services (DANS) (submittedVersion, other-oa)
  • arXiv (Cornell University)
Funders
  • Stichting voor Fundamenteel Onderzoek der Materie
  • Nederlandse Organisatie voor Wetenschappelijk Onderzoek
Topics
  • Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Quantum chaos and dynamical systems
  • Physical Sciences › Physics and Astronomy › Condensed Matter Physics › Quantum and electron transport phenomena
  • Physical Sciences › Mathematics › Mathematical Physics › Spectral Theory in Mathematical Physics
Keywords
random matrix theory, quantum transport, scattering matrix, mesoscopic systems, quantum dots, disordered wires, point contacts, tunnel barrier, superconducting junctions, Andreev reflection, Poisson kernel, nonlinear sigma model, supersymmetry, localization, universal conductance fluctuations, weak localization, Coulomb blockade

About these checks

Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.

Statistics and arithmetic are recomputed, not judged.

Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.

What counts as a claim ›How we measure confidence ›How we check this ›

Are you an author, or do you see a problem with this page? Request a review