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

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Random-matrix theory of quantum transport

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Beenakker, C. W. J.·1997·Reviews of Modern Physics

DOI 10.1103/revmodphys.69.731

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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.

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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: green
arxiv.org
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

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