Random Matrix Theory and Quantum Chromodynamics
Akemann G (2017)
In: Stochastic processes and random matrices : Lecture notes of the Les Houches Summer School, Volume 104, 6th-31st July 2015. Schehr G, Altland A, Fyodorov YV, O'Connell, N, Cugliandolo LF (Eds); Oxford: Oxford Univ. Press: 228-282.
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| Veröffentlicht | Englisch
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Autor*in
Herausgeber*in
Schehr, Grégory;
Altland, Alexander;
Fyodorov, Yan V.;
O'Connell,, Neil;
Cugliandolo, Leticia F.
Einrichtung
Abstract / Bemerkung
These notes are based on the lectures delivered at the Les Houches Summer
School in July 2015. They are addressed at a mixed audience of physicists and
mathematicians with some basic working knowledge of random matrix theory. The
first part is devoted to the solution of the chiral Gaussian Unitary Ensemble
in the presence of characteristic polynomials, using orthogonal polynomial
techniques. This includes all eigenvalue density correlation functions,
smallest eigenvalue distributions and their microscopic limit at the origin.
These quantities are relevant for the description of the Dirac operator
spectrum in Quantum Chromodynamics with three colours in four Euclidean
space-time dimensions. In the second part these two theories are related based
on symmetries, and the random matrix approximation is explained. In the last
part recent developments are covered including the effect of finite chemical
potential and finite space-time lattice spacing, and their corresponding
orthogonal polynomials. We also give some open random matrix problems.
Erscheinungsjahr
2017
Buchtitel
Stochastic processes and random matrices : Lecture notes of the Les Houches Summer School, Volume 104, 6th-31st July 2015
Seite(n)
228-282
Konferenz
104. Les Houches Summer School
Konferenzort
Les Houches
Konferenzdatum
2015-07-06 – 2015-07-31
ISBN
978-0-19-879731-9
Page URI
https://pub.uni-bielefeld.de/record/2905169
Zitieren
Akemann G. Random Matrix Theory and Quantum Chromodynamics. In: Schehr G, Altland A, Fyodorov YV, O'Connell, N, Cugliandolo LF, eds. Stochastic processes and random matrices : Lecture notes of the Les Houches Summer School, Volume 104, 6th-31st July 2015. Oxford: Oxford Univ. Press; 2017: 228-282.
Akemann, G. (2017). Random Matrix Theory and Quantum Chromodynamics. In G. Schehr, A. Altland, Y. V. Fyodorov, N. O'Connell,, & L. F. Cugliandolo (Eds.), Stochastic processes and random matrices : Lecture notes of the Les Houches Summer School, Volume 104, 6th-31st July 2015 (pp. 228-282). Oxford: Oxford Univ. Press.
Akemann, Gernot. 2017. “Random Matrix Theory and Quantum Chromodynamics”. In Stochastic processes and random matrices : Lecture notes of the Les Houches Summer School, Volume 104, 6th-31st July 2015, ed. Grégory Schehr, Alexander Altland, Yan V. Fyodorov, Neil O'Connell,, and Leticia F. Cugliandolo, 228-282. Oxford: Oxford Univ. Press.
Akemann, G. (2017). “Random Matrix Theory and Quantum Chromodynamics” in Stochastic processes and random matrices : Lecture notes of the Les Houches Summer School, Volume 104, 6th-31st July 2015, Schehr, G., Altland, A., Fyodorov, Y. V., O'Connell,, N., and Cugliandolo, L. F. eds. (Oxford: Oxford Univ. Press), 228-282.
Akemann, G., 2017. Random Matrix Theory and Quantum Chromodynamics. In G. Schehr, et al., eds. Stochastic processes and random matrices : Lecture notes of the Les Houches Summer School, Volume 104, 6th-31st July 2015. Oxford: Oxford Univ. Press, pp. 228-282.
G. Akemann, “Random Matrix Theory and Quantum Chromodynamics”, Stochastic processes and random matrices : Lecture notes of the Les Houches Summer School, Volume 104, 6th-31st July 2015, G. Schehr, et al., eds., Oxford: Oxford Univ. Press, 2017, pp.228-282.
Akemann, G.: Random Matrix Theory and Quantum Chromodynamics. In: Schehr, G., Altland, A., Fyodorov, Y.V., O'Connell,, N., and Cugliandolo, L.F. (eds.) Stochastic processes and random matrices : Lecture notes of the Les Houches Summer School, Volume 104, 6th-31st July 2015. p. 228-282. Oxford Univ. Press, Oxford (2017).
Akemann, Gernot. “Random Matrix Theory and Quantum Chromodynamics”. Stochastic processes and random matrices : Lecture notes of the Les Houches Summer School, Volume 104, 6th-31st July 2015. Ed. Grégory Schehr, Alexander Altland, Yan V. Fyodorov, Neil O'Connell,, and Leticia F. Cugliandolo. Oxford: Oxford Univ. Press, 2017. 228-282.
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