Families of two-dimensional Coulomb gases on an ellipse: correlation functions and universality

Nagao T, Akemann G, Kieburg M, Parra I (2020)
Journal of Physics A, Mathematical and Theoretical 53(7): 075201.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Autor*in
Nagao, Taro; Akemann, GernotUniBi; Kieburg, Mario; Parra, Ivan
Abstract / Bemerkung
We investigate a one-parameter family of Coulomb gases in two dimensions, which are confined to an ellipse due to a hard wall constraint, and are subject to an additional external potential. At inverse temperature we can use the technique of planar orthogonal polynomials, borrowed from random matrix theory, to explicitly determine all k-point correlation functions for a fixed number of particles N. These are given by the determinant of the kernel of the corresponding orthogonal polynomials, which in our case are the Gegenbauer polynomials, or a subset of the asymmetric Jacobi polynomials, depending on the choice of external potential, as shown in a companion paper recently published by three of the authors. In the rotationally invariant case, when the ellipse becomes the unit disc, our findings agree with that of the ensemble of truncated unitary random matrices. The thermodynamical large-N limit is investigated in the local scaling regime in the bulk and at the edge of the spectrum at weak and strong non-Hermiticity. We find new universality classes in these limits and recover the sine- and Bessel-kernel in the Hermitian limit. The limiting global correlation functions of particles in the interior of the ellipse are more difficult to obtain but found in the special cases corresponding to the Chebyshev polynomials.
Stichworte
two-dimensional Coulomb gas; planar orthogonal polynomials; weak; non-Hermiticity; universality
Erscheinungsjahr
2020
Zeitschriftentitel
Journal of Physics A, Mathematical and Theoretical
Band
53
Ausgabe
7
Art.-Nr.
075201
ISSN
1751-8113
eISSN
1751-8121
Page URI
https://pub.uni-bielefeld.de/record/2942734

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Nagao T, Akemann G, Kieburg M, Parra I. Families of two-dimensional Coulomb gases on an ellipse: correlation functions and universality. Journal of Physics A, Mathematical and Theoretical. 2020;53(7): 075201.
Nagao, T., Akemann, G., Kieburg, M., & Parra, I. (2020). Families of two-dimensional Coulomb gases on an ellipse: correlation functions and universality. Journal of Physics A, Mathematical and Theoretical, 53(7), 075201. doi:10.1088/1751-8121/ab604c
Nagao, T., Akemann, G., Kieburg, M., and Parra, I. (2020). Families of two-dimensional Coulomb gases on an ellipse: correlation functions and universality. Journal of Physics A, Mathematical and Theoretical 53:075201.
Nagao, T., et al., 2020. Families of two-dimensional Coulomb gases on an ellipse: correlation functions and universality. Journal of Physics A, Mathematical and Theoretical, 53(7): 075201.
T. Nagao, et al., “Families of two-dimensional Coulomb gases on an ellipse: correlation functions and universality”, Journal of Physics A, Mathematical and Theoretical, vol. 53, 2020, : 075201.
Nagao, T., Akemann, G., Kieburg, M., Parra, I.: Families of two-dimensional Coulomb gases on an ellipse: correlation functions and universality. Journal of Physics A, Mathematical and Theoretical. 53, : 075201 (2020).
Nagao, Taro, Akemann, Gernot, Kieburg, Mario, and Parra, Ivan. “Families of two-dimensional Coulomb gases on an ellipse: correlation functions and universality”. Journal of Physics A, Mathematical and Theoretical 53.7 (2020): 075201.

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