Universality in the number variance and counting statistics of the real and symplectic Ginibre ensemble
Akemann G, Byun S-S, Ebke M, Schehr G (2023)
Journal of Physics A: Mathematical and Theoretical 56(49): 495202.
Zeitschriftenaufsatz
| Veröffentlicht | Englisch
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Autor*in
Akemann, GernotUniBi;
Byun, Sung-Soo;
Ebke, Markus;
Schehr, Gregory
Einrichtung
Abstract / Bemerkung
In this article, we compute and compare the statistics of the number of eigenvalues in a centred disc of radius R in all three Ginibre ensembles. We determine the mean and variance as functions of R in the vicinity of the origin, where the real and symplectic ensembles exhibit respectively an additional attraction to or repulsion from the real axis, leading to different results. In the large radius limit, all three ensembles coincide and display a universal bulk behaviour of for the mean, and O(R) for the variance. We present detailed conjectures for the bulk and edge scaling behaviours of the real Ginibre ensemble, having real and complex eigenvalues. For the symplectic ensemble we can go beyond the Gaussian case (corresponding to the Ginibre ensemble) and prove the universality of the full counting statistics both in the bulk and at the edge of the spectrum for rotationally invariant potentials, extending a recent work which considered the mean and the variance. This statistical behaviour coincides with the universality class of the complex Ginibre ensemble, which has been shown to be associated with the ground state of non-interacting fermions in a two-dimensional rotating harmonic trap. All our analytical results and conjectures are corroborated by numerical simulations.
Stichworte
number variance;
counting statistics;
Ginibre ensembles
Erscheinungsjahr
2023
Zeitschriftentitel
Journal of Physics A: Mathematical and Theoretical
Band
56
Ausgabe
49
Art.-Nr.
495202
Urheberrecht / Lizenzen
ISSN
1751-8113
eISSN
1751-8121
Finanzierungs-Informationen
Open-Access-Publikationskosten wurden durch die Universität Bielefeld gefördert.
Page URI
https://pub.uni-bielefeld.de/record/2981910
Zitieren
Akemann G, Byun S-S, Ebke M, Schehr G. Universality in the number variance and counting statistics of the real and symplectic Ginibre ensemble. Journal of Physics A: Mathematical and Theoretical . 2023;56(49): 495202.
Akemann, G., Byun, S. - S., Ebke, M., & Schehr, G. (2023). Universality in the number variance and counting statistics of the real and symplectic Ginibre ensemble. Journal of Physics A: Mathematical and Theoretical , 56(49), 495202. https://doi.org/10.1088/1751-8121/ad0885
Akemann, Gernot, Byun, Sung-Soo, Ebke, Markus, and Schehr, Gregory. 2023. “Universality in the number variance and counting statistics of the real and symplectic Ginibre ensemble”. Journal of Physics A: Mathematical and Theoretical 56 (49): 495202.
Akemann, G., Byun, S. - S., Ebke, M., and Schehr, G. (2023). Universality in the number variance and counting statistics of the real and symplectic Ginibre ensemble. Journal of Physics A: Mathematical and Theoretical 56:495202.
Akemann, G., et al., 2023. Universality in the number variance and counting statistics of the real and symplectic Ginibre ensemble. Journal of Physics A: Mathematical and Theoretical , 56(49): 495202.
G. Akemann, et al., “Universality in the number variance and counting statistics of the real and symplectic Ginibre ensemble”, Journal of Physics A: Mathematical and Theoretical , vol. 56, 2023, : 495202.
Akemann, G., Byun, S.-S., Ebke, M., Schehr, G.: Universality in the number variance and counting statistics of the real and symplectic Ginibre ensemble. Journal of Physics A: Mathematical and Theoretical . 56, : 495202 (2023).
Akemann, Gernot, Byun, Sung-Soo, Ebke, Markus, and Schehr, Gregory. “Universality in the number variance and counting statistics of the real and symplectic Ginibre ensemble”. Journal of Physics A: Mathematical and Theoretical 56.49 (2023): 495202.
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