Universality of the Number Variance in Rotational Invariant Two-Dimensional Coulomb Gases

Akemann G, Byun S-S, Ebke M (2023)
Journal of Statistical Physics 190(1): 9.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Akemann, GernotUniBi; Byun, Sung-Soo; Ebke, Markus
Abstract / Bemerkung
An exact map was established by Lacroix-A-Chez-Toine et al. in (Phys Rev A 99(2):021602, 2019) between the N complex eigenvalues of complex non-Hermitian random matrices from the Ginibre ensemble, and the positions of N non-interacting Fermions in a rotating trap in the ground state. An important quantity is the statistics of the number of Fermions N-a in a disc of radius a. Extending the work (Lacroix-A-Chez-Toine et al., in Phys Rev A 99(2):021602, 2019) covering Gaussian and rotationally invariant potentials Q, we present a rigorous analysis in planar complex and symplectic ensembles, which both represent 2D Coulomb gases. We show that the variance of N-a is universal in the large-N limit, when measured in units of the mean density proportional to Delta Q, which itself is non-universal. This holds in the large-N limit in the bulk and at the edge, when a finite fraction or almost all Fermions are inside the disc. In contrast, at the origin, when few eigenvalues are contained, it is the singularity of the potential that determines the universality class. We present three explicit examples from the Mittag-Leffler ensemble, products of Ginibre matrices, and truncated unitary random matrices. Our proofs exploit the integrable structure of the underlying determinantal respectively Pfaffian point processes and a simple representation of the variance in terms of truncated moments at finite-N.
Stichworte
Number variance; Coulomb gas; Non-Hermitian random matrices
Erscheinungsjahr
2023
Zeitschriftentitel
Journal of Statistical Physics
Band
190
Ausgabe
1
Art.-Nr.
9
ISSN
0022-4715
eISSN
1572-9613
Finanzierungs-Informationen
Open-Access-Publikationskosten wurden durch die Universität Bielefeld im Rahmen des DEAL-Vertrags gefördert.
Page URI
https://pub.uni-bielefeld.de/record/2966972

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Akemann G, Byun S-S, Ebke M. Universality of the Number Variance in Rotational Invariant Two-Dimensional Coulomb Gases. Journal of Statistical Physics . 2023;190(1): 9.
Akemann, G., Byun, S. - S., & Ebke, M. (2023). Universality of the Number Variance in Rotational Invariant Two-Dimensional Coulomb Gases. Journal of Statistical Physics , 190(1), 9. https://doi.org/10.1007/s10955-022-03005-2
Akemann, Gernot, Byun, Sung-Soo, and Ebke, Markus. 2023. “Universality of the Number Variance in Rotational Invariant Two-Dimensional Coulomb Gases”. Journal of Statistical Physics 190 (1): 9.
Akemann, G., Byun, S. - S., and Ebke, M. (2023). Universality of the Number Variance in Rotational Invariant Two-Dimensional Coulomb Gases. Journal of Statistical Physics 190:9.
Akemann, G., Byun, S.-S., & Ebke, M., 2023. Universality of the Number Variance in Rotational Invariant Two-Dimensional Coulomb Gases. Journal of Statistical Physics , 190(1): 9.
G. Akemann, S.-S. Byun, and M. Ebke, “Universality of the Number Variance in Rotational Invariant Two-Dimensional Coulomb Gases”, Journal of Statistical Physics , vol. 190, 2023, : 9.
Akemann, G., Byun, S.-S., Ebke, M.: Universality of the Number Variance in Rotational Invariant Two-Dimensional Coulomb Gases. Journal of Statistical Physics . 190, : 9 (2023).
Akemann, Gernot, Byun, Sung-Soo, and Ebke, Markus. “Universality of the Number Variance in Rotational Invariant Two-Dimensional Coulomb Gases”. Journal of Statistical Physics 190.1 (2023): 9.
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2024-02-09T10:17:02Z
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