P. Leboeuf, A. Monastra, O. Bohigas, “The Riemannium”, Regul. Chaotic Dyn., 6:2 (2001), 205

Regular and Chaotic Dynamics

RUS ENG

JOURNALS PEOPLE ORGANISATIONS CONFERENCES SEMINARS VIDEO LIBRARY PACKAGE AMSBIB

JavaScript is disabled in your browser. Please switch it on to enable full functionality of the website

	General information
	Latest issue
	Archive
	Impact factor

	Search papers
	Search references

	RSS
	Latest issue
	Current issues
	Archive issues
	What is RSS

Regul. Chaotic Dyn.:
Year:
Volume:
Issue:
Page:
	Find

Personal entry:
Login:
Password:
	Save password
	Enter
	Forgotten password?
	Register

Regular and Chaotic Dynamics, 2001, Volume 6, Issue 2, Pages 205–210
DOI: https://doi.org/10.1070/RD2001v006n02ABEH000170 (Mi rcd838)

This article is cited in 19 scientific papers (total in 19 papers)

The Riemannium

P. Leboeuf, A. Monastra, O. Bohigas

Laboratoire de Physique Théorique et Modèles Statistiques, Unité Mixte de Recherche de l'Université Paris XI et du CNRS Bât. 100, Université de Paris-Sud, 91405 Orsay Cedex, France

Citations (19)

DOI: https://doi.org/10.1070/RD2001v006n02ABEH000170

Abstract: The properties of a fictitious, fermionic, many-body system based on the complex zeros of the Riemann zeta function are studied. The imaginary part of the zeros are interpreted as mean-field single-particle energies, and one fills them up to a Fermi energy

E_{F}

$E_F$ . The distribution of the total energy is shown to be non-Gaussian, asymmetric and independent of

E_{F}

$E_F$ in the limit

E_{F} \to \infty

$E_F \to \infty$ . The moments of the limit distribution are computed analytically. The autocorrelation function, the finite energy corrections, and a comparison with random matrix theory are also discussed.

Received: 21.03.2001

Bibliographic databases:

Document Type: Article

MSC: 11M26, 82B44

Language: English

Citation: P. Leboeuf, A. Monastra, O. Bohigas, “The Riemannium”, Regul. Chaotic Dyn., 6:2 (2001), 205–210

Citation in format AMSBIB

\Bibitem{LebMonBoh01}

\by P.~Leboeuf, A.~Monastra, O.~Bohigas

\paper The Riemannium

\jour Regul. Chaotic Dyn.

\yr 2001

\vol 6

\issue 2

\pages 205--210

\mathnet{http://mi.mathnet.ru/rcd838}

\crossref{https://doi.org/10.1070/RD2001v006n02ABEH000170}

\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1843665}

\zmath{https://zbmath.org/?q=an:0988.11039}

Linking options:

https://www.mathnet.ru/eng/rcd838

https://www.mathnet.ru/eng/rcd/v6/i2/p205

This publication is cited in the following 19 articles:

Wolf M., “Will a Physicist Prove the Riemann Hypothesis?”, Rep. Prog. Phys., 83:3 (2020), 036001
Sierra G., “The Riemann Zeros as Spectrum and the Riemann Hypothesis”, Symmetry-Basel, 11:4 (2019), 494
C. Castro Perelman, “On the Riemann Hypothesis, complex scalings and logarithmic time reversal”, Journal of Geometry and Physics, 129 (2018), 133
Johann Bartel, R. K. Bhaduri, Matthias Brack, M. V. N. Murthy, “Asymptotic prime partitions of integers”, Phys. Rev. E, 95:5 (2017)
J. G. Dueñas, N. F. Svaiter, “Riemann zeta zeros and zero-point energy”, Int. J. Mod. Phys. A, 29:09 (2014), 1450051
Germán Sierra, “The Riemann zeros as energy levels of a Dirac fermion in a potential built from the prime numbers in Rindler spacetime”, J. Phys. A: Math. Theor., 47:32 (2014), 325204
R Band, J M Harrison, C H Joyner, “Finite pseudo orbit expansions for spectral quantities of quantum graphs”, J. Phys. A: Math. Theor., 45:32 (2012), 325204
JONATHAN M HARRISON, KLAUS KIRSTEN, “VACUUM ENERGY OF SCHRÖDINGER OPERATORS ON METRIC GRAPHS”, Int. J. Mod. Phys. Conf. Ser., 14 (2012), 357
Piotr Chmielowski, “General Covariance, Spectrum of Riemannium, and a Stress Test Calculation Formula”, SSRN Journal, 2011
Dániel Schumayer, David A. W. Hutchinson, “Colloquium: Physics of the Riemann hypothesis”, Rev. Mod. Phys., 83:2 (2011), 307
G Berkolaiko, J M Harrison, J H Wilson, “Mathematical aspects of vacuum energy on quantum graphs”, J. Phys. A: Math. Theor., 42:2 (2009), 025204
W. T. Lu, Weiqiao Zeng, S. Sridhar, “Duality between quantum and classical dynamics for integrable billiards”, Phys. Rev. E, 73:4 (2006)
A. Relaño, J. Retamosa, E. Faleiro, R. A. Molina, A. P. Zuker, “1∕fnoise and very high spectral rigidity”, Phys. Rev. E, 73:2 (2006)
Oriol Bohigas, “Quantum Chaos”, Nuclear Physics A, 751 (2005), 343
Michael Trott, The Mathematica GuideBook for Programming, 2004, 1
P. Leboeuf, International Conference on Theoretical Physics, 2003, 727
P. Leboeuf, A.G. Monastra, “Quantum thermodynamic fluctuations of a chaotic Fermi-gas model”, Nuclear Physics A, 724:1-2 (2003), 69
O. Bohigas, P. Leboeuf, “Nuclear Masses: Evidence of Order-Chaos Coexistence”, Phys. Rev. Lett., 88:9 (2002)
P. Leboeuf, A.G. Monastra, “Thermodynamics of Small Fermi Systems: Quantum Statistical Fluctuations”, Annals of Physics, 297:1 (2002), 127

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

Statistics & downloads:
Abstract page:	100

Registration to the website

Logotypes