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Title: | Landau levels and Riemann zeros |
Authors: | Sierra, Germán CSIC ORCID; Townsend, Paul K. | Keywords: | Mathematical Physics Mesoscopic Systems and Quantum Hall Effect High Energy Physics - Theory Number Theory Quantum Physics [PACS] Algebraic structures and number theory [PACS] Quantum chaos; semiclassical methods |
Issue Date: | 12-Sep-2008 | Publisher: | American Physical Society | Citation: | Physical Review Letters 101(11): 110201 (2008) | Series: | IFT-UAM/CSIC 08-26 DAMTP-2008-46 |
Abstract: | The number N(E) of complex zeros of the Riemann zeta function with positive imaginary part less than E is the sum of a `smooth' function Ñ(E) and a 'fluctuation'. Berry and Keating have shown that the asymptotic expansion of Ñ(E) counts states of positive energy less than E in a 'regularized' semi-classical model with classical Hamiltonian H=xp. For a different regularization, Connes has shown that it counts states 'missing' from a continuum. Here we show how the 'absorption spectrum' model of Connes emerges as the lowest Landau level limit of a specific quantum mechanical model for a charged particle on a planar surface in an electric potential and uniform magnetic field. We suggest a role for the higher Landau levels in the fluctuation part of N(E). | Description: | 4 pages, 2 figures.-- PACS numbers: 02.10.De, 05.45.Mt.-- ArXiv pre-print available at: http://arxiv.org/abs/0805.4079 | Publisher version (URL): | http://dx.doi.org/10.1103/PhysRevLett.101.110201 | URI: | http://hdl.handle.net/10261/5531 | DOI: | 10.1103/PhysRevLett.101.110201 | ISSN: | 0031-9007 |
Appears in Collections: | (IFT) Artículos |
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File | Description | Size | Format | |
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0805.4079v1.pdf | Pre-print article | 183,33 kB | Adobe PDF | ![]() View/Open |
Sierra_Townsend_PRL_101_2008.pdf | Final version | 223,11 kB | Adobe PDF | ![]() View/Open |
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