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Finding zeros of the Riemann zeta function by periodic driving of cold atoms

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Creffield, Charles E. and Sierra, G. (2015) Finding zeros of the Riemann zeta function by periodic driving of cold atoms. Physical review A, 91 (6). ISSN 1050-2947

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Official URL: http://dx.doi.org/10.1103/PhysRevA.91.063608


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Abstract

The Riemann hypothesis, which states that the nontrivial zeros of the Riemann zeta function all lie on a certain line in the complex plane, is one of the most important unresolved problems in mathematics. We propose here an approach to finding a physical system to study the Riemann zeros, which is based on applying a time-periodic driving field. This driving allows us to tune the quasienergies of the system (the analog of the eigenenergies for static systems), so that they are directly governed by the zeta function. We further show by numerical simulations that this allows the Riemann zeros to be measured in currently accessible cold- atom experiments.


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Additional Information:

©2015 American Physical Society.
The authors thank Michael Berry for stimulating discussions. C.E.C. was supported by the Spanish MINECO through Grants No. FIS2010-21372 and No. FIS2013-41716-P, and G.S. by Grant No. FIS2012-33642, QUITEMAD, and the Severo Ochoa Programme under Grant SEV-2012-0249.

Uncontrolled Keywords:Optics; Physics, Atomic, Molecular & Chemical
Subjects:Sciences > Physics > Materials
Sciences > Physics > Solid state physics
ID Code:32916
Deposited On:28 Aug 2015 09:20
Last Modified:08 Feb 2018 15:06

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