Open circular billiards and the Riemann hypothesis

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dc.creatorBunimovich, L. A.
dc.creatorDettmann, C. P.
dc.date2004-08-04
dc.date2005-02-16
dc.date.accessioned2026-07-07T05:35:51Z
dc.date.available2026-07-07T05:35:51Z
dc.descriptionA comparison of escape rates from one and from two holes in an experimental container (e.g. a laser trap) can be used to obtain information about the dynamics inside the container. If this dynamics is simple enough one can hope to obtain exact formulas. Here we obtain exact formulas for escape from a circular billiard with one and with two holes. The corresponding quantities are expressed as sums over zeroes of the Riemann zeta function. Thus we demonstrate a direct connection between recent experiments and a major unsolved problem in mathematics, the Riemann hypothesis.
dc.description5 pages, 4 embedded postscript figures; v2: more explicit on how the Reimann Hypothesis arises from a comparison of one and two hole escape rates
dc.identifierhttps://arxiv.org/abs/nlin/0408009
dc.identifierhttp://arxiv.org/abs/nlin/0408009
dc.identifierPhys. Rev. Lett. 94, 100201 (2005)
dc.identifierdoi:10.1103/PhysRevLett.94.100201
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/80795
dc.subjectExactly Solvable and Integrable Systems
dc.subjectMathematical Physics
dc.subjectNumber Theory
dc.titleOpen circular billiards and the Riemann hypothesis
dc.typetext

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