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Open circular billiards and the Riemann hypothesis - MaRDI portal

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Open circular billiards and the Riemann hypothesis

From MaRDI portal
Publication:6501645

DOI10.1103/PHYSREVLETT.94.100201arXivnlin/0408009WikidataQ81557474 ScholiaQ81557474MaRDI QIDQ6501645

Author name not available (Why is that?)


Abstract: A 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.












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