Phys. Rev. Lett. 94, 100201 (2005) [4 pages]Open Circular Billiards and the Riemann HypothesisReceived 5 August 2004; published 18 March 2005 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 zeros of the Riemann zeta function. Thus we demonstrate a direct connection between recent experiments and a major unsolved problem in mathematics, the Riemann hypothesis. © 2005 The American Physical Society URL:
http://link.aps.org/doi/10.1103/PhysRevLett.94.100201
DOI:
10.1103/PhysRevLett.94.100201
PACS:
02.10.De, 02.30.Ik, 05.60.Cd, 45.50.Dd
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