Open circular billiards and the Riemann hypothesis

LA Bunimovich, CP Dettmann

Research output: Contribution to journalArticle (Academic Journal)peer-review

41 Citations (Scopus)
300 Downloads (Pure)


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.
Translated title of the contributionOpen circular billiards and the Riemann hypothesis
Original languageEnglish
Article numberArt. no. 100201
Pages (from-to)1 - 4
Number of pages4
JournalPhysical Review Letters
Issue number10
Publication statusPublished - Mar 2005

Bibliographical note

Publisher: American Physical Society
Other identifier: IDS Number: 909DF

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