Nonlinear Sciences – Exactly Solvable and Integrable Systems
Scientific paper
2004-08-04
Phys. Rev. Lett. 94, 100201 (2005)
Nonlinear Sciences
Exactly Solvable and Integrable Systems
5 pages, 4 embedded postscript figures; v2: more explicit on how the Reimann Hypothesis arises from a comparison of one and tw
Scientific paper
10.1103/PhysRevLett.94.100201
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.
Bunimovich Leonid A.
Dettmann Carl P.
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