Number theory

    Physics is never far from the properties of the number systems used to describe it. The structure factor of fractals at infinity depends on the Pisot-Vijaraghavan property, in which all high powers of an irrational number (such as the golden ratio) are close to integers. The escape from an open integrable billiard in the limit of small holes depends on the Riemann zeta function and more generally Dirichlet L-functions, which in turn are related to the distribution of prime numbers.

  1. Structure factor of deterministic fractals with rotations C. P. Dettmann and N. E. Frankel, Fractals 1, 253-261 (1993) pdf [New journal at the time; missed from most databases]
  2. Open circular billiards and the Riemann hypothesis, L. A. Bunimovich and C. P. Dettmann, Phys. Rev. Lett. 94 100201 (2005) ps pdf arxivRH day slides
  3. Open mushrooms: Stickiness revisited, C. P. Dettmann and O. Georgiou, J. Phys. A.: Math. Theor. 44 195102 (2011). [Highlighted in a JPA Insights article.] pdf arxiv poster
  4. New horizons in multidimensional diffusion: The Lorentz gas and the Riemann Hypothesis, C. P. Dettmann, J. Stat. Phys. 146 181-204 (2012). pdf arxiv animation (4.8M)
  5. Faster than expected escape for a class of fully chaotic maps, O. Georgiou, C. P. Dettmann, E. G. Altmann, Chaos 22 043115 (2012). arxiv pdf
  6. Open circle maps: Small hole asymptotics, C. P. Dettmann, Nonlinearity 26 307-317 (2013). pdf arxiv
  7. Escape from a circle and Riemann hypotheses, L. A. Bunimovich and C. P. Dettmann, submitted ps pdf

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