Open systems

  1. Fractal basins and chaotic trajectories in multi-black-hole space-times. C. P. Dettmann, N. E. Frankel and N. J. Cornish, Phys. Rev. D, 50, R618-R621 (1994) pdf arxiv
  2. Chaos and fractals around black holes C. P. Dettmann, N. E. Frankel and N. J. Cornish, Fractals 3 161-181 (1995) pdf arxiv
  3. Chaos in special relativistic dynamics S. Drake, C. P. Dettmann, N. E. Frankel and N. J. Cornish, Phys. Rev. E 53,1351-1361 (1996) pdf
  4. Self-similar magnetoresistance of a semiconductor Sinai billiard, R. P. Taylor, R. Newbury, A. S. Sachrajda, Y. Feng, P. T. Coleridge, C. P. Dettmann, N. Zhu, H. Guo, A. Delage, P. J. Kelly and Z. Wasilewski, Phys. Rev. Lett., 78, 1952-1955 (1997) pdf ps[Physical experiment demonstrating tunable chaos and self-similar magnetoresistance fluctuations]
  5. Fractal behavior in the magnetoresistance of chaotic billiards, R. Newbury, R. P. Taylor, A. S. Sachrajda, Y. Feng, P. T. Coleridge, C. P. Dettmann and T. M. Fromhold, Jpn. J. Appl. Phys. 36,3991-3995 (1997)
  6. Fractal transistors, R. P. Taylor, A. P. Micolich, R. Newbury, C. P. Dettmann and T. M. Fromhold, Semicond. Sci. Tech. 12,1459-1464 (1997)
  7. Geometry-induced fractal behavior in a semiconductor billiard, A. P. Micolich, R. P. Taylor, R. Newbury, J. P. Bird, R. Wirtz, C. P. Dettmann, Y. Aoyagi and T. Sugano, J. Phys.: Cond. Mat. 10,1339-1347 (1998)
  8. Experimental and theoretical investigations of clusters in the magneto-fingerprints of Sinai billiards, R. P. Taylor, A. P. Micolich, R. Newbury, T. M. Fromhold, C. P. Dettmann and C. R. Tench, Mat. Sci. Eng. B 51, 212-215 (1998)
  9. Experimental and theoretical investigations of electron dynamics in a semiconductor Sinai billiard, A. P. Micolich, R. P. Taylor, R. Newbury, C. P. Dettmann and T. M. Fromhold, Aust. J. Phys. 51, 547-555 (1998)
  10. Trace formulas for stochastic evolution operators: Weak noise perturbation theory P. Cvitanovic', C. P. Dettmann, R. Mainieri, and G. Vattay, J. Stat. Phys. 93, 981-999 (1998) ps.gz (1.2M when uncompressed) arxiv
  11. Traces and determinants of strongly stochastic operators C. P. Dettmann, Phys. Rev. E 59, 5231-5234 (1999) pdf ps html arxiv
  12. Trace formulas for stochastic evolution operators: Smooth conjugation method P. Cvitanovic', C. P. Dettmann, R. Mainieri, and G. Vattay, Nonlinearity 12, 939-953 (1999) ps arxiv
  13. Spectrum of stochastic evolution operators: Local matrix representation approach P. Cvitanovic', N. Sondergaard, G. Palla, G. Vattay, and C. P. Dettmann, Phys. Rev. E 60, 3936-3941 (1999) pdf ps Two distinct arxiv versions:arxiv arxiv
  14. Microscopic chaos and diffusion C. P. Dettmann and E. G. D. Cohen, J. Stat. Phys. 101, 775-817 (2000) ps.gz (28 pages; 2.1M when uncompressed) arxiv
  15. Noise corrections to stochastic trace formulas G. Palla, G. Vattay, A. Voros, N. Sondergaard, C. P. Dettmann, Found. Phys. 31, 641-657 (2001). arxiv
  16. Fractal asymptotics, C. P. Dettmann, Physica D 187, 214-222 (2004). ps arxiv
  17. Open circular billiards and the Riemann hypothesis, L. A. Bunimovich and C. P. Dettmann, Phys. Rev. Lett. 94 100201 (2005) ps pdf RH day slides
  18. Peeping at chaos: Nondestructive monitoring of chaotic systems by measuring long-time escape rates L. A. Bunimovich and C. P. Dettmann, EPL, 80 40001 (2007). pdf arxivanimation (6.1M)
  19. Directional emission from an optical microdisk resonator with a point scatterer C. P. Dettmann, G. V. Morozov, M. M. A. Sieber and H. Waalkens, EPL, 82 34002 (2008). pdf arxiv
  20. Internal and external resonances of dielectric disks, C. P. Dettmann, G. V. Morozov, M. M. A. Sieber and H. Waalkens, EPL, 87, 34003 (2009). pdf arxiv
  21. Survival probability for the stadium billiard, C. P. Dettmann and O. Georgiou, Physica D, 238, 2395-2403 (2009). pdf arxiv animation (30.5M)
  22. Unidirectional Emission from Circular Dielectric Microresonators with a Point Scatterer, C. P. Dettmann, G. V. Morozov, M. M. A. Sieber and H. Waalkens, Phys. Rev. A, 80, 063813 (2009). [Selected to appear in the PRA "Kaleidoscope"] pdf arxiv poster
  23. Transmission and reflection in the stadium billiard: Time-dependent asymmetric transport, C. P. Dettmann and O. Georgiou, Phys. Rev. E 83 036212 (2011). [Selected to appear in the PRE "Kaleidoscope"] pdf arxiv poster
  24. 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
  25. Escape of particles in a time-dependent potential well, D. R. Costa, C. P. Dettmann and E. D. Leonel, Phys. Rev. E, 83 066211 (2011). pdf
  26. Scaling invariance for the escape of particles from a periodically corrugated waveguide, E. D. Leonel, D. R. Costa and C. P. Dettmann, Phys. Lett. A 376 421-425 (2012). pdf
  27. 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)
  28. Escape and transport for an open bouncer: Stretched exponential decays, C. P. Dettmann and E. D. Leonel, Physica D 241 403-408 (2012). pdf arxiv
  29. Recurrence of particles in static and time varying oval billiards, E. D. Leonel and C. P. Dettmann, Phys. Lett. A 376 1669-1674 (2012). pdf arxiv
  30. Dependence of chaotic diffusion on the size and position of holes, G. Knight, O. Georgiou, C. P. Dettmann, R. Klages, Chaos 22 023132 (2012). pdf arxiv
  31. Quantifying intermittency in the open drivebelt billiard, C. P. Dettmann and O. Georgiou, Chaos 22 026113 (2012). pdf arxiv
  32. Stickiness in a bouncer model: A slowing mechanism for Fermi acceleration, A. L. P. Livorati, T. Kroetz, C. P. Dettmann, I. L. Caldas, E. D. Leonel, Phys. Rev. E 86 036203 (2012). pdf arxiv
  33. 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
  34. Open circle maps: Small hole asymptotics, C. P. Dettmann, Nonlinearity 26 307-317 (2013). pdf arxiv
  35. Scaling invariance of the diffusion coefficient in a family of two-dimensional Hamiltonian mappings, J. A. de Oliveira, C. P. Dettmann, D. R. Costa and E. D. Leonel, Phys. Rev. E 87 062904 (2013). pdf
  36. Escape through a time-dependent hole in the doubling map, A. L. P. Livorati, O. Georgiou, C. P. Dettmann and E. D. Leonel, Phys. Rev. E, 89 052913 (2014). arxiv pdf
  37. Survival probability for open spherical billiards, C. P. Dettmann and M. R. Rahman, Chaos 24 043130 (2014). arxiv pdf
  38. Network connectivity in non-convex domains with reflections, O. Georgiou, M. Z. Bocus, M. R. Rahman, C. P. Dettmann and J. P. Coon, IEEE Commun. Lett. 19 427-430 (2015). pdf arxiv.
  39. Universal hitting time statistics for integrable flows, C. P. Dettmann, J. Marklof and A. Strombergsson, J. Stat. Phys. 166 714-749 (2017). arxiv pdf.
  40. Spherical billiards with almost complete escape, C. P. Dettmann and M. R. Rahman, Chaos 31 123119 (2021). pdf.
  41. A billiard in an open circle and the Riemann zeta function L. A. Bunimovich and C. P. Dettmann, Exper. Math. (published online). pdf.
  42. Conference paper: Far-field emission pattern of a dielectric circular microresonator with a point scatterer, C. P. Dettmann, G. V. Morozov, M. M. A. Sieber and H. Waalkens, ICTON 2007, 4 197-200 (2007)
  43. Conference paper: TM and TE directional modes of an optical microdisk resonator with a point scatterer, C. P. Dettmann, G. V. Morozov, M. M. A. Sieber and H. Waalkens, ICTON 2008, 4, 65-68 (2008). pdf
  44. Conference paper: Optical microdisk resonator with a small but finite size scatterer, C. P. Dettmann, G. V. Morozov, M. M. A. Sieber and H. Waalkens, Third International Conference on Mathematical Modelling of Wave Phenomena (MMWP08), 287-289 (2008). pdf
  45. Conference paper: Systematization of All Resonance Modes in Circular Dielectric Cavities, C. P. Dettmann, G. V. Morozov, M. M. A. Sieber and H. Waalkens, ICTON 2009, 763-766 (2009). pdf
  46. Conference paper: Microdisk resonators with two point scatterers, C. P. Dettmann, G. V. Morozov, M. M. A. Sieber and H. Waalkens, ICTON 2011, 462-464 (2011). pdf
  47. Conference paper: How sticky is the chaos/order boundary? C. P. Dettmann, Contemporary Mathematics 698 111-128 (2017). pdf arxiv.
  48. Book chapter: The Lorentz gas as a paradigm for nonequilibrium stationary states, C. P. Dettmann, pp 315-365 in Hard ball systems and the Lorentz gas (edited by D. Szasz), Encyclopaedia of Mathematical Sciences Vol 101 (Springer, 2000). Full size version, 50 pages pdf. Environmental microscopic version, 25 pages pdf.
  49. Book chapter: Recent advances in open billiards with some open problems, C. P. Dettmann, in Frontiers in the study of chaotic dynamical systems with open problems (Ed. Z. Elhadj and J. C. Sprott, World Scientific, 2011) arxiv [Image featured in Plus magazine]

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