Integrable and related dynamics

    An integrable system is one with enough constants of motion to render it completely predictable. The work here includes chaotic relativistic generalisations of the integrable two centre problem, a square semiconductor billiard geometry, the surprising phenomenon of diffusion in systems which, although not strictly integrable, have no exponential sensitivity to initial conditions characteristic of chaos, the computation of escape from open integrable systems using number theory, the use of the integrable harmonic osicllator as a stringent test of a new type of thermostat, and circular microresonators.

  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. Microscopic chaos from Brownian motion? C. P. Dettmann, E. G. D. Cohen and H. van Beijeren, Nature 401, 875-875 (1999) ps.gz (1.0M when uncompressed) arxiv
  11. 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
  12. Note on chaos and diffusion C. P. Dettmann and E. G. D. Cohen, J. Stat. Phys. 103, 589-599 (2001) ps arxiv
  13. 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
  14. Thermostats for "slow" configurational modes A. A. Samoletov, C. P. Dettmann and M. A. J. Chaplain, J. Stat. Phys. 128 1321-1336 (2007) [Origin of the "Nose-Hoover-Langevin" thermostat] pdf arxiv
  15. 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
  16. 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
  17. 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
  18. Notes on configurational thermostat schemes, A. A. Samoletov, C. P. Dettmann and M. A. J. Chaplain, J. Chem. Phys. 132 246101 (2010) pdf arxiv
  19. 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
  20. Diffusion in the Lorentz gas, C. P. Dettmann, Commun. Theor. Phys. 62 521-540 (2014). pdf arxiv
  21. Survival probability for open spherical billiards, C. P. Dettmann and M. R. Rahman, Chaos 24 043130 (2014). arxiv pdf
  22. Circular, elliptic and oval billiards in a gravitational field, D. R. Costa, C. P. Dettmann and E. D. Leonel, Commun. Nonlin. Sci. Numer. Sim., 22 731-746 (2015). pdf
  23. Linear and nonlinear stability of periodic orbits in annular billiards, C. P. Dettmann and V. Fain, Chaos 27 043106 (2017). arxiv.
  24. Splitting of separatrices, scattering maps, and energy growth for a billiard inside a time-dependent symmetric domain close to an ellipse, C. P. Dettmann, V. Fain and D. Turaev, Nonlinearity 31 667-700 (2018). arxiv.
  25. Spherical billiards with almost complete escape, C. P. Dettmann and M. R. Rahman, submitted pdf.
  26. 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)
  27. 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
  28. 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
  29. 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
  30. 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
  31. Conference paper: How sticky is the chaos/order boundary? C. P. Dettmann, Contemporary Mathematics 698 111-128 (2017). pdf arxiv.

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