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.
- 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
- Chaos and fractals around black holes C. P. Dettmann, N. E. Frankel and N. J. Cornish, Fractals 3 161-181 (1995) pdf arxiv
- 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
- 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]
- 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)
- Fractal transistors, R. P. Taylor, A. P. Micolich, R. Newbury, C. P. Dettmann and T. M. Fromhold, Semicond. Sci. Tech. 12,1459-1464 (1997)
- 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)
- 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)
- 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)
- 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
- 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
- Note on chaos and diffusion C. P. Dettmann and E. G. D. Cohen, J. Stat. Phys. 103, 589-599 (2001) ps arxiv
- 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
- 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
- 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
- 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
- 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
- Notes on configurational thermostat schemes, A. A. Samoletov, C. P. Dettmann and M. A. J. Chaplain, J. Chem. Phys. 132 246101 (2010) pdf arxiv
- 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
- Diffusion in the Lorentz gas, C. P. Dettmann, Commun. Theor. Phys. 62 521-540 (2014). pdf arxiv
- Survival probability for open spherical billiards, C. P. Dettmann and M. R. Rahman, Chaos 24 043130 (2014). arxiv pdf
- 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
- Linear and nonlinear stability of periodic orbits in annular billiards, C. P. Dettmann and V. Fain, Chaos 27 043106 (2017). arxiv.
- 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.
- Spherical billiards with almost complete escape, C. P. Dettmann and M. R. Rahman, Chaos 31 123119 (2021). pdf.
- 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)
- 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
- 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
- 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
- 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
- Conference paper: How sticky is the chaos/order boundary? C. P. Dettmann, Contemporary Mathematics 698 111-128 (2017). pdf arxiv.
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