Time-dependent dynamics

    It is impossible to completely shield any physical system from the environment, so the latter must be modelled, by either deterministic or stochastic forcing, or thermostats. Stochastic systems can be understood using periodic orbits of the unperturbed dynamics. Depending on the parameters, the forcing can destabilised or, remarkably, stabilise, the motion. In the context of billiards we can consider time-dependent (eg sinusoidally vibrating) walls. In each collision the particle normally changes its speed. Often, many such collisions occur with effectively random changes in speed, well approximated by a normal diffusion process. If the speed is unbounded, this leads to the phenomenon of Fermi acceleration, originally proposed to understand the origin of high energy cosmic rays.

  1. Stochastic dynamics of relativistic turbulence. C. P. Dettmann and N. E. Frankel, Phys. Rev. E 53, 5502-5505 (1996) pdf
  2. 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
  3. Traces and determinants of strongly stochastic operators C. P. Dettmann, Phys. Rev. E 59, 5231-5234 (1999) pdf ps html arxiv
  4. 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
  5. 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
  6. Noise corrections to stochastic trace formulas G. Palla, G. Vattay, A. Voros, N. Sondergaard, C. P. Dettmann, Found. Phys. 31, 641-657 (2001). arxiv
  7. Fractal asymptotics, C. P. Dettmann, Physica D 187, 214-222 (2004). ps arxiv
  8. Stochastic stabilization of cosmological photons. C. P. Dettmann, J. P. Keating, and S. D. Prado, J. Phys. A.: Math. Theor.37 L377-L383 (2004) pdf. arxiv animation (0.3M) [Featured in the June 2010 issue of Mathematics Today, pdf available here.]
  9. Stochastic stabilization of chaos and the cosmic microwave background. C. P. Dettmann, J. P. Keating and S. D. Prado, Int. J. Mod. Phys. D 13 1461-1468 (2004). pdf
  10. 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
  11. Asymptotic expansions for the escape rate of stochastically perturbed unimodal maps, C. P. Dettmann and T. B. Howard, Physica D, 238, 2404-2408 (2009). pdf arxiv early poster
  12. Notes on configurational thermostat schemes, A. A. Samoletov, C. P. Dettmann and M. A. J. Chaplain, J. Chem. Phys. 132 246101 (2010) pdf arxiv
  13. 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
  14. 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
  15. 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
  16. 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
  17. 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
  18. 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, submitted pdf
  19. Periodic volume fluctuations with infinite horizon: Intermittency enhanced Fermi acceleration, C. P. Dettmann and E. D. Leonel, submitted pdf
  20. Proceedings: Stochastic stabilization of the cosmic microwave background radiation. C. P. Dettmann, J. P. Keating and S. D. Prado, Proceedings of the Tenth Marcel Grossmann Meeting on General Relativity, ed M. Novello, S. Perez-Bergliaffa and R. Ruffini, World Scientific, Singapore (2006) ps pdf.
  21. Poster: Averaging quasiperiodic systems, C. P. Dettmann and T. B. Howard, August 2008 pdf

These publications are copyright. For allowed usage, please check the publisher's website by clicking on the journal name.

Return to Publications page; Home page.