1 / 6

Phase Space Portraits of Chaotic Systems and Kicked Rotor Dynamics

This article discusses phase space portraits of weakly and strongly chaotic systems, focusing on the kicked rotor with stochasticity parameters. It also explores relaxation and noise in chaotic systems and presents eigenvalues, eigenfunctions, and decay factors for the Kicked Top model. Additionally, it analyzes the diffusion coefficient for different values of K.

christopherjshaw
Download Presentation

Phase Space Portraits of Chaotic Systems and Kicked Rotor Dynamics

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. (b) (a) Figure 1: Phase space portraits of the weakly chaotic kicked rotor with stochasticity parameter K = 2 (a), and of the strongly chaotic kicked rotor with K = 10 (b). S. Fishman and S. Rahav, Relaxation and Noise in Chaotic Systems, in Dynamics of Dissipation, Lecture Notes in Physics Vol. 597, (Springer-Verlag, Berlin Heidelberg 2002), Edited by P. Garbaczewski and R. Olkiewicz (Proceeding of “38 Winter School of Theoretical Physics: Dynamical Semigroups: Dissipation, Chaos, Quanta”, February 2002, Ladek, Poland)

  2. Classical Accelerator Modes Figure 2: Phase portrait of the Standard map where (a) and (b) are sequences of island chains of the first and second generations, respectively, with periods 3 and 8 for K=K(1); (c) and (d) are the same as (a) and (b) for K=K(2) with period 5 for the first generation and 11 for the second one. A. Iomin, S. Fishman and G.M. Zaslavsky, Phys. Rev. E, 65, 036215 (2002)

  3. Kicked Top Table 1: Eigenvalues of U(N) for t = 10.2 truncated at lmax = 30, 40, 50 and 60 J. Weber, F. Haake, P.A. Braun, C. Manderfeld and P. Seba, J. Phys. A 34, 7195 (2001).

  4. Kicked Top Figure 3: The eigenfunctions corresponding to the eigenvalues 0.7696 (a), −0.3388±i0.6243 (b), −0.0058±i0.7080 (c), 0.6480 (d) of U(N) for t = 10.2, and lmax = 60. J. Weber, F. Haake, P.A. Braun, C. Manderfeld and P. Seba, J. Phys. A 34, 7195 (2001).

  5. Kicked Top Figure 4: The decay of C(n) (dots) with ρ(0) corresponding to the eigenfunction shown in figure (b) of the previous slide. The numerical fit (line) yields a decay factor 0.7706. J. Weber, F. Haake, P.A. Braun, C. Manderfeld and P. Seba, J. Phys. A 34, 7195 (2001).

  6. Kicked rotor Figure 5: The fast relaxation rates gfor various functions f and g with k = 0 Figure 6: The diffusion coefficient D for K ≤ 20 M. Khodas, S.Fishman and O. Agam, Phys. Rev. E, 62, 4769 (2000). All the figures (except figure 2) and table can also be found at:S. Fishman and S. Rahav, Relaxation and Noise in Chaotic Systems, in Dynamics of Dissipation, Lecture Notes in Physics Vol. 597, (Springer-Verlag, Berlin Heidelberg 2002), Edited by P. Garbaczewski and R. Olkiewicz (Proceeding of “38 Winter School of Theoretical Physics: Dynamical Semigroups: Dissipation, Chaos, Quanta”, February 2002, Ladek, Poland).

More Related