Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userExperimental investigation of the elastic enhancement factor in a transient region between regular and chaotic dynamics
142
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
We present the results of an experimental study of the elastic enhancement factor W for a microwave rectangular cavity simulating a two-dimensional quantum billiard in a transient region between regular and chaotic dynamics. The cavity was coupled to a vector network analyzer via two microwave antennas. The departure of the system from the integrable one due to presence of antennas acting as scatterers is characterised by the parameter of chaoticity k = 2.8. The experimental results for the rectangular cavity are compared with the ones obtained for a microwave rough cavity simulating a chaotic quantum billiard. The experimental results were obtained for the frequency range v = 16 - 18.5 GHz and moderate absorption strength y = 5.2 - 7.4. We show that the elastic enhancement factor for the rectangular cavity lies below the theoretical value W = 3 predicted for integrable systems and it is significantly higher than the one obtained for the rough cavity. The results obtained for the microwave rough cavity are smaller than the ones obtained within the framework of Random Matrix Theory and lie between them and the ones predicted within a recently introduced model of the two-channel coupling (V. Sokolov and O. Zhirov, arXiv:1411.6211v2[nucl-th], 12 Dec 2014).
rate research
Read More
We consider the motion of a particle subjected to the constant gravitational field and scattered inelasticaly by hard boundaries which possess the shape of parabola, wedge, and hyperbola. The billiard itself performs oscillations. The linear dependence of the restitution coefficient on the particle velocity is assumed. We demonstrate that this dynamical system can be either regular or chaotic, which depends on the billiard shape and the oscillation frequency. The trajectory calculations are compared with the experimental data; a good agreement has been achieved. Moreover, the properties of the system has been studied by means of the Lyapunov exponents and the Kaplan-Yorke dimension. Chaotic and nonuniform patterns visible in the experimental data are interpreted as a result of large embedding dimension.
The dynamics in three-dimensional billiards leads, using a Poincare section, to a four-dimensional map which is challenging to visualize. By means of the recently introduced 3D phase-space slices an intuitive representation of the organization of the mixed phase space with regular and chaotic dynamics is obtained. Of particular interest for applications are constraints to classical transport between different regions of phase space which manifest in the statistics of Poincare recurrence times. For a 3D paraboloid billiard we observe a slow power-law decay caused by long-trapped trajectories which we analyze in phase space and in frequency space. Consistent with previous results for 4D maps we find that: (i) Trapping takes place close to regular structures outside the Arnold web. (ii) Trapping is not due to a generalized island-around-island hierarchy. (iii) The dynamics of sticky orbits is governed by resonance channels which extend far into the chaotic sea. We find clear signatures of partial transport barriers. Moreover, we visualize the geometry of stochastic layers in resonance channels explored by sticky orbits.
We study the chaotic dynamics of graphene structures, considering both a periodic, defect free, graphene sheet and graphene nanoribbons (GNRs) of various widths. By numerically calculating the maximum Lyapunov exponent, we quantify the chaoticity for a spectrum of energies in both systems. We find that for all cases, the chaotic strength increases with the energy density, and that the onset of chaos in graphene is slow, becoming evident after more than $10^4$ natural oscillations of the system. For the GNRs, we also investigate the impact of the width and chirality (armchair or zigzag edges) on their chaotic behavior. Our results suggest that due to the free edges the chaoticity of GNRs is stronger than the periodic graphene sheet, and decreases by increasing width, tending asymptotically to the bulk value. In addition, the chaotic strength of armchair GNRs is higher than a zigzag ribbon of the same width. Further, we show that the composition of ${}^{12}C$ and ${}^{13}C$ carbon isotopes in graphene has a minor impact on its chaotic strength.
Many important high-dimensional dynamical systems exhibit complex chaotic behaviour. Their complexity means that their dynamics are necessarily comprehended under strong reducing assumptions. It is therefore important to have a clear picture of these reducing assumptions range of validity. The highly influential chaotic hypothesis of Gallavotti and Cohen states that the large-scale dynamics of high-dimensional systems are effectively hyperbolic, which implies many felicitous statistical properties. We demonstrate, contrary to the chaotic hypothesis, the existence of non-hyperbolic large-scale dynamics in a mean-field coupled system. To do this we reduce the system to its thermodynamic limit, which we approximate numerically with a Chebyshev Galerkin transfer operator discretisation. This enables us to obtain a high precision estimate of a homoclinic tangency, implying a failure of hyperbolicity. Robust non-hyperbolic behaviour is expected under perturbation. As a result, the chaotic hypothesis should not be assumed to hold in all systems, and a better understanding of the domain of its validity is required.
In the present work we investigate phase correlations by recourse to the Shannon entropy. Using theoretical arguments we show that the entropy provides an accurate measure of phase correlations in any dynamical system, in particular when dealing with a chaotic diffusion process. We apply this approach to different low dimensional maps in order to show that indeed the entropy is very sensitive to the presence of correlations among the successive values of angular variables, even when it is weak. Later on, we apply this approach to unveil strong correlations in the time evolution of the phases involved in the Arnolds Hamiltonian that lead to anomalous diffusion, particularly when the perturbation parameters are comparatively large. The obtained results allow us to discuss the validity of several approximations and assumptions usually introduced to derive a local diffusion coefficient in multidimensional near--integrable Hamiltonian systems, in particular the so-called reduced stochasticity approximation.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
