ترغب بنشر مسار تعليمي؟ اضغط هنا

Hyperbolic Magnetic Billiards on Surfaces of Constant Curvature

110   0   0.0 ( 0 )
 نشر من قبل Gutkin Boris
 تاريخ النشر 2000
  مجال البحث فيزياء
والبحث باللغة English
 تأليف Boris Gutkin




اسأل ChatGPT حول البحث

We consider classical billiards on surfaces of constant curvature, where the charged billiard ball is exposed to a homogeneous, stationary magnetic field perpendicular to the surface. We establish sufficient conditions for hyperbolicity of the billiard dynamics, and give lower estimation for the Lyapunov exponent. This extends our recent results for non-magnetic billiards on surfaces of constant curvature. Using these conditions, we construct large classes of magnetic billiard tables with positive Lyapunov exponents on the plane, on the sphere and on the hyperbolic plane.



قيم البحث

اقرأ أيضاً

We establish sufficient conditions for the hyperbolicity of the billiard dynamics on surfaces of constant curvature. This extends known results for planar billiards. Using these conditions, we construct large classes of billiard tables with positive Lyapunov exponents on the sphere and on the hyperbolic plane.
An approach due to Wojtkovski [9], based on the Jacobi fields, is applied to study sets of 3-period orbits in billiards on hyperbolic plane and on two-dimensional sphere. It is found that the set of 3-period orbits in billiards on hyperbolic plane, a s in the planar case, has zero measure. For the sphere, a new proof of Baryshnikovs theorem is obtained which states that 3-period orbits can form a set of positive measure provided a natural condition on the orbit length is satisfied.
265 - B. Dietz , T. Guhr , B. Gutkin 2014
We determine with unprecedented accuracy the lowest 900 eigenvalues of two quantum constant-width billiards from resonance spectra measured with flat, superconducting microwave resonators. While the classical dynamics of the constant-width billiards is unidirectional, a change of the direction of motion is possible in the corresponding quantum system via dynamical tunneling. This becomes manifest in a splitting of the vast majority of resonances into doublets of nearly degenerate ones. The fluctuation properties of the two respective spectra are demonstrated to coincide with those of a random-matrix model for systems with violated time-reversal invariance and a mixed dynamics. Furthermore, we investigate tunneling in terms of the splittings of the doublet partners. On the basis of the random-matrix model we derive an analytical expression for the splitting distribution which is generally applicable to systems exhibiting dynamical tunneling between two regions with (predominantly) chaotic dynamics.
We investigate ruled surfaces in 3d Riemannian manifolds, i.e., surfaces foliated by geodesics. In 3d space forms, we find the striction curve, distribution parameter, and the first and second fundamental forms, from which we obtain the Gaussian and mean curvatures. We also provide model-independent proof for the known fact that extrinsically flat surfaces in space forms are ruled. This allows us to identify the necessary and sufficient condition for an extrinsically flat surface in a generic 3d manifold to be ruled. Further, we show that if a 3d manifold has an extrinsically flat surface tangent to any 2d plane and if they are all ruled surfaces, then the manifold is a space form. As an application, we prove that there must exist extrinsically flat surfaces in the Riemannian product of the hyperbolic plane, or sphere, with the reals and that does not make a constant angle with the real direction.
It is shown that the equation which describes constant mean curvature surface via the generalized Weierstrass-Enneper inducing has Hamiltonian form. Its simplest finite-dimensional reduction has two degrees of freedom, integrable and its trajectories correspond to well-known Delaunay and do Carmo-Dajzcer surfaces (i.e., helicoidal constant mean curvature surfaces).
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا