Magnetic Translations in Hyperbolic Geometry
نویسنده
چکیده
We study random walks on the three-strand braid group B3, and in particular compute the drift, or average topological complexity of a random braid, as well as the probability of trivial entanglement. These results involve the study of magnetic random walks on hyperbolic graphs (hyperbolic Harper-Hofstadter problem), what enables to build a faithful representation of B3 as generalized magnetic translation operators for the problem of a quantum particle on the hyperbolic plane. PACS: 02.50.Ga, 03.65.Fd, 02.20.Bb, 02.20.Rt
منابع مشابه
Metric and periodic lines in the Poincare ball model of hyperbolic geometry
In this paper, we prove that every metric line in the Poincare ball model of hyperbolic geometry is exactly a classical line of itself. We also proved nonexistence of periodic lines in the Poincare ball model of hyperbolic geometry.
متن کاملAn Extension of Poincare Model of Hyperbolic Geometry with Gyrovector Space Approach
The aim of this paper is to show the importance of analytic hyperbolic geometry introduced in [9]. In [1], Ungar and Chen showed that the algebra of the group $SL(2,mathbb C)$ naturally leads to the notion of gyrogroups and gyrovector spaces for dealing with the Lorentz group and its underlying hyperbolic geometry. They defined the Chen addition and then Chen model of hyperbolic geomet...
متن کاملInvariant Surfaces under Hyperbolic Translations in Hyperbolic Space
In this paper, we consider hyperbolic rotation (G0), hyperbolic translation (G1) and horocyclic rotation (G2) groups in H3, which is called Minkowski model of hyperbolic space. Then, we investigate extrinsic differential geometry of invariant surfaces under subgroups of G0 in H3. Also, we give explicit parametrization of this invariant surfaces with respect to constant hyperbolic curvature of p...
متن کاملJunior Seminar: Hyperbolic Geometry Lecture Notes
Our first construction is very similar in spirit to an analogous one in Euclidean space. The group of isometries of Euclidean R is given by O(n) ⊕ R or SO(n) ⊕ R if we want to preserve orientation; the first factor is made up of rotations and reflections (in the non-orientation-preserving case) about the origin, while the second factor gives translations. Now, it turns out that O(n) is generate...
متن کاملOptical properties of a semi-infinite medium consist of graphene based hyperbolic meta-materials with tilted optical axis
In this paper, the optical properties of a semi-infinite medium composed of graphen-based hyperbolic meta-materials with the optical axis were tilted with respect to its boundary with air, by using the Maxwell equations; then the homogeneous effective medium approximation method was studied. The results showed that the orientation of the structure layers (geometric induced anisotropy) affec...
متن کامل