Search results for "Holonomy"
showing 8 items of 8 documents
Holonomic Quantum Computation
2008
In this brief review we describe the idea of holonomic quantum computation. The idea of geometric phase and holonomy is introduced in a general way and we provide few examples that should help the reader understand the issues involved.
Discretization of harmonic measures for foliated bundles
2012
We prove in this note that there is, for some foliated bundles, a bijective correspondance between Garnett's harmonic measures and measures on the fiber that are stationary for some probability measure on the holonomy group. As a consequence, we show the uniqueness of the harmonic measure in the case of some foliations transverse to projective fiber bundles.
Partially hyperbolic diffeomorphisms on Heisenberg nilmanifolds and holonomy maps
2014
Abstract In this note we show that all partially hyperbolic automorphisms on a 3-dimensional non-Abelian nilmanifold can be C 1 -approximated by structurally stable C ∞ -diffeomorphisms, whose chain recurrent set consists of one attractor and one repeller. In particular, all these partially hyperbolic automorphisms are not robustly transitive. As a corollary, the holonomy maps of the stable and unstable foliations of the approximating diffeomorphisms are twisted quasiperiodically forced circle homeomorphisms, which are transitive but non-minimal and satisfy certain fiberwise regularity properties.
Feuilletages deCP(n) : de l’holonomie hyperbolique pour les minimaux exceptionnels
1992
Let ℱ be a holomorphic foliation ofCP(n). If ℱ has a leaf L, the closure L of which is disjoint from the singular set of the foliation, we prove that there exists a loop in a leaf contained in L with contracting hyperbolic holonomy.
Coherent quantum evolution via reservoir driven holonomies.
2006
We show that in the limit of a strongly interacting environment a system initially prepared in a decoherence-free subspace (DFS) coherently evolves in time, adiabatically following the changes of the DFS. If the reservoir cyclicly evolves in time, the DFS states acquire a holonomy.
BPS preons in M-theory and supergravity
2007
7 pages.-- PACS nrs.: 11.30.Pb, 11.25.-w, 04.65.+e, 11.10.Kk.-- ISI Article Identifier: 000247103400029.-- ArXiv pre-print available at: http://arxiv.org/abs/hep-th/0702099
Dynamics for a 2-vertex Quantum Gravity Model
2010
We use the recently introduced U(N) framework for loop quantum gravity to study the dynamics of spin network states on the simplest class of graphs: two vertices linked with an arbitrary number N of edges. Such graphs represent two regions, in and out, separated by a boundary surface. We study the algebraic structure of the Hilbert space of spin networks from the U(N) perspective. In particular, we describe the algebra of operators acting on that space and discuss their relation to the standard holonomy operator of loop quantum gravity. Furthermore, we show that it is possible to make the restriction to the isotropic/homogeneous sector of the model by imposing the invariance under a global …
Higher Order Integrability in Generalized Holonomy
2004
Supersymmetric backgrounds in M-theory often involve four-form flux in addition to pure geometry. In such cases, the classification of supersymmetric vacua involves the notion of generalized holonomy taking values in SL(32,R), the Clifford group for eleven-dimensional spinors. Although previous investigations of generalized holonomy have focused on the curvature \Rm_{MN}(\Omega) of the generalized SL(32,R) connection \Omega_M, we demonstrate that this local information is incomplete, and that satisfying the higher order integrability conditions is an essential feature of generalized holonomy. We also show that, while this result differs from the case of ordinary Riemannian holonomy, it is n…