Geometry of non-holonomic diffusion

On singular non-holonomic geometry

The aim of the paper is to prove that every smooth generalized vector subbundle D of a vector bundle E is the image of a smooth endomorphism Φ on the fibers of E that induces authomorphisms of fibers of D and is called here a natural anchor. Two new constructions of finite sets of smooth generators of the fibers of D are obtained, using any finite set of generators of the module Γ(E). Natural a...

Non-holonomic Control Ii : Non-holonomic Quantum Devices

In this paper, we show how the non-holonomic control technique can be employed to build completely controlled quantum devices. Examples of such controlled structures are provided.

Non-rigid Registration by Geometry-Constrained Diffusion

Assume that only partial knowledge about a non-rigid registration is given: certain points, curves or surfaces in one 3D image are known to map to certain points, curves or surfaces in another 3D image. In trying to identify the non-rigid displacement field, we face a generalized aperture problem since along the curves and surfaces, point correspondences are not given. We will advocate the view...

Non-Holonomic Attitude Control

Non-holonomic Control I

In this paper, we present a universal control technique, the non-holonomic control, which allows us to impose any arbitrarily prescribed unitary evolution to any quantum system through the alternate application of two well-chosen perturbations.