Search results for "differential geometry"

showing 2 items of 462 documents

Optimal control of the Schrödinger equation with two or three levels

2007

In this paper, we present how techniques of “control theory”, “sub-Riemannian geometry” and “singular Riemannian geometry” can be applied to some classical problems of quantum mechanics and yield improvements to some previous results.

symbols.namesakeYield (engineering)Control theoryOptimal trajectorysymbolsApplied mathematicsMathematics::Differential GeometryRiemannian geometryOptimal controlPrincipal bundleSchrödinger equationMathematics
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Relationship between volume and energy of vector fields

2001

Abstract A unified study of energy and volume functionals is presented here by determining the critical points of a functional that extends simultaneously energy and volume and that is defined on the product of the manifold of smooth maps C∞(M,N) times the manifold M of riemannian metrics on M. The restriction of this functional to different submanifolds of the space of vector fields X (M)× M is also considered, and used to study several functionals generalizing volume and energy or total bending of vector fields

volumeenergy and total bending of vector fieldscritical pointsMathematical analysisBendingVolume and energy functionalsSpace (mathematics)Manifoldvariational problemsComputational Theory and MathematicsVolume (thermodynamics)Product (mathematics)Fundamental vector fieldVector fieldGeometry and TopologyMathematics::Differential GeometryAnalysisEnergy (signal processing)MathematicsDifferential Geometry and its Applications
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