Search results for "Vector Potential"

showing 10 items of 31 documents

Gauge theory of the long-range proximity effect and spontaneous currents in superconducting heterostructures with strong ferromagnets

2017

We present the generalized quasiclassical theory of the long-range superconducting proximity effect in heterostructures with strong ferromagnets, where the exchange splitting is of the order of Fermi energy. In the ferromagnet the propagation of equal-spin Cooper pairs residing on the spin-split Fermi surfaces is shown to be governed by the spin-dependent Abelian gauge field which results either from the spin-orbital coupling or from the magnetic texture. This additional gauge field enters into the quasiclassical equations in superposition with the usual electromagnetic vector potential and results in the generation of spontaneous superconducting currents and phase shifts in various geometr…

02 engineering and technology01 natural sciencesSuperposition principleCondensed Matter::Superconductivity0103 physical sciencesProximity effect (superconductivity)Boundary value problemGauge theory010306 general physicsPhysicsSuperconductivityta114Condensed matter physicsJosephson effectMeissner effectFermi energy021001 nanoscience & nanotechnologyferromagnetismcoherence lengthQuantum electrodynamicsproximity effectCondensed Matter::Strongly Correlated ElectronsCooper pair0210 nano-technologyVector potentialPhysical Review B
researchProduct

On electric and magnetic problems for vector fields in anisotropic nonhomogeneous media

1983

r= 3~2, initiated by Saranen [ 131. In the above, n is the outward-drawn unit normal to the boundary and A denotes the exterior product. According to the simple models for static magnetic fields (resp. electric fields) which are governed by (0.1) (resp. (0.2)), we call (0.1) the magnetic type problem and (0.2) the electric type problem. Considering bounded smooth domains a c R3, we discussed in [ 131, by means of an appropriate Hilbert space method, the solvability and the representation of the solutions for both problems (0.1) and (0.2). Such a new approach was necessary to cover the general nonhomogeneous cases where v and E are matrix-valued functions. Here our aim is twofold. First, we …

Applied MathematicsMathematical analysisScalar (mathematics)Hilbert spaceGauss's law for magnetismsymbols.namesakeElectric fieldBounded functionsymbolsVector fieldExterior algebraAnalysisVector potentialMathematicsJournal of Mathematical Analysis and Applications
researchProduct

Chiral anomalies in even and odd dimensions

1985

Odd dimensional Yang-Mills theories with an extra ‘topological mass” term, defined by the Chern-Simons secondary characteristic, are discussed. It is shown in detail how the topological mass affects the equal time charge commutation relations and how the modified commutation relations are related to non-abelian chiral anomalies in even dimensions. We also study the SU(3) chiral model (Wess-Zumino model) in four dimensions and we show how a gauge invariant interaction with an external SU(3) vector potential can be defined with the help of the Chern-Simons characteristic in five dimensions.

Chiral anomalyPhysicsHigh Energy Physics::Lattice53C80Statistical and Nonlinear PhysicsCharge (physics)Gauge (firearms)58G25Wess–Zumino modelHigh Energy Physics::TheoryChiral modelInvariant (mathematics)81E20Mathematical PhysicsGauge anomalyMathematical physicsVector potential
researchProduct

Effective-Lagrangian formulation of generalized vector dominance. II

1975

As in a preceding paper we generalize the Lagrangian of Lee and Zumino to include several mutually interacting vector mesons. The treatment is more general in the sense that all possible interactions between the vector mesons, compatible with the field-current proportionality relations, are now discussed. It is moreover demonstrated that also the fields corresponding to the physical vector mesons satisfy a field-current proportionality relation of exactly the same form. Comparison of the different schemes and their implications for the magnetic moments of the vector mesons are discussed.

Coupling constantElectromagnetic fieldPhysicsMagnetic momentMesonHigh Energy Physics::LatticeNuclear TheoryCurrent algebraProportionality (mathematics)Quantum mechanicsEffective lagrangianHigh Energy Physics::ExperimentVector potentialMathematical physicsPhysical Review D
researchProduct

Minimal unit vector fields

2002

We compute the first variation of the functional that assigns each unit vector field the volume of its image in the unit tangent bundle. It is shown that critical points are exactly those vector fields that determine a minimal immersion. We also find a necessary and sufficient condition that a vector field, defined in an open manifold, must fulfill to be minimal, and obtain a simpler equivalent condition when the vector field is Killing. The condition is fulfilled, in particular, by the characteristic vector field of a Sasakian manifold and by Hopf vector fields on spheres.

Curl (mathematics)Killing vector fieldsSolenoidal vector fieldVector operatorcritical pointsGeneral Mathematicsminimal vector fieldsMathematical analysis53C4253C20Hopf vector fields53C25Sasakian manifoldsKilling vector fieldUnit vectorFundamental vector fieldMathematics::Differential GeometryVolume of vector fieldsComplex lamellar vector fieldVector potentialMathematicsTohoku Mathematical Journal
researchProduct

Volume, energy and generalized energy of unit vector fields on Berger spheres: stability of Hopf vector fields

2005

We study to what extent the known results concerning the behaviour of Hopf vector fields, with respect to volume, energy and generalized energy functionals, on the round sphere are still valid for the metrics obtained by performing the canonical variation of the Hopf fibration.

Curl (mathematics)Vector calculus identitiesSolenoidal vector fieldUnit vectorGeneral MathematicsMathematical analysisFundamental vector fieldVector fieldComplex lamellar vector fieldMathematicsVector potentialProceedings of the Royal Society of Edinburgh: Section A Mathematics
researchProduct

Generic 3-parameter families of vector fields on the plane, unfolding a singularity with nilpotent linear part. The cusp case of codimension 3

1987

AbstractA cusp type germ of vector fields is a C∞ germ at 0∈ℝ2, whose 2-jet is C∞ conjugate toWe define a submanifold of codimension 5 in the space of germs consisting of germs of cusp type whose 4-jet is C0 equivalent toOur main result can be stated as follows: any local 3-parameter family in (0, 0) ∈ ℝ2 × ℝ3 cutting transversally in (0, 0) is fibre-C0 equivalent to

Cusp (singularity)Pure mathematicsNilpotentSingularitySolenoidal vector fieldApplied MathematicsGeneral MathematicsMathematical analysisVector fieldCodimensionSubmanifoldVector potentialMathematicsErgodic Theory and Dynamical Systems
researchProduct

General duality in vector optimization

1993

Vector minimization of a relation F valued in an ordered vector space under a constraint A consists in finding x 0 ∊ A w,0 ∊ Fx$0 such that w,0 is minimal in FA. To a family of vector minimization problemsminimize , one associates a Lagrange relation where ξ belongs to an arbitrary class Ξ of mappings, the main purpose being to recover solutions of the original problem from the vector minimization of the Lagrange relation for an appropriate ξ. This ξ turns out to be a solution of a dual vector maximization problem. Characterizations of exact and approximate duality in terms of vector (generalized with respect to Ξ) convexity and subdifferentiability are given. They extend the theory existin…

Discrete mathematicsControl and OptimizationVector operatorDual spaceApplied MathematicsDuality (optimization)Management Science and Operations ResearchVector optimizationUnit vectorOrdered vector spaceApplied mathematicsVector potentialMathematicsNormed vector spaceOptimization
researchProduct

Biorthonormal-basis method for the vector description of optical-fiber modes

1998

This paper gives the theoretical basis for the development of real vector modal methods to describe optical-fiber modes. To this end, the vector wave equations, which determine the electromagnetic fields, are written in terms of a pair of linear, nonself-adjoint operators, whose eigenvectors satisfy biorthogonality relations. The key of our method is to obtain a matrix representation of the vector wave equations in a basis that is defined by the modes of an auxiliary system. Our proposed technique can be applied to fibers with any profile, even those with a complex refractive index. An example is discussed to illustrate our approach.

Electromagnetic fieldNormal modeMathematical analysisMatrix representationCalculusPolarization (waves)Wave equationDirection vectorAtomic and Molecular Physics and OpticsEigenvalues and eigenvectorsVector potentialMathematicsJournal of Lightwave Technology
researchProduct

The electromagnetic and Proca fields revisited: A unified quantization

1997

Quantizing the electromagnetic field with a group formalism faces the difficulty of how to turn the traditional gauge transformation of the vector potential, Aμ(x) → Aμ(x) + ∂μφ(x), into a group law. In this paper, it is shown that the problem can be solved by looking at gauge transformations in a slightly different manner which, in addition, does not require introducing any BRST-like parameter. This gauge transformation does not appear explicitly in the group law of the symmetry but rather as the trajectories associated with generalized equations of motion generated by vector fields with null Noether invariants. In the new approach the parameters of the local group, U(1)(x, t), acquire dyn…

Electromagnetic fieldPhysicsHigh Energy Physics - TheoryNuclear and High Energy PhysicsPhotonQuantization (signal processing)Equations of motionFOS: Physical sciencesAstronomy and AstrophysicsMatemática AplicadaCampos electromagnéticosCampos electromagnéticos ProcaAtomic and Molecular Physics and OpticsCuantización unificadasymbols.namesakeHigh Energy Physics - Theory (hep-th)Proca Cuantización unificadasymbolsVector fieldGauge theoryNoether's theoremMathematical physicsVector potential
researchProduct