Time-dependent Mechanics and Lagrangian submanifolds of Dirac manifolds

A description of time-dependent Mechanics in terms of Lagrangian submanifolds of Dirac manifolds (in particular, presymplectic and Poisson manifolds) is presented. Two new Tulczyjew triples are discussed. The first one is adapted to the restricted Hamiltonian formalism and the second one is adapted to the extended Hamiltonian formalism

Enhanced Magnetic Anisotropy of Mn12-acetate

Thin films of the Single Molecule Magnet (Mn12-acetate) have been fabricated on a Si-substrate by the Dip-and-Dry method, a simple and robust technique. Atomic force microscopy and X-ray photoelectron spectroscopy characterizations reveal that homogeneous, thin films of a few molecular layers with smoothness at the molecular level are deposited. Significant changes in magnetic properties of Mn12-acetate exposed to the same solvent were observed in zero-field-cooled and field-cooled magnetization, as well as ac-susceptibility measurements. The blocking temperature was found to increase to TB > 10 K at low magnetic fields, indicating an enhanced magnetic anisotropy.Comment: 14 pages, 4 figure

Renormalization Group Study of Chern-Simons Field Coupled to Scalar Matter in a Modified BPHZ Subtraction Scheme

We apply a soft version of the BPHZ subtraction scheme to the computation of two-loop corrections from an Abelian Chern-Simons field coupled to (massive) scalar matter with a $\lambda(\Phi^\dag\Phi)^2$ and $\nu(\Phi^\dag\Phi)^3$ self-interactions. The two-loop renormalization group functions are calculated. We compare our results with those in the literature.Comment: 15 pages, 7 figures, revtex. To appear in Phys. Rev.

Detection of a magnetic bead by hybrid nanodevices using scanning gate microscopy

open8sìHybrid ferromagnetic(Py)/non-magnetic metal(Au) junctions with a width of 400 nm are studied by magnetotransport measurements, magnetic scanning gate microscopy (SGM) with a magnetic bead (MB) attached to the probe, and micromagnetic simulations. In the transverse geometry, the devices demonstrate a characteristic magnetoresistive behavior that depends on the direction of the in plane magnetic field, with minimum/maximum variation when the field is applied parallel/perpendicular to the Py wire. The SGM is performed with a NdFeB bead of 1.6 μm diameter attached to the scanning probe. Our results demonstrate that the hybrid junction can be used to detect this type of MB. A rough approximation of the sensing volume of the junction has the shape of elliptical cylinder with the volume of ∼1.51 μm3. Micromagnetic simulations coupled to a magnetotransport model including anisotropic magnetoresistance and planar Hall effects are in good agreement with the experimental findings, enabling the interpretation of the SGM images.openCorte-León, H.; Krzysteczko, P.; Marchi, F.; Motte, J.-F.; Manzin, A.; Schumacher, H. W.; Antonov, V.; Kazakova, O.Corte León, H.; Krzysteczko, P.; Marchi, F.; Motte, J. F.; Manzin, Alessandra; Schumacher, H. W.; Antonov, V.; Kazakova, O

Multivector Field Formulation of Hamiltonian Field Theories: Equations and Symmetries

We state the intrinsic form of the Hamiltonian equations of first-order Classical Field theories in three equivalent geometrical ways: using multivector fields, jet fields and connections. Thus, these equations are given in a form similar to that in which the Hamiltonian equations of mechanics are usually given. Then, using multivector fields, we study several aspects of these equations, such as the existence and non-uniqueness of solutions, and the integrability problem. In particular, these problems are analyzed for the case of Hamiltonian systems defined in a submanifold of the multimomentum bundle. Furthermore, the existence of first integrals of these Hamiltonian equations is considered, and the relation between {\sl Cartan-Noether symmetries} and {\sl general symmetries} of the system is discussed. Noether's theorem is also stated in this context, both the ``classical'' version and its generalization to include higher-order Cartan-Noether symmetries. Finally, the equivalence between the Lagrangian and Hamiltonian formalisms is also discussed.Comment: Some minor mistakes are corrected. Bibliography is updated. To be published in J. Phys. A: Mathematical and Genera

Self-similar and charged spheres in the diffusion approximation

We study spherical, charged and self--similar distributions of matter in the diffusion approximation. We propose a simple, dynamic but physically meaningful solution. For such a solution we obtain a model in which the distribution becomes static and changes to dust. The collapse is halted with damped mass oscillations about the absolute value of the total charge.Comment: 15 pages, 7 figure

Classical field theory on Lie algebroids: Variational aspects

The variational formalism for classical field theories is extended to the setting of Lie algebroids. Given a Lagrangian function we study the problem of finding critical points of the action functional when we restrict the fields to be morphisms of Lie algebroids. In addition to the standard case, our formalism includes as particular examples the case of systems with symmetry (covariant Euler-Poincare and Lagrange Poincare cases), Sigma models or Chern-Simons theories.Comment: Talk deliverd at the 9th International Conference on Differential Geometry and its Applications, Prague, September 2004. References adde

Invariant Forms and Automorphisms of Locally Homogeneous Multisymplectic Manifolds

It is shown that the geometry of locally homogeneous multisymplectic manifolds (that is, smooth manifolds equipped with a closed nondegenerate form of degree > 1, which is locally homogeneous of degree k with respect to a local Euler field) is characterized by their automorphisms. Thus, locally homogeneous multisymplectic manifolds extend the family of classical geometries possessing a similar property: symplectic, volume and contact. The proof of the first result relies on the characterization of invariant differential forms with respect to the graded Lie algebra of infinitesimal automorphisms, and on the study of the local properties of Hamiltonian vector fields on locally multisymplectic manifolds. In particular it is proved that the group of multisymplectic diffeomorphisms acts (strongly locally) transitively on the manifold. It is also shown that the graded Lie algebra of infinitesimal automorphisms of a locally homogeneous multisymplectic manifold characterizes their multisymplectic diffeomorphisms.Comment: 25 p.; LaTeX file. The paper has been partially rewritten. Some terminology has been changed. The proof of some theorems and lemmas have been revised. The title and the abstract are slightly modified. An appendix is added. The bibliography is update

Finsler and Lagrange Geometries in Einstein and String Gravity

We review the current status of Finsler-Lagrange geometry and generalizations. The goal is to aid non-experts on Finsler spaces, but physicists and geometers skilled in general relativity and particle theories, to understand the crucial importance of such geometric methods for applications in modern physics. We also would like to orient mathematicians working in generalized Finsler and Kahler geometry and geometric mechanics how they could perform their results in order to be accepted by the community of ''orthodox'' physicists. Although the bulk of former models of Finsler-Lagrange spaces where elaborated on tangent bundles, the surprising result advocated in our works is that such locally anisotropic structures can be modelled equivalently on Riemann-Cartan spaces, even as exact solutions in Einstein and/or string gravity, if nonholonomic distributions and moving frames of references are introduced into consideration. We also propose a canonical scheme when geometrical objects on a (pseudo) Riemannian space are nonholonomically deformed into generalized Lagrange, or Finsler, configurations on the same manifold. Such canonical transforms are defined by the coefficients of a prime metric and generate target spaces as Lagrange structures, their models of almost Hermitian/ Kahler, or nonholonomic Riemann spaces. Finally, we consider some classes of exact solutions in string and Einstein gravity modelling Lagrange-Finsler structures with solitonic pp-waves and speculate on their physical meaning.Comment: latex 2e, 11pt, 44 pages; accepted to IJGMMP (2008) as a short variant of arXiv:0707.1524v3, on 86 page