Scalar potential

About: Scalar potential is a research topic. Over the lifetime, 3642 publications have been published within this topic receiving 78868 citations. The topic is also known as: potential.

New technique for solving three-dimensional multiply connected eddy-current problems

Abstract: In three-dimensional eddy-current computation, when the conductors are multiply connected, the use of a scalar potential in exterior regions leads to a multivalued problem. To avoid this difficulty, in a hybrid finite-element/boundary-integral model, the authors propose to use the electric field as the state variable in both conducting and nonconducting regions. A vectorial boundary-integral method, based on the use of a current sheet on the boundary, is applied in exterior regions. A spanning tree technique is introduced to ensure the null divergence of the boundary current sheet. This technique permits also a reduction in the number of boundary unknowns.

Anderson’s Orthogonality Catastrophe

Abstract: We give an upper bound on the modulus of the ground-state overlap of two non-interacting fermionic quantum systems with N particles in a large but finite volume Ld of d-dimensional Euclidean space. The underlying one-particle Hamiltonians of the two systems are standard Schrodinger operators that differ by a non-negative compactly supported scalar potential. In the thermodynamic limit, the bound exhibits an asymptotic power-law decay in the system size L, showing that the ground-state overlap vanishes for macroscopic systems. The decay exponent can be interpreted in terms of the total scattering cross section averaged over all incident directions. The result confirms and generalises P. W. Anderson’s informal computation (Phys. Rev. Lett. 18:1049–1051, 1967).

Duality and Hidden Symmetries in Gravitational Theories

Abstract: Duality is presently considered the key to the Holy Grail of String Theory— it is supposed to provide links between the five known different superstring theories in ten dimensions, hoped to be just different limits of one unique eleven dimensional theory [1]. The main role of duality is to relate two different regimes— e.g. one of weak and one of strong coupling— of these theories. In most cases duality is not a very precise concept, just because the strong coupling regime is a matter of speculation. This is rather different from the duality transformations in the gravitational theories considered in this work, which have a very precise meaning— not the least because we are dealing with classical field theories (compare, however, [2] and for a modest attempt to use duality symmetry in Quantum Gravity, see [3]). The historical example of all these dualities is the duality between electric and magnetic fields in electrodynamics, which, when expressed in terms of the field strength, is just an example of the mathematical notion of Hodge duality for differential forms. Actually, the source-free Maxwell equations are not only invariant under a discrete duality, but under a continous one-parameter group of duality rotations. It is this kind of transformations, which is the subject of this article. Whereas, in general, the electromagnetic duality rotations are an ‘on-shell’ symmetry, i.e. a symmetry of the equations of motion and not of the action, the situation changes,if one considers time-independent solutions. In this case also the magnetic field can be derived from a (pseudo) scalar potential and the duality rotations expressed in terms of scalar potentials become a bona fide "off-shell' symmetry of the "dimensionally reduced' three dimensional theory. This replacement of the vector potential by a scalar one has analogues in higher dimensions playing an important role in the construction of supergravity theories through the process of dimensional reduction. A typical example is the (pseudo) scalar "axion',obtained as the dual of a gauge field 2-form in 4 dimensions. This scalar axion combines nicely with another scalar,the dilaton to a doublet giving rise to an SL(2) group of non-linear duality transformations [4]. A particular element of this group,replacing the dilaton by its inverse,lies at the heart of string duality ("S- duality')[5],where the expectation value of the dilaton plays the role of a string coupling constant.

Bound states for Dirac equation with Wood-Saxon potential

Abstract: The s wave exact bound state solutions of Dirac equation are obtained when the Wood-Saxon -type scalar potential is not less than its vector potential.

Multifield Dynamics in Higgs-otic Inflation

Abstract: In Higgs-otic inflation a complex neutral scalar combination of the $h^0$ and $H^0$ MSSM Higgs fields plays the role of inflaton in a chaotic fashion. The potential is protected from large trans-Planckian corrections at large inflaton if the system is embedded in string theory so that the Higgs fields parametrize a D-brane position. The inflaton potential is then given by a DBI+CS D-brane action yielding an approximate linear behaviour at large field. The inflaton scalar potential is a 2-field model with specific non-canonical kinetic terms. Previous computations of the cosmological parameters (i.e. scalar and tensor perturbations) did not take into account the full 2-field character of the model, ignoring in particular the presence of isocurvature perturbations and their coupling to the adiabatic modes. It is well known that for generic 2-field potentials such effects may significantly alter the observational signatures of a given model. We perform a full analysis of adiabatic and isocurvature perturbations in the Higgs-otic 2-field model. We show that the predictivity of the model is increased compared to the adiabatic approximation. Isocurvature perturbations moderately feed back into adiabatic fluctuations. However, the isocurvature component is exponentially damped by the end of inflation. The tensor to scalar ratio varies in a region $r=0.08-0.12$, consistent with combined Planck/BICEP results.