Symmetry consideration and eg bands in NdNiO3 and YNiO3

Group theoretical analyses are applied to the magnetic and electronic structures of NdNiO3 and YNiO3, whose electronic structures have been studied very recently by the LSDA+U method. The Jahn-Teller distortion cannot satisfy the experimentally observed magnetic diffraction. The resultant ground state magnetic stuructures are monoclinic P_ba in NdNiO3 case and P_b2_1/a in YNiO3 case, respectively.Comment: 6 pages, 3 figures, Proc. Int. Symp. ISSP-Kashiwa 200

Self-similar solutions and collective coordinate methods for Nonlinear Schrodinger Equations

In this paper we study the phase of self-similar solutions to general Nonlinear Schr\"odinger equations. From this analysis we gain insight on the dynamics of nontrivial solutions and a deeper understanding of the way collective coordinate methods work. We also find general evolution equations for the most relevant dynamical parameter $w(t)$ corresponding to the width of the solution. These equations are exact for self-similar solutions and provide a shortcut to find approximate evolution equations for the width of non-self-similar solutions similar to those of collective coordinate methods

Nahm dualities on the torus - a synthesis

We give a unified description of self-dual SU(2) gauge fields on tori of size lt x ls^3 based on a mixture of analytical and numerical methods using the Nahm transformation, extended to the case of twisted boundary conditions. We show how torus calorons (lt/ls small) are Nahm dual to the torus instantons (lt/ls large). Holonomies are dual to the locations of constituents, this duality becoming exact in the limiting cases ls or lt --> infinity. Implications for the moduli spaces are discussed.Comment: Latex, 22 pages, 8 figures in 11 postscript file

Kaluza's theory in generalized coordinates

Maxwell's equations can be obtained in generalized coordinates by considering the electromagnetic field as an external agent. The work here presented shows how to obtain the electrodynamics for a charged particle in generalized coordinates eliminating the concept of external force. Based on Kaluza's formalism, the one here presented extends the 5x5 metric into a 6x6 space-time giving enough room to include magnetic monopoles in a very natural way.Comment: 11 pages, RevTex. Accepted for publication in the Journal of Matematical Physic

Electron iduced light emission in photonic crystals

The interaction of a fast electron with a photonic crystal is studied by solving the Maxwell equations exactly for the external field provided by the electron in the presence of the crystal. The polarization currents and charges produced by the passage of the electron give rise to the emission of the so-called Smith-Purcell radiation. The emitted light probability is obtained by integrating the Poynting vector over planes parallel to the crystal at a large distance from the latter. Both reflected and transmitted light components are analyzed and related to the photonic band structure of the crystal. Emission spectra are compared with the energy loss probability and also with the reflectance and transmittance of the crystal.Comment: 9 pages, 3 figures, nano-7/ecoss-21 proceedings, submitted to Surface Scienc

Simplest miniversal deformations of matrices, matrix pencils, and contragredient matrix pencils

V. I. Arnold [Russian Math. Surveys 26 (2) (1971) 29-43] constructed a simple normal form for a family of complex n-by-n matrices that smoothly depend on parameters with respect to similarity transformations that smoothly depend on the same parameters. We construct analogous normal forms for a family of real matrices and a family of matrix pencils that smoothly depend on parameters, simplifying their normal forms by D. M. Galin [Uspehi Mat. Nauk 27 (1) (1972) 241-242] and by A. Edelman, E. Elmroth, B. Kagstrom [Siam J. Matrix Anal. Appl. 18 (3) (1997) 653-692].Comment: 20 page

Particle production from symmetry breaking after inflation and leptogenesis

Recent studies suggest that the process of symmetry breaking after inflation typically occurs very fast, within a single oscillation of the symmetry-breaking field, due to the spinodal growth of its long-wave modes, otherwise known as `tachyonic preheating'. We show how this sudden transition from the false to the true vacuum can induce a significant production of particles, bosons and fermions, coupled to the symmetry-breaking field. We find that this new mechanism of particle production in the early Universe may have interesting consequences for the origin of supermassive dark matter and the generation of the observed baryon asymmetry through leptogenesis.Comment: 17 pages, 2 figures. Significantly enlarged version, including a more detailed discussion of leptogenesis. To appear in Physics Letters

Multi-Caloron solutions

We discuss the construction of multi-caloron solutions with non-trivial holonomy, both as approximate superpositions and exact self-dual solutions. The charge k SU(n) moduli space can be described by kn constituent monopoles. Exact solutions help us to understand how these constituents can be seen as independent objects, which seems not possible with the approximate superposition. An "impurity scattering" calculation provides relatively simple expressions. Like at zero temperature an explicit parametrization requires solving a quadratic ADHM constraint, achieved here for a class of axially symmetric solutions. We will discuss the properties of these exact solutions in detail, but also demonstrate that interesting results can be obtained without explicitly solving for the constraint.Comment: 31 pages, 7 figures (in 19 parts

Deformed commutators on quantum group module-algebras

AbstractWe construct quantum commutators on module-algebras of quasi-triangular Hopf algebras. These are quantum-group covariant and have generalized antisymmetry and Leibniz properties. If the Hopf algebra is triangular they additionally satisfy a generalized Jacobi identity, turning the module-algebra into a quantum-Lie algebra

Classification of Inflationary Potentials

Brans-Dicke gravity is remarkable not only in that General Relativity and Mach's Principle find a common enlarged scenario where they are mutually consistent, but also in that it provides a very interesting quantum cosmological model within the inflationary paradigm. The interplay between the Brans-Dicke scalar $\Phi$ and the inflaton field $\sigma$ plays an important r\^{o}le during the course of inflation, and although the dynamics as such is governed by the potential, the onset and the end of inflation are determined by the values of both fields jointly. The relative position of the beginning-- and end-of-inflation curves (BoI and EoI respectively) is the most relevant factor in determining the resulting quantum cosmological scenario. The classification of potentials that is given in this paper is based on the criterion of whether the BoI and EoI boundaries enclose a finite or infinite area in the ($\sigma$,$\Phi$) plane where inflation takes place. It is shown that this qualitative classification distinguishes two classes of potentials that yield very different cosmologies and it is argued that only those theories in which BoI and EoI enclose a finite area in the ($\sigma$,$\Phi$) plane are compatible with our observable universe.Comment: 4 pages, 3 figure