Galilean Lee Model of the Delta Function Potential

The scattering cross section associated with a two dimensional delta function has recently been the object of considerable study. It is shown here that this problem can be put into a field theoretical framework by the construction of an appropriate Galilean covariant theory. The Lee model with a standard Yukawa interaction is shown to provide such a realization. The usual results for delta function scattering are then obtained in the case that a stable particle exists in the scattering channel provided that a certain limit is taken in the relevant parameter space. In the more general case in which no such limit is taken finite corrections to the cross section are obtained which (unlike the pure delta function case) depend on the coupling constant of the model.Comment: 7 pages, latex, no figure

Macroscopic Anisotropy and Symmetry Breaking in the Pyrochlore Antiferromagnet Gd2_{2}Ti2_{2}O7_{7}}

In the Heisenberg antiferromagnet $Gd_2Ti_2O_7$, the exchange interactions are geometrically frustrated by the pyrochlore lattice structure. This ESR study reveals a strong temperature dependent anisotropy with respect to a [111] body diagonal below a temperature $T_A=80$ K, despite the spin only nature of the $Gd^{3+}$ ion. Anisotropy and symmetry breaking can nevertheless appear through the superexchange interaction. The presence of short range planar correlation restricted to specific Kagom\'{e} planes is sufficient to explain the two ESR modes studied in this work.Comment: 4 pages, 5 figure

Estimating the number of change-points in a two-dimensional segmentation model without penalization

In computational biology, numerous recent studies have been dedicated to the analysis of the chromatin structure within the cell by two-dimensional segmentation methods. Motivated by this application, we consider the problem of retrieving the diagonal blocks in a matrix of observations. The theoretical properties of the least-squares estimators of both the boundaries and the number of blocks proposed by L\'evy-Leduc et al. [2014] are investigated. More precisely, the contribution of the paper is to establish the consistency of these estimators. A surprising consequence of our results is that, contrary to the onedimensional case, a penalty is not needed for retrieving the true number of diagonal blocks. Finally, the results are illustrated on synthetic data.Comment: 30 pages, 8 figure

Localization Properties of Quantized Magnetostatic Modes in Nanocubes

We investigate the dynamical properties of a system of interacting magnetic dipoles disposed in sites of an sc lattice and forming a cubic-shaped sample of size determined by the cube edge length (N-1)a (a being the lattice constant, N representing the number of dipolar planes). The dipolar field resulting from the dipole-dipole interactions is calculated numerically in points of the axis connecting opposite cube face centers (central axis) by collecting individual contributions to this field coming from each of the N atomic planes perpendicular to the central axis. The applied magnetic field is assumed to be oriented along the central axis, magnetizing uniformly the whole sample, all the dipoles being aligned parallelly in the direction of the applied field. The frequency spectrum of magnetostatic waves propagating in the direction of the applied field is found numerically by solving the Landau-Lifshitz equation of motion including the local (nonhomogeneous) dipolar field component; the mode amplitude spatial distributions (mode profiles) are depicted as well. It is found that only the two energetically highest modes have bulk-extended character. All the remaining modes are of localized nature; more precisely, the modes forming the lower part of the spectrum are localized in the subsurface region, while the upper-spectrum modes are localized around the sample center. We show that the mode localization regions narrow down as the cube size, N, increases (we investigated the range of N=21 to N=101), and in sufficiently large cubes one obtains practically only center-localized and surface-localized magnetostatic modes.Comment: 20 pages, 9 figures in postscript, useing Revtex4.cl

(In)finite extensions of algebras from their Inonu-Wigner contractions

The way to obtain massive non-relativistic states from the Poincare algebra is twofold. First, following Inonu and Wigner the Poincare algebra has to be contracted to the Galilean one. Second, the Galilean algebra is to be extended to include the central mass operator. We show that the central extension might be properly encoded in the non-relativistic contraction. In fact, any Inonu-Wigner contraction of one algebra to another, corresponds to an infinite tower of abelian extensions of the latter. The proposed method is straightforward and holds for both central and non-central extensions. Apart from the Bargmann (non-zero mass) extension of the Galilean algebra, our list of examples includes the Weyl algebra obtained from an extension of the contracted SO(3) algebra, the Carrollian (ultra-relativistic) contraction of the Poincare algebra, the exotic Newton-Hooke algebra and some others. The paper is dedicated to the memory of Laurent Houart (1967-2011).Comment: 7 pages, revtex style; v2: Minor corrections, references added; v3: Typos correcte

From laser cooling to aging: a unified Levy flight description

Intriguing phenomena such as subrecoil laser cooling of atoms, or aging phenomenon in glasses, have in common that the systems considered do not reach a steady-state during the experiments, although the experimental time scales are very large compared to the microscopic ones. We revisit some standard models describing these phenomena, and reformulate them in a unified framework in terms of lifetimes of the microscopic states of the system. A universal dynamical mechanism emerges, leading to a generic time-dependent distribution of lifetimes, independently of the physical situation considered.Comment: 8 pages, 2 figures; accepted for publication in American Journal of Physic

Fostering collective intelligence education

New educational models are necessary to update learning environments to the digitally shared communication and information. Collective intelligence is an emerging field that already has a significant impact in many areas and will have great implications in education, not only from the side of new methodologies but also as a challenge for education. This paper proposes an approach to a collective intelligence model of teaching using Internet to combine two strategies: idea management and real time assessment in the class. A digital tool named Fabricius has been created supporting these two elements to foster the collaboration and engagement of students in the learning process. As a result of the research we propose a list of KPI trying to measure individual and collective performance. We are conscious that this is just a first approach to define which aspects of a class following a course can be qualified and quantified.Postprint (published version