2,599 research outputs found
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
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
On alpha stable distribution of wind driven water surface wave slope
We propose a new formulation of the probability distribution function of wind
driven water surface slope with an -stable distribution probability.
The mathematical formulation of the probability distribution function is given
under an integral formulation. Application to represent the probability of time
slope data from laboratory experiments is carried out with satisfactory
results. We compare also the -stable model of the water surface slopes
with the Gram-Charlier development and the non-Gaussian model of Liu et
al\cite{Liu}. Discussions and conclusions are conducted on the basis of the
data fit results and the model analysis comparison.Comment: final version of the manuscript: 25 page
Modulating the phase transition temperature of giant magnetocaloric thin films by ion irradiation
Magnetic refrigeration based on the magnetocaloric effect at room temperature
is one of the most attractive alternative to the current gas
compression/expansion method routinely employed. Nevertheless, in giant
magnetocaloric materials, optimal refrigeration is restricted to the narrow
temperature window of the phase transition (Tc). In this work, we present the
possibility of varying this transition temperature into a same giant
magnetocaloric material by ion irradiation. We demonstrate that the transition
temperature of iron rhodium thin films can be tuned by the bombardment of ions
of Ne 5+ with varying fluences up to 10 14 ions cm --2 , leading to optimal
refrigeration over a large 270--380 K temperature window. The Tc modification
is found to be due to the ion-induced disorder and to the density of new
point-like defects. The variation of the phase transition temperature with the
number of incident ions opens new perspectives in the conception of devices
using giant magnetocaloric materials
Vortex solutions in axial or chiral coupled non-relativistic spinor- Chern-Simons theory
The interaction of a spin 1/2 particle (described by the non-relativistic
"Dirac" equation of L\'evy-Leblond) with Chern-Simons gauge fields is studied.
It is shown, that similarly to the four dimensional spinor models, there is a
consistent possibility of coupling them also by axial or chiral type currents.
Static self dual vortex solutions together with a vortex-lattice are found with
the new couplings.Comment: Plain TEX, 10 page
Perturbative Expansion in the Galilean Invariant Spin One-Half Chern-Simons Field Theory
A Galilean Chern-Simons field theory is formulated for the case of two
interacting spin-1/2 fields of distinct masses M and M'. A method for the
construction of states containing N particles of mass M and N' particles of
mass M' is given which is subsequently used to display equivalence to the
spin-1/2 Aharonov-Bohm effect in the N = N' =1 sector of the model. The latter
is then studied in perturbation theory to determine whether there are
divergences in the fourth order (one loop) diagram. It is found that the
contribution of that order is finite (and vanishing) for the case of parallel
spin projections while the antiparallel case displays divergences which are
known to characterize the spin zero case in field theory as well as in quantum
mechanics.Comment: 14 pages LaTeX, including 2 figures using eps
Spinor vortices in non-relativistic Chern-Simons theory
The non-relativistic `Dirac' equation of L\'evy-Leblond is used to describe a
spin {\small 1/2} particle interacting with a Chern-Simons gauge field. Static,
purely magnetic, self-dual spinor vortices are constructed. The solution can be
`exported' to a uniform magnetic background field.Comment: 7 pages, Plain Te
- …