3,534 research outputs found
Spin Excitations and Sum Rules in the Heisenberg Antiferromagnet
Various bounds for the energy of collective excitations in the Heisenberg
antiferromagnet are presented and discussed using the formalism of sum rules.
We show that the Feynman approximation significantly overestimates (by about
30\% in the square lattice) the spin velocity due to the non
negligible contribution of multi magnons to the energy weighted sum rule. We
also discuss a different, Goldstone type bound depending explicitly on the
order parameter (staggered magnetization). This bound is shown to be
proportional to the dispersion of classical spin wave theory with a
q-independent normalization factor. Rigorous bounds for the excitation energies
in the anisotropic Heisenberg model are also presented.Comment: 26 pages, Plain TeX including 1 PostScript figure, UTF-307-10/9
Single Impurity Anderson Model with Coulomb Repulsion between Conduction Electrons on the Nearest-Neighbour Ligand Orbital
We study how the Kondo effect is affected by the Coulomb interaction between
conduction electrons on the basis of a simplified model. The single impurity
Anderson model is extended to include the Coulomb interaction on the
nearest-neighbour ligand orbital. The excitation spectra are calculated using
the numerical renormalization group method. The effective bandwidth on the
ligand orbital, , is defined to classify the state. This quantity
decreases as the Coulomb interaction increases. In the
region, the low energy properties are described by the Kondo state, where
is the hybridization width. As decreases in this region, the
Kondo temperature is enhanced, and its magnitude becomes comparable to
for . In the region, the local
singlet state between the electrons on the and ligand orbitals is formed.Comment: 5 pages, 3 figures, LaTeX, to be published in J. Phys. Soc. Jpn Vol.
67 No.
A theory of the electric quadrupole contribution to resonant x-ray scattering: Application to multipole ordering phases in Ce_{1-x}La_{x}B_{6}
We study the electric quadrupole (E2) contribution to resonant x-ray
scattering (RXS). Under the assumption that the rotational invariance is
preserved in the Hamiltonian describing the intermediate state of scattering,
we derive a useful expression for the RXS amplitude. One of the advantages the
derived expression possesses is the full information of the energy dependence,
lacking in all the previous studies using the fast collision approximation. The
expression is also helpful to classify the spectra into multipole order
parameters which are brought about. The expression is suitable to investigate
the RXS spectra in the localized f electron systems. We demonstrate the
usefulness of the formula by calculating the RXS spectra at the Ce L_{2,3}
edges in Ce_{1-x}La_{x}B_{6} on the basis of the formula. We obtain the spectra
as a function of energy in agreement with the experiment of
Ce_{0.7}La_{0.3}B_{6}. Analyzing the azimuthal angle dependence, we find the
sixfold symmetry in the \sigma-\sigma' channel and the threefold onein the
\sigma-\pi' channel not only in the antiferrooctupole (AFO) ordering phase but
also in the antiferroquadrupole (AFQ) ordering phase, which behavior depends
strongly on the domain distribution. The sixfold symmetry in the AFQ phase
arises from the simultaneously induced hexadecapole order. Although the AFO
order is plausible for phase IV in Ce_{1-x}La_{x}B_{6}, the possibility of the
AFQ order may not be ruled out on the basis of azimuthal angle dependence
alone.Comment: 12 pages, 6 figure
Depth Estimation via Affinity Learned with Convolutional Spatial Propagation Network
Depth estimation from a single image is a fundamental problem in computer
vision. In this paper, we propose a simple yet effective convolutional spatial
propagation network (CSPN) to learn the affinity matrix for depth prediction.
Specifically, we adopt an efficient linear propagation model, where the
propagation is performed with a manner of recurrent convolutional operation,
and the affinity among neighboring pixels is learned through a deep
convolutional neural network (CNN). We apply the designed CSPN to two depth
estimation tasks given a single image: (1) To refine the depth output from
state-of-the-art (SOTA) existing methods; and (2) to convert sparse depth
samples to a dense depth map by embedding the depth samples within the
propagation procedure. The second task is inspired by the availability of
LIDARs that provides sparse but accurate depth measurements. We experimented
the proposed CSPN over two popular benchmarks for depth estimation, i.e. NYU v2
and KITTI, where we show that our proposed approach improves in not only
quality (e.g., 30% more reduction in depth error), but also speed (e.g., 2 to 5
times faster) than prior SOTA methods.Comment: 14 pages, 8 figures, ECCV 201
Reflecting on the Physics of Notations applied to a visualisation case study
This paper presents a critical reflection upon the concept of 'physics of notations' proposed by Moody. This is based upon the post hoc application of the concept in the analysis of a visualisation tool developed for a common place mathematics tool. Although this is not the intended design and development approach presumed or preferred by the physics of notations, there are benefits to analysing an extant visualisation. In particular, our analysis benefits from the visualisation having been developed and refined employing graphic design professionals and extensive formative user feedback. Hence the rationale for specific visualisation features is to some extent traceable. This reflective analysis shines a light on features of both the visualisation and domain visualised, illustrating that it could have been analysed more thoroughly at design time. However the same analysis raises a variety of interesting questions about the viability of scoping practical visualisation design in the framework proposed by the physics of notations
Spin and charge gaps in the one-dimensional Kondo-lattice model with Coulomb interaction between conduction electrons
The density-matrix renormalization-group method is applied to the
one-dimensional Kondo-lattice model with the Coulomb interaction between the
conduction electrons. The spin and charge gaps are calculated as a function of
the exchange constant and the Coulomb interaction . It is shown that
both the spin and charge gaps increase with increasing and . The spin
gap vanishes in the limit of for any with an
exponential form, . The
exponent, , is determined as a function of . The charge gap
is generally much larger than the spin gap. In the limit of ,
the charge gap vanishes as for but for a finite
it tends to a finite value, which is the charge gap of the Hubbard model.Comment: RevTeX, 4 pages, 3 Postscript figure
Spectrum of the Hermitian Wilson-Dirac Operator for a Uniform Magnetic Field in Two Dimensions
It is shown that the eigenvalue problem for the hermitian Wilson-Dirac
operator of for a uniform magnetic field in two dimensions can be reduced to
one-dimensional problem described by a relativistic analog of the Harper
equation. An explicit formula for the secular equations is given in term of a
set of polynomials. The spectrum exhibits a fractal structure in the infinite
volume limit. An exact result concerning the index theorem for the overlap
Dirac operator is obtained.Comment: 8 pages, latex, 3 eps figures, minor correction
Multi-Bunch Solutions of Differential-Difference Equation for Traffic Flow
Newell-Whitham type car-following model with hyperbolic tangent optimal
velocity function in a one-lane circuit has a finite set of the exact solutions
for steady traveling wave, which expressed by elliptic theta function. Each
solution of the set describes a density wave with definite number of
car-bunches in the circuit. By the numerical simulation, we observe a
transition process from a uniform flow to the one-bunch analytic solution,
which seems to be an attractor of the system. In the process, the system shows
a series of cascade transitions visiting the configurations closely similar to
the higher multi-bunch solutions in the set.Comment: revtex, 7 pages, 5 figure
The Kondo lattice model with correlated conduction electrons
We investigate a Kondo lattice model with correlated conduction electrons.
Within dynamical mean-field theory the model maps onto an impurity model where
the host has to be determined self-consistently. This impurity model can be
derived from an Anderson-Hubbard model both by equating the low-energy
excitations of the impurity and by a canonical transformation. On the level of
dynamical mean-field theory this establishes the connection of the two lattice
models. The impurity model is studied numerically by an extension of the
non-crossing approximation to a two-orbital impurity. We find that with
decreasing temperature the conduction electrons first form quasiparticles
unaffected by the presence of the lattice of localized spins. Then, reducing
the temperature further, the particle-hole symmetric model turns into an
insulator. The quasiparticle peak in the one-particle spectral density splits
and a gap opens. The size of the gap increases when the correlations of the
conduction electrons become stronger. These findings are similar to the
behavior of the Anderson-Hubbard model within dynamical mean-field theory and
are obtained with much less numerical effort.Comment: 7 pages RevTeX with 3 ps figures, accepted by PR
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