285 research outputs found
An extension of Fourier analysis for the n-torus in the magnetic field and its application to spectral analysis of the magnetic Laplacian
We solved the Schr{\"o}dinger equation for a particle in a uniform magnetic
field in the n-dimensional torus. We obtained a complete set of solutions for a
broad class of problems; the torus T^n = R^n / {\Lambda} is defined as a
quotient of the Euclidean space R^n by an arbitrary n-dimensional lattice
{\Lambda}. The lattice is not necessary either cubic or rectangular. The
magnetic field is also arbitrary. However, we restrict ourselves within
potential-free problems; the Schr{\"o}dinger operator is assumed to be the
Laplace operator defined with the covariant derivative. We defined an algebra
that characterizes the symmetry of the Laplacian and named it the magnetic
algebra. We proved that the space of functions on which the Laplacian acts is
an irreducible representation space of the magnetic algebra. In this sense the
magnetic algebra completely characterizes the quantum mechanics in the magnetic
torus. We developed a new method for Fourier analysis for the magnetic torus
and used it to solve the eigenvalue problem of the Laplacian. All the
eigenfunctions are given in explicit forms.Comment: 32 pages, LaTeX, minor corrections are mad
Spin Polaron Effective Magnetic Model for La_{0.5}Ca_{0.5}MnO_3
The conventional paradigm of charge order for La_{1-x}Ca_xMnO_3 for x=0.5 has
been challenged recently by a Zener polaron picture emerging from experiments
and theoretical calculations. The effective low energy Hamiltonian for the
magnetic degrees of freedom has been found to be a cubic Heisenberg model, with
ferromagnetic nearest neighbor and frustrating antiferromagnetic next nearest
neighbor interactions in the planes, and antiferromagnetic interaction between
planes. With linear spin wave theory and diagonalization of small clusters up
to 27 sites we find that the behavior of the model interpolates between the A
and CE-type magnetic structures when a frustrating intraplanar interaction is
tuned. The values of the interactions calculated by ab initio methods indicate
a possible non-bipartite picture of polaron ordering differing from the
conventional one.Comment: 21 pages and 8 figures (included), Late
Understanding Selectivity of Mesoporous Silica-Grafted Diglycolamide-Type Ligands in the Solid-Phase Extraction of Rare Earths
Rare earth elements (REEs) and their compounds are essential for rapidly developing modern technologies. These materials are especially critical in the area of green/sustainable energy; however, only very high-purity fractions are appropriate for these applications. Yet, achieving efficient REE separation and purification in an economically and environmentally effective way remains a challenge. Moreover, current extraction technologies often generate large amounts of undesirable wastes. In that perspective, the development of selective, reusable, and extremely efficient sorbents is needed. Among numerous ligands used in the liquid-liquid extraction (LLE) process, the diglycolamide-based (DGA) ligands play a leading role. Although these ligands display notable extraction performance in the liquid phase, their extractive chemistry is not widely studied when such ligands are tethered to a solid support. A detailed understanding of the relationship between chemical structure and function (i.e., extraction selectivity) at the molecular level is still missing although it is a key factor for the development of advanced sorbents with tailored selectivity. Herein, a series of functionalized mesoporous silica (KIT-6) solid phases were investigated as sorbents for the selective extraction of REEs. To better understand the extraction behavior of these sorbents, different spectroscopic techniques (solid-state NMR, X-ray photoelectron spectroscopy, XPS, and Fourier transform infrared spectroscopy, FT-IR) were implemented. The obtained spectroscopic results provide useful insights into the chemical environment and reactivity of the chelating ligand anchored on the KIT-6 support. Furthermore, it can be suggested that depending on the extracted metal and/or structure of the ligand and its attachment to KIT-6, different functional groups (i.e., C= O, N-H, or silanols) act as the main adsorption centers and preferentially capture targeted elements, which in turn may be associated with the different selectivity of the synthesized sorbents. Thus, by determining how metals interact with different supports, we aim to better understand the solid-phase extraction process of hybrid (organo)silica sorbents and design better extraction materials
Neel probability and spin correlations in some nonmagnetic and nondegenerate states of hexanuclear antiferromagnetic ring Fe6: Application of algebraic combinatorics to finite Heisenberg spin systems
The spin correlations \omega^z_r, r=1,2,3, and the probability p_N$ of
finding a system in the Neel state for the antiferromagnetic ring Fe(III)6 (the
so-called `small ferric wheel') are calculated. States with magnetization M=0,
total spin 0<=S<=15 and labeled by two (out of four) one-dimensional
irreducible representations (irreps) of the point symmetry group D_6 are taken
into account. This choice follows from importance of these irreps in analyzing
low-lying states in each S-multiplet. Taking into account the Clebsch--Gordan
coefficients for coupling total spins of sublattices (SA=SB=15/2) the global
Neel probability p*_N can be determined. Dependencies of these quantities on
state energy (per bond and in the units of exchange integral J) and the total
spin S are analyzed. Providing we have determined p_N(S) etc. for other
antiferromagnetic rings (Fe10, for instance) we could try to approximate
results for the largest synthesized ferric wheel Fe18. Since thermodynamic
properties of Fe6 have been investigated recently, in the present
considerations they are not discussed, but only used to verify obtained values
of eigenenergies. Numerical results re calculated with high precision using two
main tools: (i) thorough analysis of symmetry properties including methods of
algebraic combinatorics and (ii) multiple precision arithmetic library GMP. The
system considered yields more than 45 thousands basic states (the so-called
Ising configurations), but application of the method proposed reduces this
problem to 20-dimensional eigenproblem for the ground state (S=0). The largest
eigenproblem has to be solved for S=4; its dimension is 60. These two facts
(high precision and small resultant eigenproblems) confirm efficiency and
usefulness of such an approach, so it is briefly discussed here.Comment: 13 pages, 7 figs, 5 tabs, revtex
Magnetic translation groups in an n-dimensional torus
A charged particle in a uniform magnetic field in a two-dimensional torus has
a discrete noncommutative translation symmetry instead of a continuous
commutative translation symmetry. We study topology and symmetry of a particle
in a magnetic field in a torus of arbitrary dimensions. The magnetic
translation group (MTG) is defined as a group of translations that leave the
gauge field invariant. We show that the MTG on an n-dimensional torus is
isomorphic to a central extension of a cyclic group Z_{nu_1} x ... x
Z_{nu_{2l}} x T^m by U(1) with 2l+m=n. We construct and classify irreducible
unitary representations of the MTG on a three-torus and apply the
representation theory to three examples. We shortly describe a representation
theory for a general n-torus. The MTG on an n-torus can be regarded as a
generalization of the so-called noncommutative torus.Comment: 29 pages, LaTeX2e, title changed, re-organized, to be published in
Journal of Mathematical Physic
SprayâDried Mesoporous Mixed CuâNi Oxide@Graphene Nanocomposite Microspheres for High Power and Durable LiâIon Battery Anodes
Exfoliated grapheneâwrapped mesoporous CuâNi oxide (CNO) nanocast composites are developed using a straightforward nanostructure engineering strategy. The synergistic effect of hierarchical mesoporous CNO nanobuilding blocks that are homogeneously wrapped by graphene nanosheets (GNSs) using a rapid spray drying technique effectively preserves the electroactive species against the volume changes resulting from the charge/discharge process. Owing to the intriguing structural/morphological features arising from the caging effect of exfoliated graphene sheets, these 3D/2D CNO@GNS nanocomposite microspheres are promising as highâperformance Liâion battery anode materials. They exhibit unprecedented electrochemical behavior, such as high reversible specific capacity (initial discharge capacities exceeding 1700 mAh gâ1 at low 0.1 mA gâ1, stable 850 and 730 mAh gâ1 at 1 and 5 mA gâ1 after 800 and 1300 cycles, respectively, and higher than 400 mAh gâ1 at very high current density of 10 mA gâ1 after more than 2000 cycles), excellent coulombic efficiency and longâterm stability (more than 3000 cycles with >55% capacity retention) at high current density that are remarkable compared to most transition metal oxides and nanocomposites prepared by conventional techniques. This simple, yet innovative, material design is inspiring to develop advanced conversion materials for Liâion batteries or other energy storage devices
Geometric entropy, area, and strong subadditivity
The trace over the degrees of freedom located in a subset of the space
transforms the vacuum state into a density matrix with non zero entropy. This
geometric entropy is believed to be deeply related to the entropy of black
holes. Indeed, previous calculations in the context of quantum field theory,
where the result is actually ultraviolet divergent, have shown that the
geometric entropy is proportional to the area for a very special type of
subsets. In this work we show that the area law follows in general from simple
considerations based on quantum mechanics and relativity. An essential
ingredient of our approach is the strong subadditive property of the quantum
mechanical entropy.Comment: Published versio
HIRDES - The High-Resolution Double-Echelle Spectrograph for the World Space Observatory Ultraviolet (WSO/UV)
The World Space Observatory Ultraviolet (WSO/UV) is a multi-national project
grown out of the needs of the astronomical community to have future access to
the UV range. WSO/UV consists of a single UV telescope with a primary mirror of
1.7m diameter feeding the UV spectrometer and UV imagers. The spectrometer
comprises three different spectrographs, two high-resolution echelle
spectrographs (the High-Resolution Double-Echelle Spectrograph, HIRDES) and a
low-dispersion long-slit instrument. Within HIRDES the 102-310nm spectral band
is split to feed two echelle spectrographs covering the UV range 174-310nm and
the vacuum-UV range 102-176nm with high spectral resolution (R>50,000). The
technical concept is based on the heritage of two previous ORFEUS SPAS
missions. The phase-B1 development activities are described in this paper
considering performance aspects, design drivers, related trade-offs (mechanical
concepts, material selection etc.) and a critical functional and environmental
test verification approach. The current state of other WSO/UV scientific
instruments (imagers) is also described.Comment: Accepted for publication in Advances in Space Researc
On morphological hierarchical representations for image processing and spatial data clustering
Hierarchical data representations in the context of classi cation and data
clustering were put forward during the fties. Recently, hierarchical image
representations have gained renewed interest for segmentation purposes. In this
paper, we briefly survey fundamental results on hierarchical clustering and
then detail recent paradigms developed for the hierarchical representation of
images in the framework of mathematical morphology: constrained connectivity
and ultrametric watersheds. Constrained connectivity can be viewed as a way to
constrain an initial hierarchy in such a way that a set of desired constraints
are satis ed. The framework of ultrametric watersheds provides a generic scheme
for computing any hierarchical connected clustering, in particular when such a
hierarchy is constrained. The suitability of this framework for solving
practical problems is illustrated with applications in remote sensing
Analysis of Agglomerative Clustering
The diameter -clustering problem is the problem of partitioning a finite
subset of into subsets called clusters such that the maximum
diameter of the clusters is minimized. One early clustering algorithm that
computes a hierarchy of approximate solutions to this problem (for all values
of ) is the agglomerative clustering algorithm with the complete linkage
strategy. For decades, this algorithm has been widely used by practitioners.
However, it is not well studied theoretically. In this paper, we analyze the
agglomerative complete linkage clustering algorithm. Assuming that the
dimension is a constant, we show that for any the solution computed by
this algorithm is an -approximation to the diameter -clustering
problem. Our analysis does not only hold for the Euclidean distance but for any
metric that is based on a norm. Furthermore, we analyze the closely related
-center and discrete -center problem. For the corresponding agglomerative
algorithms, we deduce an approximation factor of as well.Comment: A preliminary version of this article appeared in Proceedings of the
28th International Symposium on Theoretical Aspects of Computer Science
(STACS '11), March 2011, pp. 308-319. This article also appeared in
Algorithmica. The final publication is available at
http://link.springer.com/article/10.1007/s00453-012-9717-
- âŠ