204 research outputs found
Self-adjoint symmetry operators connected with the magnetic Heisenberg ring
We consider symmetry operators a from the group ring C[S_N] which act on the
Hilbert space H of the 1D spin-1/2 Heisenberg magnetic ring with N sites. We
investigate such symmetry operators a which are self-adjoint (in a sence
defined in the paper) and which yield consequently observables of the
Heisenberg model. We prove the following results: (i) One can construct a
self-adjoint idempotent symmetry operator from every irreducible character of
every subgroup of S_N. This leads to a big manifold of observables. In
particular every commutation symmetry yields such an idempotent. (ii) The set
of all generating idempotents of a minimal right ideal R of C[S_N] contains one
and only one idempotent which ist self-adjoint. (iii) Every self-adjoint
idempotent e can be decomposed into primitive idempotents e = f_1 + ... + f_k
which are also self-adjoint and pairwise orthogonal. We give a computer
algorithm for the calculation of such decompositions. Furthermore we present 3
additional algorithms which are helpful for the calculation of self-adjoint
operators by means of discrete Fourier transforms of S_N. In our investigations
we use computer calculations by means of our Mathematica packages PERMS and
HRing.Comment: 13 page
Drying of a Microdroplet of Water Suspension of Nanoparticles: from Surface Aggregates to Microcrystal
The method of formation of nanoparticle aggregates such as high-coverage
spherical shells of microspheres or 3-D micro crystals grown in the geometry
unaffected by a substrate is described. In the reported experiment, the
evaporation of single levitated water droplet containing 200 nm diameter
polystyrene spheres was studied. Successive stages of the drying process were
discussed by analyzing the intensity of light elastically scattered by the
evaporating droplet. The numerically simulated self-assembly coincides nicely
with the observed morphologies resulting from transformation of a droplet of
suspension into a solid microcrystal via kinetically driven self-assembly of
nanostructures.Comment: 5 pages, 6 figure
On local linearization of control systems
We consider the problem of topological linearization of smooth (C infinity or
real analytic) control systems, i.e. of their local equivalence to a linear
controllable system via point-wise transformations on the state and the control
(static feedback transformations) that are topological but not necessarily
differentiable. We prove that local topological linearization implies local
smooth linearization, at generic points. At arbitrary points, it implies local
conjugation to a linear system via a homeomorphism that induces a smooth
diffeomorphism on the state variables, and, except at "strongly" singular
points, this homeomorphism can be chosen to be a smooth mapping (the inverse
map needs not be smooth). Deciding whether the same is true at "strongly"
singular points is tantamount to solve an intriguing open question in
differential topology
The position of a duodenal diverticulum in the area of the major duodenal papilla and its potential clinical implications
Background: Although duodenal diverticula are associated with less frequent pathology than the colonic diverticula in the large intestine, their periampullary position may have significant clinical implications. The aim of the study was to identify any possible correlation between the type of localisation of the major duodenal papilla, duodenal diverticula, and some particular clinical issues.
Materials and methods: In total, 628 patients (408 females and 220 males; aged 21–91 years), who underwent endoscopic retrograde cholangiopancreatography were included in this study. The patients were divided into two groups: a study group comprising 66 (10.5%) patients with periampullary position of diverticula (group A), and a control group comprising 562 (89.5%) patients without diverticula (group B).
Results: A duodenal diverticulum was diagnosed in the periampullary position in 66/628 (10.5%) patients: 41 women (aged 52–91 years) and 25 men (aged 54–83 years).
Conclusions: Three types of localisation were observed for the major duodenal papilla with regard to the diverticula, with the most common type being next to each other (type III). In patients with diverticula, similar frequencies of gallstone occurrence are observed in men and women. Patients with papilla in the diverticulum who underwent cholecystectomy are more prone to develop lithiasis
Proximity of Iron Pnictide Superconductors to a Quantum Tricritical Point
We determine the nature of the magnetic quantum critical point in the doped
LaFeAsO using a set of constrained density functional calculations that provide
ab initio coefficients for a Landau order parameter analysis. The system turns
out to be remarkably close to a quantum tricritical point, where the nature of
the phase transition changes from first to second order. We compare with the
effective field theory and discuss the experimental consequences.Comment: 4 pages, 4 figure
Fermi surface instabilities at finite Temperature
We present a new method to detect Fermi surface instabilities for interacting
systems at finite temperature. We first apply it to a list of cases studied
previously, recovering already known results in a very economic way, and
obtaining most of the information on the phase diagram analytically. As an
example, in the continuum limit we obtain the critical temperature as an
implicit function of the magnetic field and the chemical potential
. By applying the method to a model proposed to describe reentrant
behavior in , we reproduce the phase diagram obtained
experimentally and show the presence of a non-Fermi Liquid region at
temperatures above the nematic phase.Comment: 10 pages, 10 figure
Scaling laws near the conformal window of many-flavor QCD
We derive universal scaling laws for physical observables such as the
critical temperature, the chiral condensate, and the pion decay constant as a
function of the flavor number near the conformal window of many-flavor QCD in
the chiral limit. We argue on general grounds that the associated critical
exponents are all interrelated and can be determined from the critical exponent
of the running gauge coupling at the Caswell-Banks-Zaks infrared fixed point.
We illustrate our findings with the aid of nonperturbative functional
Renormalization Group (RG) calculations and low-energy QCD models.Comment: 18 pages, 4 figures, references added and discussion expanded
(matches JHEP version
- …