272 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
Interfacial morphology and correlations in adsorption at a chemically structured substrate - exact results in d=2
Adsorption at a 1-dimensional planar substrate equipped with a localized
chemical inhomogeneity is studied within the framework of a continuum
interfacial model from the point of view of interfacial morphology and
correlation function properties. Exact expressions for the one-point and
two-point probability distribution functions and
, being the
interface position above a fixed point of the substrate, are derived
for temperature corresponding to the inhomogeneity's wetting transition. It is
demonstrated that in the limit of macroscopic inhomogeneity's size the net
effect of the remaining homogeneous parts of the substrate on the interfacial
morphology above the inhomogeneity is exactly equivalent to appropriate pinning
of the interface at its boundaries. The structure of the average interfacial
morphology and correlation function in this limit are discussed and compared to
earlier results obtained for systems with homogeneous substrate
An alternative approach to the construction of Schur-Weyl transform
We propose an alternative approach for the construction of the unitary matrix
which performs generalized unitary rotations of the system consisting of
independent identical subsystems (for example spin system). This matrix, when
applied to the system, results in a change of degrees of freedom, uncovering
the information hidden in non-local degrees of freedom. This information can be
used, inter alia, to study the structure of entangled states, their
classification and may be useful for construction of quantum algorithms.Comment: 6 page
Harvesting, coupling and control of single exciton coherences in photonic waveguide antennas
We perform coherent non-linear spectroscopy of individual excitons strongly
confined in single InAs quantum dots (QDs). The retrieval of their
intrinsically weak four-wave mixing (FWM) response is enabled by a
one-dimensional dielectric waveguide antenna. Compared to a similar QD embedded
in bulk media, the FWM detection sensitivity is enhanced by up to four orders
of magnitude, over a broad operation bandwidth. Three-beam FWM is employed to
investigate coherence and population dynamics within individual QD transitions.
We retrieve their homogenous dephasing in a presence of spectral wandering.
Two-dimensional FWM reveals off-resonant F\"orster coupling between a pair of
distinct QDs embedded in the antenna. We also detect a higher order QD
non-linearity (six-wave mixing) and use it to coherently control the FWM
transient. Waveguide antennas enable to conceive multi-color coherent
manipulation schemes of individual emitters.Comment: 7 pages, 8 Figure
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
-symmetric perturbations to the XY model from functional renormalization
We employ the second order of the derivative expansion of the nonperturbative
renormalization group to study cubic (-symmetric) perturbations
to the classical model in dimensionality . In we provide
accurate estimates of the eigenvalue corresponding to the leading
irrelevant perturbation and follow the evolution of the physical picture upon
reducing spatial dimensionality from towards , where we
approximately recover the onset of the Kosterlitz-Thouless physics. We analyze
the interplay between the leading irrelevant eigenvalues related to
-symmetric and -symmetric perturbations and their
approximate collapse for . We compare and discuss different
implementations of the derivative expansion in cases involving one and two
invariants of the corresponding symmetry group.Comment: 13 pages, 6 figure
Antireflective photonic structure for coherent nonlinear spectroscopy of single magnetic quantum dots
This work presents epitaxial growth and optical spectroscopy of CdTe quantum
dots (QDs) in (Cd,Zn,Mg)Te barriers placed on the top of (Cd,Zn,Mg)Te
distributed Bragg reflector. The formed photonic mode in our half-cavity
structure permits to enhance the local excitation intensity and extraction
efficiency of the QD photoluminescence, while suppressing the reflectance
within the spectral range covering the QD transitions. This allows to perform
coherent, nonlinear, resonant spectroscopy of individual QDs. The coherence
dynamics of a charged exciton is measured via four-wave mixing, with the
estimated dephasing time ps. The same structure contains
QDs doped with single Mn ions, as detected in photoluminescence spectra.
Our work therefore paves the way toward investigating and controlling an
exciton coherence coupled, via ,- exchange interaction, with an
individual spin of a magnetic dopant.Comment: 6 pages, 5 figure
Variations in the topography of the infraorbital canal/groove complex: a proposal for classification and its potential usefulness in orbital floor surgery
Background: The aim of the study was to precisely describe and classify the infraorbital canal/groove (IOC/G) complex in dry human skulls and to evaluate the presence of asymmetry in the IOC/G complex.Materials and methods: Seventy orbits of 35 human skulls were investigated.The following distances were measured: the distance between the posterior and anterior margin of the infraorbital groove (S-C); the posterior margin of the infraorbital canal and the infraorbital foramen (C-IOF); and the total length of the infraorbital canal-groove complex (S-C-IOF). The symmetry of the contralateral measurements was analysed.Results: Three types of the IOC/G complex were distinguished: types I, II, III, whose respective incidences were 11.4%, 68.6%, 20.0%. The mean length of the infraorbital groove plus canal complex on the right and left with standard deviation were 27.78 ± 3.69 mm and 28.06 ± 3.37 mm, respectively.Conclusions: The results presented in this study may be particularly helpful for surgery in patients with blow-out fractures and different endoscopic and reconstructive procedures in the region of the inferior orbital wall. The type III IOC/G complex, according to our classification, seems the most likely to be exposed to trauma during surgical manipulations.
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
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