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 $P_\Gamma (l_\Gamma)$ and $P_{\Gamma_1, \Gamma_2}(l_{\Gamma_1},l_{\Gamma_2})$, $l_\Gamma$ being the interface position above a fixed point $\Gamma$ 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

Z4\mathbb{Z}_4-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 ($\mathbb{Z}_4$-symmetric) perturbations to the classical $XY$ model in dimensionality $d\in [2,4]$. In $d=3$ we provide accurate estimates of the eigenvalue $y_4$ corresponding to the leading irrelevant perturbation and follow the evolution of the physical picture upon reducing spatial dimensionality from $d=3$ towards $d=2$, where we approximately recover the onset of the Kosterlitz-Thouless physics. We analyze the interplay between the leading irrelevant eigenvalues related to $O(2)$-symmetric and $\mathbb{Z}_4$-symmetric perturbations and their approximate collapse for $d\to 2$. 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 $T_2=(210\,\pm\,40)$ ps. The same structure contains QDs doped with single Mn$^{2+}$ ions, as detected in photoluminescence spectra. Our work therefore paves the way toward investigating and controlling an exciton coherence coupled, via $s$,$p$-$d$ 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