Lie group weight multiplicities from conformal field theory

Dominant weight multiplicities of simple Lie groups are expressed in terms of the modular matrices of Wess-Zumino-Witten conformal field theories, and related objects. Symmetries of the modular matrices give rise to new relations among multiplicities. At least for some Lie groups, these new relations are strong enough to completely fix all multiplicities.Comment: 12 pages, Plain TeX, no figure

Quantum probabilities as Bayesian probabilities

In the Bayesian approach to probability theory, probability quantifies a degree of belief for a single trial, without any a priori connection to limiting frequencies. In this paper we show that, despite being prescribed by a fundamental law, probabilities for individual quantum systems can be understood within the Bayesian approach. We argue that the distinction between classical and quantum probabilities lies not in their definition, but in the nature of the information they encode. In the classical world, maximal information about a physical system is complete in the sense of providing definite answers for all possible questions that can be asked of the system. In the quantum world, maximal information is not complete and cannot be completed. Using this distinction, we show that any Bayesian probability assignment in quantum mechanics must have the form of the quantum probability rule, that maximal information about a quantum system leads to a unique quantum-state assignment, and that quantum theory provides a stronger connection between probability and measured frequency than can be justified classically. Finally we give a Bayesian formulation of quantum-state tomography.Comment: 6 pages, Latex, final versio

Mutually unbiased bases: tomography of spin states and star-product scheme

Mutually unbiased bases (MUBs) are considered within the framework of a generic star-product scheme. We rederive that a full set of MUBs is adequate for a spin tomography, i.e. knowledge of all probabilities to find a system in each MUB-state is enough for a state reconstruction. Extending the ideas of the tomographic-probability representation and the star-product scheme to MUB-tomography, dequantizer and quantizer operators for MUB-symbols of spin states and operators are introduced, ordinary and dual star-product kernels are found. Since MUB-projectors are to obey specific rules of the star-product scheme, we reveal the Lie algebraic structure of MUB-projectors and derive new relations on triple- and four-products of MUB-projectors. Example of qubits is considered in detail. MUB-tomography by means of Stern-Gerlach apparatus is discussed.Comment: 11 pages, 1 table, partially presented at the 17th Central European Workshop on Quantum Optics (CEWQO'2010), June 6-11, 2010, St. Andrews, Scotland, U

Electron and Phonon Confinement and New Surface Phonon Modes in CdSe-CdS Core-Shell Nanocrystals

Optical and vibrational properties of bare and CdS shelled CdSe nanocrystalline particles are investigated. To confirm the formation of such nanocrystals in our samples we estimate their average particle sizes and size distributions using TEM measurements. From the line profile analysis of the images the core-shell structure in the particles has been confirmed. The blue shift in optical absorption spectra, analyzed using theoretical estimates based on the effective bond order model, establishes the electron confinement in the nanoparticles. Unique characteristics of the nanocrystals (which are absent in the corresponding bulk material), such as confinement of optical phonons and the appearance of surface phonons, are then discussed. Making use of the dielectric response function model we are able to match the experimental and theoretical values of the frequencies of the surface phonons. We believe that our studies using optical probes provide further evidence on the existence of core-shell structures in CdSe-CdS type materials.Comment: 19 pages 8 figure

Temperature dependence of trapped magnetic field in MgB2 bulk superconductor

Based on DC magnetization measurements, the temperature dependencies of the trapped magnetic field have been calculated for two MgB2 samples prepared by two different techniques: the high-pressure sintering and the hot pressing. Experimentally measured trapped field values for the first sample coincide remarkably well with calculated ones in the whole temperature range. This proves, from one side, the validity of the introduced calculation approach, and demonstrates, from another side, the great prospects of the hot pressing technology for large scale superconducting applications of the MgB2.Comment: 3 pages, 3 figures, submitted to AP

Suppression of the ferromagnetic state in LaCoO3 films by rhombohedral distortion

Epitaxially strained LaCoO3 (LCO) thin films were grown with different film thickness, t, on (001) oriented (LaAlO3)0.3(SrAl0.5Ta0.5O3)0.7 (LSAT) substrates. After initial pseudomorphic growth the films start to relieve their strain partly by the formation of periodic nano-twins with twin planes predominantly along the direction. Nano-twinning occurs already at the initial stage of growth, albeit in a more moderate way. Pseudomorphic grains, on the other hand, still grow up to a thickness of at least several tenths of nanometers. The twinning is attributed to the symmetry lowering of the epitaxially strained pseudo-tetragonal structure towards the relaxed rhombohedral structure of bulk LCO. However, the unit-cell volume of the pseudo-tetragonal structure is found to be nearly constant over a very large range of t. Only films with t > 130 nm show a significant relaxation of the lattice parameters towards values comparable to those of bulk LCO.Comment: 31 pages, 10 figure

Interaction of Spatially Localized LHW with Banana Particles

The paper proposes a novel mechanism of LHW stochastic acceleration of electrons in a tokamak

Topological defects for the free boson CFT

Two different conformal field theories can be joined together along a defect line. We study such defects for the case where the conformal field theories on either side are single free bosons compactified on a circle. We concentrate on topological defects for which the left- and right-moving Virasoro algebras are separately preserved, but not necessarily any additional symmetries. For the case where both radii are rational multiples of the self-dual radius we classify these topological defects. We also show that the isomorphism between two T-dual free boson conformal field theories can be described by the action of a topological defect, and hence that T-duality can be understood as a special type of order-disorder duality.Comment: 43 pages, 4 figure

A super-analogue of Kontsevich's theorem on graph homology

In this paper we will prove a super-analogue of a well-known result by Kontsevich which states that the homology of a certain complex which is generated by isomorphism classes of oriented graphs can be calculated as the Lie algebra homology of an infinite-dimensional Lie algebra of symplectic vector fields.Comment: 15 page

The superconducting gaps in FeSe studied by soft point-contact Andreev reflection spectroscopy

FeSe single crystals have been studied by soft point-contact Andreev-reflection spectroscopy. Superconducting gap features in the differential resistance dV/dI(V) of point contacts such as a characteristic Andreev-reflection double-minimum structure have been measured versus temperature and magnetic field. Analyzing dV/dI within the extended two-gap Blonder-Tinkham-Klapwijk model allows to extract both the temperature and magnetic field dependence of the superconducting gaps. The temperature dependence of both gaps is close to the standard BCS behavior. Remarkably, the magnitude of the double-minimum structure gradually vanishes in magnetic field, while the minima position only slightly shifts with field indicating a weak decrease of the superconducting gaps. Analyzing the dV/dI(V) spectra for 25 point contacts results in the averaged gap values = 1.8+/-0.4meV and =1.0+/-0.2 meV and reduced values 2/kTc=4.2+/-0.9 and 2/kTc=2.3+/-0.5 for the large (L) and small (S) gap, respectively. Additionally, the small gap contribution was found to be within tens of percent decreasing with both temperature and magnetic field. No signatures in the dV/dI spectra were observed testifying a gapless superconductivity or presence of even smaller gaps.Comment: 8 pages, 4 figs., 3 tables. Shortened version without fig.4 and Table 3 is accepted for publication in Phys. Rev.