Ewens measures on compact groups and hypergeometric kernels

On unitary compact groups the decomposition of a generic element into product of reflections induces a decomposition of the characteristic polynomial into a product of factors. When the group is equipped with the Haar probability measure, these factors become independent random variables with explicit distributions. Beyond the known results on the orthogonal and unitary groups (O(n) and U(n)), we treat the symplectic case. In U(n), this induces a family of probability changes analogous to the biassing in the Ewens sampling formula known for the symmetric group. Then we study the spectral properties of these measures, connected to the pure Fisher-Hartvig symbol on the unit circle. The associated orthogonal polynomials give rise, as $n$ tends to infinity to a limit kernel at the singularity.Comment: New version of the previous paper "Hua-Pickrell measures on general compact groups". The article has been completely re-written (the presentation has changed and some proofs have been simplified). New references added

Phylogeny of the Infraorder Pentatomomorpha Based on Fossil and Extant Morphology, with Description of a New Fossil Family from China

<div><h3>Background</h3><p>An extinct new family of Pentatomomorpha, Venicoridae Yao, Ren & Cai <b>fam. nov.</b>, with 2 new genera and 2 new species (<em>Venicoris solaris</em> Yao, Ren & Rider <b>gen. & sp. nov.</b> and <em>Clavaticoris zhengi</em> Yao, Ren & Cai <b>gen. & sp. nov.</b>) are described from the Early Cretaceous Yixian Formation in Northeast China.</p> <h3>Methodology/Principal Findings</h3><p>A cladistic analysis based on a combination of fossil and extant morphological characters clarified the phylogenetic status of the new family and has allowed the reconstruction of intersuperfamily and interfamily relationships within the Infraorder Pentatomomorpha. The fossil record and diversity of Pentatomomorpha during the Mesozoic is discussed.</p> <h3>Conclusions/Significance</h3><p>Pentatomomorpha is a monophyletic group; Aradoidea and the Trichophora are sister groups; these fossils belong to new family, treated as the sister group of remainder of Trichophora; Pentatomoidea is a monophyletic group; Piesmatidae should be separated as a superfamily, Piesmatoidea. Origin time of Pentatomomorpha should be tracked back to the Middle or Early Triassic.</p> </div

Effect of water on fracture of rocks under diametral compression

Abstract The researchers study the effect of water on the strength of small-size specimens made of metamorphic rocks (carbonaceous quartzite, serpentine) and an analog of sedimentary rocks (sand-and-cement mixture, or artificial sandstone) exposed to diametral compression. It is found that the specimens exhibit the same brittle deformation behavior after water storage for a day. All specimens show reduced strength while quartzite and serpentine feature a decrease in deformability down to failure. Microscopic fracturing is viscoelastic and independent of water. It is suggested that the influence of water on the deformation behavior of the specimens can be explained by the Rebinder effect.</jats:p

Allowed and forbidden transitions in artificial hydrogen and helium atoms

The strength of radiative transitions in atoms is governed by selection rules. Spectroscopic studies of allowed transitions in hydrogen and helium provided crucial evidence for the Bohr's model of an atom. Forbidden transitions, which are actually allowed by higher-order processes or other mechanisms, indicate how well the quantum numbers describe the system. We apply these tests to the quantum states in semiconductor quantum dots (QDs), which are regarded as artificial atoms. Electrons in a QD occupy quantized states in the same manner as electrons in real atoms. However, unlike real atoms, the confinement potential of the QD is anisotropic, and the electrons can easily couple with phonons of the material. Understanding the selection rules for such QDs is an important issue for the manipulation of quantum states. Here we investigate allowed and forbidden transitions for phonon emission in one- and two-electron QDs (artificial hydrogen and helium atoms) by electrical pump-and-probe experiments, and find that the total spin is an excellent quantum number in artificial atoms. This is attractive for potential applications to spin based information storage.Comment: slightly longer version of Nature 419, 278 (2002

Selection before backcross during exotic germplasm introgression

Introgression of genes from exotic germplasm into breeding populations can broaden the genetic base of crop improvement. Only a very small percentage of genetic variability has been used in crop breeding programs. Traditionally, F1 plants are used to backcross to the adapted lines or populations. An alternative approach is to backcross the F2 individuals selected for agronomic acceptability. Our objective was to determine whether selection before backcross would lead to more progenies with both high yield and acceptable levels of agronomic performance than direct backcross without selection. To test the feasibility of the proposed approach, we conducted parallel experiments in which two exotic sorghum accessions were crossed to two adapted sorghum parents and further backcrossing was conducted with either F1 or selected F2 plants. Fifty random S1 families were evaluated in three test environments. Although selection before backcross resulted in a higher frequency of families with maturity equal to or earlier than those of the adapted parents, no consistent changes in grain yield and plant height were observed between populations with and without selection. Similar results were found with either an inbred or a population as the recurrent parents. Given these findings and the extra generation required, we do not recommend selection before backcross in the process of introgression of exotic germplasm

Coherent Structures at the Ocean Surface in Convectively Unstable Conditions

The turbulent boundary layer at the ocean surface has some dynamical similarities to the atmospheric boundary layer. The atmospheric turbulent boundary layer may exhibit not only random fluctuations but also spatially coherent, organized motion. Thorpe conjectured that such organized motion should also be found in the upper ocean boundary layer in convectively unstable conditions. Here I report on observations made in the tropical Atlantic Ocean which confirm this view. Horizontal temperature profiles obtained at a depth of 2m at night revealed ramp-like structures. Vertical velocity profiles in the upper few metres of the ocean was determined using a free-rising profiler, and exhibited abrupt changes corresponding to sudden changes in temperature. These features are known to be characteristic of spatially coherent, organized motions in turbulent boundary layers

Felix Alexandrovich Berezin and his work

This is a survey of Berezin's work focused on three topics: representation theory, general concept of quantization, and supermathematics.Comment: LaTeX, 27 page

Demonstration of conditional gate operation using superconducting charge qubits

Since the first demonstration of coherent control of a quantum state of a superconducting charge qubit a variety of Josephson-junction-based qubits have been implemented with remarkable progress in coherence time and read-out schemes. Although the current level of this solid-state device is still not as advanced as that of the most advanced microscopic-system-based qubits, these developments, together with the potential scalability, have renewed its position as a strong candidate as a building block for the quantum computer. Recently, coherent oscillation and microwave spectroscopy in capacitively-coupled superconducting qubits have been reported. The next challenging step toward quantum computation is a realization of logic gates. Here we demonstrate a conditional gate operation using a pair of coupled superconducting charge qubits. Using a pulse technique, we prepare different input states and show that they can be transformed by controlled-NOT (C-NOT) gate operation in the amplitude of the states. Although the phase evolution during the gate operation is still to be clarified, the present results are a major step toward the realization of a universal solid-state quantum gate

PSR J1926-0652: A Pulsar with Interesting Emission Properties Discovered at FAST

We describe PSR J1926-0652, a pulsar recently discovered with the Five-hundred-meter Aperture Spherical radio Telescope (FAST). Using sensitive single-pulse detections from FAST and long-term timing observations from the Parkes 64-m radio telescope, we probed phenomena on both long and short time scales. The FAST observations covered a wide frequency range from 270 to 800 MHz, enabling individual pulses to be studied in detail. The pulsar exhibits at least four profile components, short-term nulling lasting from 4 to 450 pulses, complex subpulse drifting behaviours and intermittency on scales of tens of minutes. While the average band spacing P3 is relatively constant across different bursts and components, significant variations in the separation of adjacent bands are seen, especially near the beginning and end of a burst. Band shapes and slopes are quite variable, especially for the trailing components and for the shorter bursts. We show that for each burst the last detectable pulse prior to emission ceasing has different properties compared to other pulses. These complexities pose challenges for the classic carousel-type models.Comment: 13pages with 12 figure

Higher Order Quantum Superintegrability: a new "Painlev\'e conjecture"

We review recent results on superintegrable quantum systems in a two-dimensional Euclidean space with the following properties. They are integrable because they allow the separation of variables in Cartesian coordinates and hence allow a specific integral of motion that is a second order polynomial in the momenta. Moreover, they are superintegrable because they allow an additional integral of order $N>2$. Two types of such superintegrable potentials exist. The first type consists of "standard potentials" that satisfy linear differential equations. The second type consists of "exotic potentials" that satisfy nonlinear equations. For $N= 3$, 4 and 5 these equations have the Painlev\'e property. We conjecture that this is true for all $N\geq3$. The two integrals X and Y commute with the Hamiltonian, but not with each other. Together they generate a polynomial algebra (for any $N$) of integrals of motion. We show how this algebra can be used to calculate the energy spectrum and the wave functions.Comment: 23 pages, submitted as a contribution to the monographic volume "Integrability, Supersymmetry and Coherent States", a volume in honour of Professor V\'eronique Hussin. arXiv admin note: text overlap with arXiv:1703.0975