Correlations and Pairing Between Zeros and Critical Points of Gaussian Random Polynomials

We study the asymptotics of correlations and nearest neighbor spacings between zeros and holomorphic critical points of $p_N$, a degree N Hermitian Gaussian random polynomial in the sense of Shiffman and Zeldtich, as N goes to infinity. By holomorphic critical point we mean a solution to the equation $\frac{d}{dz}p_N(z)=0.$ Our principal result is an explicit asymptotic formula for the local scaling limit of \E{Z_{p_N}\wedge C_{p_N}}, the expected joint intensity of zeros and critical points, around any point on the Riemann sphere. Here $Z_{p_N}$ and $C_{p_N}$ are the currents of integration (i.e. counting measures) over the zeros and critical points of $p_N$, respectively. We prove that correlations between zeros and critical points are short range, decaying like e^{-N\abs{z-w}^2}. With \abs{z-w} on the order of $N^{-1/2},$ however, \E{Z_{p_N}\wedge C_{p_N}}(z,w) is sharply peaked near $z=w,$ causing zeros and critical points to appear in rigid pairs. We compute tight bounds on the expected distance and angular dependence between a critical point and its paired zero.Comment: 35 pages, 3 figures. Some typos corrected and Introduction revise

Asymptotic analysis of an elastic rod with rounded ends

We derive a one-dimensional model for an elastic shuttle, that is, a thin rod with rounded ends and small fixed terminals, by means of an asymptotic procedure of dimension reduction. In the model, deformation of the shuttle is described by a system of ordinary differential equations with variable degenerating coefficients, and the number of the required boundary conditions at the end points of the one-dimensional image of the rod depends on the roundness exponent m is an element of(0,1). Error estimates are obtained in the case m is an element of(0,1/4) by using an anisotropic weighted Korn inequality, which was derived in an earlier paper by the authors. We also briefly discuss boundary layer effects, which can be neglected in the case m is an element of(0,1/4) but play a crucial role in the formulation of the limit problem for m >= 1/4.Peer reviewe

Quantum Phase Transition in a Resonant Level Coupled to Interacting Leads

An interacting one-dimensional electron system, the Luttinger liquid, is distinct from the "conventional" Fermi liquids formed by interacting electrons in two and three dimensions. Some of its most spectacular properties are revealed in the process of electron tunneling: as a function of the applied bias or temperature the tunneling current demonstrates a non-trivial power-law suppression. Here, we create a system which emulates tunneling in a Luttinger liquid, by controlling the interaction of the tunneling electron with its environment. We further replace a single tunneling barrier with a double-barrier resonant level structure and investigate resonant tunneling between Luttinger liquids. For the first time, we observe perfect transparency of the resonant level embedded in the interacting environment, while the width of the resonance tends to zero. We argue that this unique behavior results from many-body physics of interacting electrons and signals the presence of a quantum phase transition (QPT). In our samples many parameters, including the interaction strength, can be precisely controlled; thus, we have created an attractive model system for studying quantum critical phenomena in general. Our work therefore has broadly reaching implications for understanding QPTs in more complex systems, such as cold atoms and strongly correlated bulk materials.Comment: 11 pages total (main text + supplementary

The GALNTL6 Gene rs558129 Polymorphism Is Associated With Power Performance

Diaz, J, alvarez Herms, J, Castaneda, A, Larruskain, J, Ramirez de la Piscina, X, Borisov, OV, Semenova, EA, Kostryukova, ES, Kulemin, NA, Andryushchenko, ON, Larin, AK, Andryushchenko, LB, Generozov, EV, Ahmetov, II, and Odriozola, A. The GALNTL6 gene rs558129 polymorphism is associated with power performance. J Strength Cond Res 34(11): 3031-3036, 2020-The largest genome-wide association study to date in sports genomics showed that endurance athletes were 1.23 times more likely to possess the C allele of the single nucleotide polymorphism rs558129 of N-acetylgalactosaminyltransferase-like 6 gene (GALNTL6), compared with controls. Nevertheless, no further study has investigated GALNTL6 gene in relation to physical performance. Considering that previous research has shown that the same polymorphism can be associated with both endurance and power phenotypes (ACTN3, ACE, and PPARA), we investigated the association between GALNTL6 rs558129 polymorphism and power performance. According to this objective we conducted 2 global studies regarding 2 different communities of athletes in Spain and Russia. The first study involved 85 Caucasian physically active men from the north of Spain to perform a Wingate anaerobic test (WAnT). In the second study we compared allelic frequencies between 173 Russian power athletes (49 strength and 124 speed-strength athletes), 169 endurance athletes, and 201 controls. We found that physically active men with the T allele of GALNTL6 rs558129 had 5.03-6.97% higher power values compared with those with the CC genotype (p < 0.05). Consistent with these findings, we have shown that the T allele was over-represented in power athletes (37.0%) compared with endurance athletes (29.3%; OR = 1.4, p = 0.032) and controls (28.6%; OR = 1.5, p = 0.015). Furthermore, the highest frequency of the T allele was observed in strength athletes (43.9%; odds ratio [OR] = 1.9, p = 0.0067 compared with endurance athletes; OR = 2.0, p = 0.0036 compared with controls). In conclusion, our data suggest that the GALNTL6 rs558129 T allele can be favorable for anaerobic performance and strength athletes. In addition, we propose a new possible functional role of GALNTL6 rs558129, gut microbiome regarding short-chain fatty acid regulation and their anti-inflammatory and resynthesis functions. Nevertheless, further studies are required to understand the mechanisms involved.The authors would like to thank all the staff and athletes who participated in the study and the ZuOK Center where sports testing were performed. J. Larruskain was supported by a PhD Studentship from the Vice-Chancellorship for Basque of the University of the Basque Country UPV/EHU (EuskararenarlokoErrektoreordetza). J. Diaz and J. Alvarez Herms have contributed equally to this manuscrip

Shot noise in mesoscopic systems

This is a review of shot noise, the time-dependent fluctuations in the electrical current due to the discreteness of the electron charge, in small conductors. The shot-noise power can be smaller than that of a Poisson process as a result of correlations in the electron transmission imposed by the Pauli principle. This suppression takes on simple universal values in a symmetric double-barrier junction (suppression factor 1/2), a disordered metal (factor 1/3), and a chaotic cavity (factor 1/4). Loss of phase coherence has no effect on this shot-noise suppression, while thermalization of the electrons due to electron-electron scattering increases the shot noise slightly. Sub-Poissonian shot noise has been observed experimentally. So far unobserved phenomena involve the interplay of shot noise with the Aharonov-Bohm effect, Andreev reflection, and the fractional quantum Hall effect.Comment: 37 pages, Latex, 10 figures (eps). To be published in "Mesoscopic Electron Transport," edited by L. P. Kouwenhoven, G. Schoen, and L. L. Sohn, NATO ASI Series E (Kluwer Academic Publishing, Dordrecht

Photoluminescence and cathodoluminescence of Eu:La2O3 nanoparticles synthesized by several methods

Abstract : Europium-doped La2O3 nanocrystalline powders with sizes ranging from 4 nm to 300 nm have been obtained by the modified Pechini, hydrothermal with conventional furnace, hydrothermal with microwave furnace, and precipitation with ultrasonic bath methods. X-ray diffraction techniques were used to study the evolution of the prepared gels towards the desired crystalline phase. We determined the size and the morphology of the nanoparticles by electronic microscopy. Finally, we studied and analyzed the luminescence properties of the trivalent europium in the hexagonal La2O3 nanocrystals by photoluminescence and cathodoluminescence

An anti-aging polymer electrolyte for flexible rechargeable zinc-ion batteries

Polymer electrolytes have been extensively applied in zinc-ion batteries, especially those based on hydrogels; however, the densification of the hydrogel electrolytes during cycling affects the durability, resulting in capacity attenuation. It is revealed in this work that the surface electrical resistance of hydrogels is particularly affected by the aging effect. Hence, an adhesive bonding solid polymer electrolyte (ABSPE) for zinc-ion batteries was developed exhibiting significantly enhanced anti-aging properties, where the surface resistance remains constant for over 200 hours, twice that of conventional hydrogel electrolytes. For the hydrogel electrolyte, the surface resistance only remains constant for less than 100 hours which is half of the time achieved by the ABSPE. The ionic conductivity increases with plasticizer loading, reaching 3.77 × 10−4 S cm−1. The kinetic mechanism probed in this work revealed a diffusion-controlled mechanism for Zn/ABSPE/β-MnO2 instead of a capacitive dominated process in the hydrogel electrolyte. In addition, a flexible device was fabricated using a carbon fibre-reinforced polymer composite; this device showed superior power supply performance even under twisting, cutting and bending conditions

Viruses: incredible nanomachines. New advances with filamentous phages

During recent decades, bacteriophages have been at the cutting edge of new developments in molecular biology, biophysics, and, more recently, bionanotechnology. In particular filamentous viruses, for example bacteriophage M13, have a virion architecture that enables precision building of ordered and defect-free two and three-dimensional structures on a nanometre scale. This could not have been possible without detailed knowledge of coat protein structure and dynamics during the virus reproduction cycle. The results of the spectroscopic studies conducted in our group compellingly demonstrate a critical role of membrane embedment of the protein both during infectious entry of the virus into the host cell and during assembly of the new virion in the host membrane. The protein is effectively embedded in the membrane by a strong C-terminal interfacial anchor, which together with a simple tilt mechanism and a subtle structural adjustment of the extreme end of its N terminus provides favourable thermodynamical association of the protein in the lipid bilayer. This basic physicochemical rule cannot be violated and any new bionanotechnology that will emerge from bacteriophage M13 should take this into account

Supercurrent reversal in quantum dots

When two superconductors become electrically connected by a weak link a zero-resistance supercurrent can flow. This supercurrent is carried by Cooper pairs of electrons with a combined charge of twice the elementary charge, e. The 2e charge quantum is clearly visible in the height of Shapiro steps in Josephson junctions under microwave irradiation and in the magnetic flux periodicity of h/2e in superconducting quantum interference devices. Several different materials have been used to weakly couple superconductors, such as tunnel barriers, normal metals, or semiconductors. Here, we study supercurrents through a quantum dot created in a semiconductor nanowire by local electrostatic gating. Due to strong Coulomb interaction, electrons only tunnel one-by-one through the discrete energy levels of the quantum dot. This nevertheless can yield a supercurrent when subsequent tunnel events are coherent. These quantum coherent tunnelling processes can result in either a positive or a negative supercurrent, i.e. in a normal or a pi-junction, respectively. We demonstrate that the supercurrent reverses sign by adding a single electron spin to the quantum dot. When excited states of the quantum dot are involved in transport, the supercurrent sign also depends on the character of the orbital wavefunctions

Effective Rheology of Bubbles Moving in a Capillary Tube

We calculate the average volumetric flux versus pressure drop of bubbles moving in a single capillary tube with varying diameter, finding a square-root relation from mapping the flow equations onto that of a driven overdamped pendulum. The calculation is based on a derivation of the equation of motion of a bubble train from considering the capillary forces and the entropy production associated with the viscous flow. We also calculate the configurational probability of the positions of the bubbles.Comment: 4 pages, 1 figur