We make explicit an argument of Heath-Brown concerning large and small gaps between nontrivial zeroes of the Riemann zeta-function, $zeta(s)$. In particular, we provide the first unconditional results on gaps (large and small) which hold for a positi
ve proportion of zeroes. To do this we prove explicit bounds on the second and fourth power moments of $S(t+h)-S(t)$, where $S(t)$ denotes the argument of $zeta(s)$ on the critical line and $h ll 1 / log T$. We also use these moments to prove explicit results on the density of the nontrivial zeroes of $zeta(s)$ of a given multiplicity.
We use 5,337 spectroscopic $v sin i$ measurements of Kepler dwarfs and subgiants from the APOGEE survey to study stellar rotation trends. We find a detection threshold of 10 km/s, which allows us to explore the spindown of intermediate-mass stars lea
ving the main sequence, merger products, young stars, and tidally-synchronized binaries. We see a clear distinction between blue stragglers and the field turnoff in $alpha$-rich stars, with a sharp rapid rotation cutoff for blue stragglers consistent with the Kraft break. We also find rapid rotation and RV variability in a sample of red straggler stars, considerably cooler than the giant branch, lending credence to the hypothesis that these are active, tidally-synchronized binaries. We see clear evidence for a transition between rapid and slow rotation on the subgiant branch in the domain predicted by modern angular momentum evolution models. We find substantial agreement between the spectroscopic and photometric properties of KIC targets added by Huber et al (2014) based on 2MASS photometry. For the unevolved lower main sequence, we see the same concentration toward rapid rotation in photometric binaries as that observed in rotation period data, but at an enhanced rate. We attribute this difference to unresolved near-equal luminosity spectroscopic binaries with velocity displacements on the order of the APOGEE resolution. Among cool unevolved stars we find an excess rapid rotator fraction of 4% caused by pipeline issues with photometric binaries.
Since the signature of the ITER treaty in 2006, a new research programme targeting the emergence of a new generation of Neutral Beam (NB) system for the future fusion reactor (DEMO Tokamak) has been underway between several laboratories in Europe. Th
e specifications required to operate a NB system on DEMO are very demanding: the system has to provide plasma heating, current drive and plasma control at a very high level of power (up to 150 MW) and energy (1 or 2 MeV), including high performances in term of wall-plug efficiency ($eta$ > 60%), high availability and reliability. To this aim, a novel NB concept based on the photodetachment of the energetic negative ion beam is under study. The keystone of this new concept is the achievement of a photoneutralizer where a high power photon flux (~3 MW) generated within a Fabry Perot cavity will overlap, cross and partially photodetach the intense negative ion beam accelerated at high energy (1 or 2 MeV). The aspect ratio of the beam-line (source, accelerator, etc.) is specifically designed to maximize the overlap of the photon beam with the ion beam. It is shown that such a photoneutralized based NB system would have the capability to provide several tens of MW of D 0 per beam line with a wall-plug efficiency higher than 60%. A feasibility study of the concept has been launched between different laboratories to address the different physics aspects, i.e., negative ion source, plasma modelling, ion accelerator simulation, photoneutralization and high voltage holding under vacuum. The paper describes the present status of the project and the main achievements of the developments in laboratories.
Tens of thousands of rotation periods have been measured in the Kepler fields, including a substantial fraction of rapid rotators. We use Gaia parallaxes to distinguish photometric binaries (PBs) from single stars on the unevolved lower main sequence
, and compare their distribution of rotation properties to those of single stars both with and without APOGEE spectroscopic characterization. We find that 59% of stars with 1.5 day < P < 7 day lie 0.3 mag above the main sequence, compared with 28% of the full rotation sample. The fraction of stars in the same period range is 1.7 $pm$ 0.1% of the total sample analyzed for rotation periods. Both the photometric binary fraction and the fraction of rapid rotators are consistent with a population of non-eclipsing short period binaries inferred from Kepler eclipsing binary data after correcting for inclination. This suggests that the rapid rotators are dominated by tidally-synchronized binaries rather than single-stars obeying traditional angular momentum evolution. We caution against interpreting rapid rotation in the Kepler field as a signature of youth. Following up this new sample of 217 candidate tidally-synchronized binaries will help further understand tidal processes in stars.
We discuss the alternative algebraic structures on the manifold of quantum states arising from alternative Hermitian structures associated with quantum bi-Hamiltonian systems. We also consider the consequences at the level of the Heisenberg picture i
n terms of deformations of the associative product on the space of observables.
The quantum-classical limits for quantum tomograms are studied and compared with the corresponding classical tomograms, using two different definitions for the limit. One is the Planck limit where $hbar to 0$ in all $hbar $-dependent physical observa
bles, and the other is the Ehrenfest limit where $hbar to 0$ while keeping constant the mean value of the energy.The Ehrenfest limit of eigenstate tomograms for a particle in a box and a harmonic oscillatoris shown to agree with the corresponding classical tomograms of phase-space distributions, after a time averaging. The Planck limit of superposition state tomograms of the harmonic oscillator demostrating the decreasing contribution of interferences terms as $hbar to 0$.
We discuss the dynamical quantum systems which turn out to be bi-unitary with respect to the same alternative Hermitian structures in a infinite-dimensional complex Hilbert space. We give a necessary and sufficient condition so that the Hermitian str
uctures are in generic position. Finally the transformations of the bi-unitary group are explicitly obtained.
In complete analogy with the classical situation (which is briefly reviewed) it is possible to define bi-Hamiltonian descriptions for Quantum systems. We also analyze compatible Hermitian structures in full analogy with compatible Poisson structures.
We discuss transformations generated by dynamical quantum systems which are bi-unitary, i.e. unitary with respect to a pair of Hermitian structures on an infinite-dimensional complex Hilbert space. We introduce the notion of Hermitian structures in g
eneric relative position. We provide few necessary and sufficient conditions for two Hermitian structures to be in generic relative position to better illustrate the relevance of this notion. The group of bi-unitary transformations is considered in both the generic and non-generic case. Finally, we generalize the analysis to real Hilbert spaces and extend to infinite dimensions results already available in the framework of finite-dimensional linear bi-Hamiltonian systems.
We report on trapping of fermionic 40K atoms in a red-detuned standing-wave optical trap, loaded from a magneto-optical trap. Typically, 10^6 atoms are loaded at a density of 10^12 cm^-3 and a temperature of 65 microK, and trapped for more than 1 s.
The optical trap appears to be the proper environment for performing collisional measurements on the cold atomic sample. In particular we measure the elastic collisional rate by detecting the rethermalization following an intentional parametric heating of the atomic sample. We also measure the inelastic two-body collisional rates for unpolarized atoms in the ground hyperfine states, through detection of trap losses.
