The spin 1/2 Calogero-Gaudin System and its q-Deformation

The spin 1/2 Calogero-Gaudin system and its q-deformation are exactly solved: a complete set of commuting observables is diagonalized, and the corresponding eigenvectors and eigenvalues are explicitly calculated. The method of solution is purely algebraic and relies on the co-algebra simmetry of the model.Comment: 15 page

Agricultural management and plant selection interactively affect rhizosphere microbial community structure and nitrogen cycling.

BACKGROUND:Rhizosphere microbial communities are key regulators of plant performance, yet few studies have assessed the impact of different management approaches on the rhizosphere microbiomes of major crops. Rhizosphere microbial communities are shaped by interactions between agricultural management and host selection processes, but studies often consider these factors individually rather than in combination. We tested the impacts of management (M) and rhizosphere effects (R) on microbial community structure and co-occurrence networks of maize roots collected from long-term conventionally and organically managed maize-tomato agroecosystems. We also explored the interaction between these factors (M × R) and how it impacts rhizosphere microbial diversity and composition, differential abundance, indicator taxa, co-occurrence network structure, and microbial nitrogen-cycling processes. RESULTS:Host selection processes moderate the influence of agricultural management on rhizosphere microbial communities, although bacteria and fungi respond differently to plant selection and agricultural management. We found that plants recruit management-system-specific taxa and shift N-cycling pathways in the rhizosphere, distinguishing this soil compartment from bulk soil. Rhizosphere microbiomes from conventional and organic systems were more similar in diversity and network structure than communities from their respective bulk soils, and community composition was affected by both M and R effects. In contrast, fungal community composition was affected only by management, and network structure only by plant selection. Quantification of six nitrogen-cycling genes (nifH, amoA [bacterial and archaeal], nirK, nrfA, and nosZ) revealed that only nosZ abundance was affected by management and was higher in the organic system. CONCLUSIONS:Plant selection interacts with conventional and organic management practices to shape rhizosphere microbial community composition, co-occurrence patterns, and at least one nitrogen-cycling process. Reframing research priorities to better understand adaptive plant-microbe feedbacks and include roots as a significant moderating influence of management outcomes could help guide plant-oriented strategies to improve productivity and agroecosystem sustainability

Hunting for open clusters in \textit{Gaia} DR2: the Galactic anticentre

The Gaia Data Release 2 (DR2) provided an unprecedented volume of precise astrometric and excellent photometric data. In terms of data mining the Gaia catalogue, machine learning methods have shown to be a powerful tool, for instance in the search for unknown stellar structures. Particularly, supervised and unsupervised learning methods combined together significantly improves the detection rate of open clusters. We systematically scan Gaia DR2 in a region covering the Galactic anticentre and the Perseus arm $(120 \leq l \leq 205$ and $-10 \leq b \leq 10)$, with the goal of finding any open clusters that may exist in this region, and fine tuning a previously proposed methodology successfully applied to TGAS data, adapting it to different density regions. Our methodology uses an unsupervised, density-based, clustering algorithm, DBSCAN, that identifies overdensities in the five-dimensional astrometric parameter space $(l,b,\varpi,\mu_{\alpha^*},\mu_{\delta})$ that may correspond to physical clusters. The overdensities are separated into physical clusters (open clusters) or random statistical clusters using an artificial neural network to recognise the isochrone pattern that open clusters show in a colour magnitude diagram. The method is able to recover more than 75% of the open clusters confirmed in the search area. Moreover, we detected 53 open clusters unknown previous to Gaia DR2, which represents an increase of more than 22% with respect to the already catalogued clusters in this region. We find that the census of nearby open clusters is not complete. Different machine learning methodologies for a blind search of open clusters are complementary to each other; no single method is able to detect 100% of the existing groups. Our methodology has shown to be a reliable tool for the automatic detection of open clusters, designed to be applied to the full Gaia DR2 catalogue.Comment: 8 pages, accepted by Astronomy and Astrophysics (A&A) the 14th May, 2019. Tables 1 and 2 available at the CD

Current induced domain wall dynamics in the presence of spin orbit torques

Current induced domain wall (DW) motion in perpendicularly magnetized nanostripes in the presence of spin orbit torques is studied. We show using micromagnetic simulations that the direction of the current induced DW motion and the associated DW velocity depend on the relative values of the field like torque (FLT) and the Slonczewski like torques (SLT). The results are well explained by a collective coordinate model which is used to draw a phase diagram of the DW dynamics as a function of the FLT and the SLT. We show that a large increase in the DW velocity can be reached by a proper tuning of both torques.Comment: 9 pages, 3 figure

Abundances and kinematics for ten anticentre open clusters

Open clusters are distributed all across the disk and are convenient tracers of its properties. In particular, outer disk clusters bear a key role for the investigation of the chemical evolution of the Galactic disk. The goal of this study is to derive homogeneous elemental abundances for a sample of ten outer disk OCs, and investigate possible links with disk structures such as the Galactic Anticenter Stellar Structure. We analyse high-resolution spectra of red giants, obtained from the HIRES@Keck and UVES@VLT archives. We derive elemental abundances and stellar atmosphere parameters by means of the classical equivalent width method. We also performed orbit integrations using proper motions. The Fe abundances we derive trace a shallow negative radial metallicity gradient of slope -0.027+/-0.007 dex.kpc-1 in the outer 12 kpc of the disk. The [alpha/Fe] gradient appears flat, with a slope of 0.006+/-0.007 dex.kpc-1 . The two outermost clusters (Be 29 and Sau 1) appear to follow elliptical orbits. Be 20 also exhibits a peculiar orbit with a large excursion above the plane. The irregular orbits of the three most metal-poor clusters (of which two are located at the edge of the Galactic disk), if confirmed by more robust astrometric measurements such as those of the Gaia mission, are compatible with an inside-out formation scenario for the Milky Way, in which extragalactic material is accreted onto the outer disk. We cannot determine if Be 20, Be 29,and Sau 1 are of extragalactic origin, as they may be old genuine Galactic clusters whose orbits were perturbed by accretion events or minor mergers in the past 5 Gyr, or they may be representants of the thick disk population. The nature of these objects is intriguing and deserves further investigations in the near future.Comment: 17 pages, 9 figures; accepted for publication in A&

A ring in a shell: the large-scale 6D structure of the Vela OB2 complex

The Vela OB2 association is a group of 10 Myr stars exhibiting a complex spatial and kinematic substructure. The all-sky Gaia DR2 catalogue contains proper motions, parallaxes (a proxy for distance) and photometry that allow us to separate the various components of Vela OB2. We characterise the distribution of the Vela OB2 stars on a large spatial scale, and study its internal kinematics and dynamic history. We make use of Gaia DR2 astrometry and published Gaia-ESO Survey data. We apply an unsupervised classification algorithm to determine groups of stars with common proper motions and parallaxes. We find that the association is made up of a number of small groups, with a total current mass over 2330 Msun. The three-dimensional distribution of these young stars trace the edge of the gas and dust structure known as the IRAS Vela Shell across 180 pc and shows clear signs of expansion. We propose a common history for Vela OB2 and the IRAS Vela Shell. The event that caused the expansion of the shell happened before the Vela OB2 stars formed, imprinted the expansion in the gas the stars formed from, and most likely triggered star formation.Comment: Accepted by A&A (02 November 2018), 13 pages, 9+2 figure

sl_2 Gaudin model with Jordanian twist

sl_2 Gaudin model with Jordanian twist is studied. This system can be obtained as the semiclassical limit of the XXX spin chain deformed by the Jordanian twist. The appropriate creation operators that yield the Bethe states of the Gaudin model and consequently its spectrum are defined. Their commutation relations with the generators of the corresponding loop algebra as well as with the generating function of integrals of motion are given. The inner products and norms of Bethe states and the relation to the solutions of the Knizhnik-Zamolodchikov equations are discussed.Comment: 22 pages; corrected typo

Correlation functions of the one-dimensional attractive Bose gas

The zero-temperature correlation functions of the one-dimensional attractive Bose gas with delta-function interaction are calculated analytically for any value of the interaction parameter and number of particles, directly from the integrability of the model. We point out a number of interesting features, including zero recoil energy for large number of particles, analogous to a M\"ossbauer effect.Comment: 4 pages, 2 figure

On the exactly solvable pairing models for bosons

We propose the new exactly solvable model for bosons corresponding to the attractive pairing interaction. Using the electrostatic analogy, the solution of this model in thermodynamic limit is found. The transition from the superfluid phase with the Bose condensate and the Bogoliubov - type spectrum of excitations in the weak coupling regime to the incompressible phase with the gap in the excitation spectrum in the strong coupling regime is observed.Comment: 19 page

Local density approximation for a perturbative equation of state

The knowledge of a series expansion of the equation of state provides a deep insight into the physical nature of a quantum system. Starting from a generic ``perturbative'' equation of state of a homogeneous ultracold gas we make predictions for the properties of the gas in the presence of harmonic confinement. The local density approximation is used to obtain the chemical potential, total and release energies, Thomas-Fermi size and density profile of a trapped system in three-, two-, and one- dimensional geometries. The frequencies of the lowest breathing modes are calculated using scaling and sum-rule approaches and could be used in an experiment as a high precision tool for obtaining the expansion terms of the equation of state. The derived formalism is applied to dilute Bose and Fermi gases in different dimensions and to integrable one-dimensional models. Physical meaning of expansion terms in a number of systems is discussed.Comment: 3 Figure