Elektroniczne maszyny liczące. Część II. Przegląd Zagadnień Łączności, 1965, nr 4 (43)

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Magnetic and quadrupolar order in a one-dimensional ferromagnet with cubic crystal-field anisotropy

The zero temperature phase diagram of a one-dimensional S=2 Heisenberg ferromagnet with single-ion cubic anisotropy is studied numerically using the density-matrix renormalization group method. Evidence is found that although the model does not involve quadrupolar couplings, there is a purely quadrupolar phase for large values of the anisotropy. The phase transition between the magnetic and quadrupolar phases is continuous and it seems to be characterized by Ising critical exponents.Comment: 11 pages, 7 figures, REVTeX, accepted in Phys. Rev. B (scheduled on June 99

Density-Matrix Spectra of Solvable Fermionic Systems

We consider non-interacting fermions on a lattice and give a general result for the reduced density matrices corresponding to parts of the system. This allows to calculate their spectra, which are essential in the DMRG method, by diagonalizing small matrices. We discuss these spectra and their typical features for various fermionic quantum chains and for the two-dimensional tight-binding model.Comment: 12 pages and 9 figure

The asymmetric simple exclusion process: an integrable model for non-equilibrium statistical mechanics

The asymmetric simple exclusion process (ASEP) plays the role of a paradigm in non-equilibrium statistical mechanics. We review exact results for the ASEP obtained by Bethe ansatz and put emphasis on the algebraic properties of this model. The Bethe equations for the eigenvalues of the Markov matrix of the ASEP are derived from the algebraic Bethe ansatz. Using these equations we explain how to calculate the spectral gap of the model and how global spectral properties such as the existence of multiplets can be predicted. An extension of the Bethe ansatz leads to an analytic expression for the large deviation function of the current in the ASEP that satisfies the Gallavotti-Cohen relation. Finally, we describe some variants of the ASEP that are also solvable by Bethe ansatz. Keywords: ASEP, integrable models, Bethe ansatz, large deviations.Comment: 24 pages, 5 figures, published in the "special issue on recent advances in low-dimensional quantum field theories", P. Dorey, G. Dunne and J. Feinberg editor

Thermal properties of large main-belt asteroids observed by Herschel PACS

Non-resolved thermal infrared observations enable studies of thermal and physical properties of asteroid surfaces provided the shape and rotational properties of the target are well determined via thermo-physical models. We used calibration-programme Herschel PACS data (70, 100, 160 $\mu$m) and state-of-the-art shape models derived from adaptive-optics observations and/or optical light curves to constrain for the first time the thermal inertia of twelve large main-belt asteroids. We also modelled previously well-characterised targets such as (1) Ceres or (4) Vesta as they constitute important benchmarks. Using the scale as a free parameter, most targets required a re-scaling $\sim$5\% consistent with what would be expected given the absolute calibration error bars. This constitutes a good cross-validation of the scaled shape models, although some targets required larger re-scaling to reproduce the IR data. We obtained low thermal inertias typical of large main belt asteroids studied before, which continues to give support to the notion that these surfaces are covered by fine-grained insulating regolith. Although the wavelengths at which PACS observed are longwards of the emission peak for main-belt asteroids, they proved to be extremely valuable to constrain size and thermal inertia and not too sensitive to surface roughness. Finally, we also propose a graphical approach to help examine how different values of the exponent used for scaling the thermal inertia as a function of heliocentric distance (i.e. temperature) affect our interpretation of the results.Comment: Accepted for publication in Astronomy & Astrophysics (preprint version

(704) Interamnia: a transitional object between a dwarf planet and a typical irregular-shaped minor body

Context. With an estimated diameter in the 320–350 km range, (704) Interamnia is the fifth largest main belt asteroid and one of the few bodies that fills the gap in size between the four largest bodies with D > 400 km (Ceres, Vesta, Pallas and Hygiea) and the numerous smaller bodies with diameter ≤200 km. However, despite its large size, little is known about the shape and spin state of Interamnia and, therefore, about its bulk composition and past collisional evolution. Aims. We aimed to test at what size and mass the shape of a small body departs from a nearly ellipsoidal equilibrium shape (as observed in the case of the four largest asteroids) to an irregular shape as routinely observed in the case of smaller (D ≤ 200 km) bodies. Methods. We observed Interamnia as part of our ESO VLT/SPHERE large program (ID: 199.C-0074) at thirteen different epochs. In addition, several new optical lightcurves were recorded. These data, along with stellar occultation data from the literature, were fed to the All-Data Asteroid Modeling algorithm to reconstruct the 3D-shape model of Interamnia and to determine its spin state. Results. Interamnia’s volume-equivalent diameter of 332 ± 6 km implies a bulk density of ρ = 1.98 ± 0.68 g cm−3, which suggests that Interamnia – like Ceres and Hygiea – contains a high fraction of water ice, consistent with the paucity of apparent craters. Our observations reveal a shape that can be well approximated by an ellipsoid, and that is compatible with a fluid hydrostatic equilibrium at the 2σ level. Conclusions. The rather regular shape of Interamnia implies that the size and mass limit, under which the shapes of minor bodies with a high amount of water ice in the subsurface become irregular, has to be searched among smaller (D ≤ 300 km) less massive (m ≤ 3 × 1019 kg) bodies

A basin-free spherical shape as an outcome of a giant impact on asteroid Hygiea

(10) Hygiea is the fourth largest main belt asteroid and the only known asteroid whose surface composition appears similar to that of the dwarf planet (1) Ceres1,2, suggesting a similar origin for these two objects. Hygiea suffered a giant impact more than 2 Gyr ago3 that is at the origin of one of the largest asteroid families. However, Hygeia has never been observed with sufficiently high resolution to resolve the details of its surface or to constrain its size and shape. Here, we report high-angular-resolution imaging observations of Hygiea with the VLT/SPHERE instrument (~20 mas at 600 nm) that reveal a basin-free nearly spherical shape with a volume-equivalent radius of 217 ± 7 km, implying a density of 1,944 ± 250 kg m−3 to 1σ. In addition, we have determined a new rotation period for Hygiea of ~13.8 h, which is half the currently accepted value. Numerical simulations of the family-forming event show that Hygiea’s spherical shape and family can be explained by a collision with a large projectile (diameter ~75–150 km). By comparing Hygiea’s sphericity with that of other Solar System objects, it appears that Hygiea is nearly as spherical as Ceres, opening up the possibility for this object to be reclassified as a dwarf planet.P.V., A.D. and B.C. were supported by CNRS/INSU/PNP. M.Brož was supported by grant 18-04514J of the Czech Science Foundation. J.H. and J.D. were supported by grant 18-09470S of the Czech Science Foundation and by the Charles University Research Programme no. UNCE/SCI/023. This project has received funding from the European Union’s Horizon 2020 research and innovation programmes under grant agreement nos 730890 and 687378. This material reflects only the authors’ views, and the European Commission is not liable for any use that may be made of the information contained herein. TRAPPIST-North is a project funded by the University of Liège, in collaboration with Cadi Ayyad University of Marrakech (Morocco). TRAPPIST-South is a project funded by the Belgian Fonds (National) de la Recherche Scientifique (F.R.S.-FNRS) under grant FRFC 2.5.594.09.F. E.J. and M.G. are F.R.S.-FNRS Senior Research Associates

The large trans-Neptunian object 2002 TC302 from combined stellar occultation, photometry, and astrometry data

Context. Deriving physical properties of trans-Neptunian objects is important for the understanding of our Solar System. This requires observational efforts and the development of techniques suitable for these studies. Aims. Our aim is to characterize the large trans-Neptunian object (TNO) 2002 TC302. Methods. Stellar occultations offer unique opportunities to determine key physical properties of TNOs. On 28 January 2018, 2002 TC302 occulted a mv ~ 15.3 star with designation 593-005847 in the UCAC4 stellar catalog, corresponding to Gaia source 130957813463146112. Twelve positive occultation chords were obtained from Italy, France, Slovenia, and Switzerland. Also, four negative detections were obtained near the north and south limbs. This represents the best observed stellar occultation by a TNO other than Pluto in terms of the number of chords published thus far. From the 12 chords, an accurate elliptical fit to the instantaneous projection of the body can be obtained that is compatible with the near misses. Results. The resulting ellipse has major and minor axes of 543 ± 18 km and 460 ± 11 km, respectively, with a position angle of 3 ± 1 degrees for the minor axis. This information, combined with rotational light curves obtained with the 1.5 m telescope at Sierra Nevada Observatory and the 1.23 m telescope at Calar Alto observatory, allows us to derive possible three-dimensional shapes and density estimations for the body based on hydrostatic equilibrium assumptions. The effective diameter in equivalent area is around 84 km smaller than the radiometrically derived diameter using thermal data from Herschel and Spitzer Space Telescopes. This might indicate the existence of an unresolved satellite of up to ~300 km in diameter, which is required to account for all the thermal flux, although the occultation and thermal diameters are compatible within their error bars given the considerable uncertainty of the thermal results. The existence of a potential satellite also appears to be consistent with other ground-based data presented here. From the effective occultation diameter combined with absolute magnitude measurements we derive a geometric albedo of 0.147 ± 0.005, which would be somewhat smaller if 2002 TC302 has a satellite. The best occultation light curves do not show any signs of ring features or any signatures of a global atmosphere.Funding from Spanish projects AYA2014-56637-C2-1-P, AYA2017-89637-R, from FEDER, and Proyecto de Excelencia de la Junta de Andalucía 2012-FQM1776 is acknowledged. We would like to acknowledge financial support by the Spanish grant AYA-RTI2018-098657-JI00 “LEO-SBNAF” (MCIU/AEI/FEDER, UE) and the financial support from the State Agency for Research of the Spanish MCIU through the “Center of Excellence Severo Ochoa” award for the Instituto de Astrofísica de Andalucía (SEV- 2017-0709). Part of the research received funding from the European Union’s Horizon 2020 Research and Innovation Programme, under grant agreement no. 687378 and from the ERC programme under Grant Agreement no. 669416 Lucky Star. The following authors acknowledge the respective CNPq grants: FB-R 309578/2017-5; RV-M 304544/2017-5, 401903/2016-8; J.I.B.C. 308150/2016-3; MA 427700/2018-3, 310683/2017-3, 473002/2013-2. This study was financed in part by the Coordenação de Aperfeiaçoamento de Pessoal de Nível Superior - Brasil (CAPES) - Finance Code 001 and the National Institute of Science and Technology of the e-Universe project (INCT do e-Universo, CNPq grant 465376/2014-2). GBR acknowledges CAPES-FAPERJ/PAPDRJ grant E26/203.173/2016, MA FAPERJ grant E-26/111.488/2013 and ARGJr FAPESP grant 2018/11239-8. E.F.-V. acknowledges support from the 2017 Preeminent Postdoctoral Program (P3) at UCF. C.K., R.S., A.F-T., and G.M. have been supported by the K-125015 and GINOP-2.3.2-15-2016-00003 grants of the Hungarian National Research, Development and Innovation Office (NKFIH), Hungary. G.M. was also supported by the Hungarian National Research, Development and Innovation Office (NKFIH) grant PD-128 360. R.K. and T.P. were supported by the VEGA 2/0031/18 grant