Generalized isotropic Lipkin-Meshkov-Glick models: ground state entanglement and quantum entropies

We introduce a new class of generalized isotropic Lipkin–Meshkov–Glick models with su(m+1) spin and long-range non-constant interactions, whose non-degenerate ground state is a Dicke state of su(m+1) type. We evaluate in closed form the reduced density matrix of a block of Lspins when the whole system is in its ground state, and study the corresponding von Neumann and Rényi entanglement entropies in the thermodynamic limit. We show that both of these entropies scale as a log L when L tends to infinity, where the coefficient a is equal to (m  −  k)/2 in the ground state phase with k vanishing magnon densities. In particular, our results show that none of these generalized Lipkin–Meshkov–Glick models are critical, since when L-->∞ their Rényi entropy R_q becomes independent of the parameter q. We have also computed the Tsallis entanglement entropy of the ground state of these generalized su(m+1) Lipkin–Meshkov–Glick models, finding that it can be made extensive by an appropriate choice of its parameter only when m-k≥3. Finally, in the su(3) case we construct in detail the phase diagram of the ground state in parameter space, showing that it is determined in a simple way by the weights of the fundamental representation of su(3). This is also true in the su(m+1) case; for instance, we prove that the region for which all the magnon densities are non-vanishing is an (m  +  1)-simplex in R^m whose vertices are the weights of the fundamental representation of su(m+1).

Vapor-liquid equilibria using the Gibbs energy and the common tangent plane criterion

Phase thermodynamics is often perceived as a difficult subject that many students never become fully comfortable with. The Gibbsian geometrical framework can help students to gain a better understanding of phase equilibria. An exercise to interpret the vapor-liquid equilibrium of a binary azeotropic mixture, using the equilibrium condition based on the common tangent plane criterion (the Gibbs stability test), is presented in this paper. From a T-composition phase diagram for the mixture, the temperature is set at different values: above, intermediate to, and below the boiling temperatures of the pure components, to intersect different regions of the system. Students prepare an Excel spreadsheet where the Gibbs energy of mixing of the vapor and liquid mixtures are calculated and represented over the whole range of compositions and then, apply the Gibbs stability test to ascertain the aggregation state of the system and to calculate the VL phase equilibrium compositions. Finally, Matlab is used to generate the 3D Gibbs energy of mixing surfaces for both phases over the whole range of temperatures which facilitates the geometrical interpretation of the vapor-liquid equilibrium.

Interplay between sublattice and spin symmetry breaking in graphene

We study the effect of sublattice symmetry breaking on the electronic, magnetic, and transport properties of two-dimensional graphene as well as zigzag terminated one- and zero-dimensional graphene nanostructures. The systems are described with the Hubbard model within the collinear mean field approximation. We prove that for the noninteracting bipartite lattice with an unequal number of atoms in each sublattice, in-gap states still exist in the presence of a staggered on-site potential ±Δ/2. We compute the phase diagram of both 2D and 1D graphene with zigzag edges, at half filling, defined by the normalized interaction strength U/t and Δ/t, where t is the first neighbor hopping. In the case of 2D we find that the system is always insulating, and we find the Uc(Δ) curve above which the system goes antiferromagnetic. In 1D we find that the system undergoes a phase transition from nonmagnetic insulator for Uand antiferromagnetic interedge coupling. The conduction properties of the magnetic phase depend on Δ and can be insulating, conducting, and even half-metallic, yet the total magnetic moment in the system is zero. We compute the transport properties of a heterojunction with two magnetic graphene ribbon electrodes connected to a finite length armchair ribbon and we find a strong spin filter effect.

A VLT/FLAMES survey for massive binaries in Westerlund 1. III. The WC9d binary W239 and implications for massive stellar evolution

Context. There is growing evidence that a treatment of binarity amongst OB stars is essential for a full theory of stellar evolution. However the binary properties of massive stars – frequency, mass ratio & orbital separation – are still poorly constrained. Aims. In order to address this shortcoming we have undertaken a multiepoch spectroscopic study of the stellar population of the young massive cluster Westerlund 1. In this paper we present an investigation into the nature of the dusty Wolf-Rayet star and candidate binary W239. Methods. To accomplish this we have utilised our spectroscopic data in conjunction with multi-year optical and near-IR photometric observations in order to search for binary signatures. Comparison of these data to synthetic non-LTE model atmosphere spectra were used to derive the fundamental properties of the WC9 primary. Results. We found W239 to have an orbital period of only ~5.05 days, making it one of the most compact WC binaries yet identified. Analysis of the long term near-IR lightcurve reveals a significant flare between 2004-6. We interpret this as evidence for a third massive stellar component in the system in a long period (>6 yr), eccentric orbit, with dust production occuring at periastron leading to the flare. The presence of a near-IR excess characteristic of hot (~1300 K) dust at every epoch is consistent with the expectation that the subset of persistent dust forming WC stars are short (<1 yr) period binaries, although confirmation will require further observations. Non-LTE model atmosphere analysis of the spectrum reveals the physical properties of the WC9 component to be fully consistent with other Galactic examples. Conclusions. The simultaneous presence of both short period Wolf-Rayet binaries and cool hypergiants within Wd 1 provides compelling evidence for a bifurcation in the post-Main Sequence evolution of massive stars due to binarity. Short period O+OB binaries will evolve directly to the Wolf-Rayet phase, either due to an episode of binary mediated mass loss – likely via case A mass transfer or a contact configuration – or via chemically homogenous evolution. Conversely, long period binaries and single stars will instead undergo a red loop across the HR diagram via a cool hypergiant phase. Future analysis of the full spectroscopic dataset for Wd 1 will constrain the proportion of massive stars experiencing each pathway; hence quantifying the importance of binarity in massive stellar evolution up to and beyond supernova and the resultant production of relativistic remnants.

Isotopic geochemistry of lavas at DSDP Holes 81-553 and 81-555

It is demonstrated by K-Ar analyses that the age of reversely magnetized basalts, which immediately predate magnetic Anomaly 24B, is 53.5 ± 1.9 m.y. Samples from deep levels appear to be grossly contaminated by an extraneous argon component with a uniform argon-40/argon-36 ratio 440. This component is thought to have been derived from fluids circulating in the lava pile during burial. The age result corroborates the assignment previously made to Anomaly 24B by Hailwood et al. (1979) and Lowrie and Alvarez (1981). It additionally suggests that lava extrusion formed part of a much larger magmatic event, which affected wide areas of the North Atlantic margins around the Paleocene/Eocene boundary, and can therefore probably be considered a good estimate of the age of this boundary. Initial 143Nd/144Nd ratios lie in the very restricted range 0.512920 ± 19 to 0.513026 ± 24 and initial 8 7Sr/86Sr ratios from ca. 0.703 to ca. 0.705. Acid leaching reduces the latter range to 0.70264 ± 4 to 0.70384 ± 4, suggesting that the higher 87Sr/86Sr ratios resulted from interaction with seawater. The array of data for treated samples is closely conformable on a 143Nd/144Nd-87Sr/86Sr diagram with the main oceanic mantle array and with previously published fields for Atlantic Ocean basalts. No evidence for any continental crustal contamination has been found. This suggests, but does not prove, that continental crust played no part in the genesis of these rocks.

Changes in the vegetation and trade winds in equatorial Northwest Africa 140,000-70,000 yr B.P., as deduced from two marine pollen records

The deep-sea cores M 16415-2 and M 16416-2 at about 9°N off Sierra Leone were analysed palynologically for the time interval 140,000-70,000 yr B.P. Results were presented in absolute (pollen concentration and pollen influx) and relative diagrams (pollen percentage). In a previous study it was evidenced that in northwest Africa pollen is mainly transported to the Atlantic by wind, so that the efficiency of aeolian pollen transport (pollen flux) could be used to evaluate changes in the intensity of the northeast trade winds. The glacial episodes (represented by the oxygen isotope stages 6 and 4) are characterized by strong northeast trade winds, whereas the last interglacial (stage 5) is characterized by weak trade winds. The pollen influx diagram shows that the intensity of the trade winds increased slightly during the relatively cool intervals of stage 5 (viz. 5.4 and 5.2). Tropical forest had maximally expanded around 124,000 yr B.P. (stage 5.5), around 98,000 yr B.P. (transition of stage 5.3 to 5.2), and around 70,000 yr B.P. (first part of stage 4): an increasing delay of the response of tropical forest to global intervals with maximum temperature is apparent during the last interglacial. As tropical forests need continuous humidity, the record of tropical forest monitors changes in climatic humidity south of the Sahara. During the last interglacial, the southern boundary of the Sahara shifted only little: expansions and contractions of the tropical forest area are correlated with contra-oscillations of the grass-dominated savanna zone. Great latitudinal shifts of the desert savanna boundary, on the contrary, occurred during the penultimate glacial interglacial transition (around 128,000 yr B.P.) to the north, and during the last interglacial-glacial transition (around 65,000 yr B.P.) to the south.

Helium isotope ratios and pore gases in deep-sea sediments of the Japan Sea

We have measured the 3He/4He and 4He/20Ne ratios and chemical compositions of gases exsolved from deep-sea sediments at two sites (798 and 799) in the Japan Sea. The 3He/4He and 4He/20Ne ratios vary from 0.642 Ratm (where Ratm is the atmospheric 3He/4He ratio of 1.393*10**-6) to 0.840 Ratm, and from 0.41 to 4.5, respectively. Helium in the samples can be explained by the mixing between atmospheric helium dissolved in bottom water of the Japan Sea and crustal helium in the sediment. The sedimentary helium is enriched in mantle-derived 3He compared with those from the Japan Trench and the Nankai Trough. This suggests that the basement of the Japan Sea has relatively large remnants of mantle-derived helium compared with that of the Pacific. Major chemical compositions of the samples are methane and nitrogen. There is a positive correlation between methane content and helium content corrected for air component. Based on the 3He/4He-Sum C/3He diagram, the major part of methane can be attributed to crustal and/or organic origin.

Geochemistry and Fe/(Ti + Ti), x, Curie temperature, and oxidation parameter z at DSDP Hole 597C

Electron microprobe and thermomagnetic analyses of selected basalt samples from Hole 597C were performed. The main purpose of this work was to investigate and estimate the degree of oxidation of the samples using the ratios of Fe to Ti and the Curie temperatures obtained from thermomagnetic curves. The results show that the magnetic properties of samples from Hole 597C change at a sub-bottom depth of 100 m, and that low-temperature and high-temperature oxidation processes prevailed above and below 100 m, respectively.

Palynological and stratigraphic record from Löddigsee in Mecklenburg-Vorpommern, Germany

A Late Pleistocene and Holocene sediment core from the nowadays terrestrialised portion of the Löddigsee in Southern Mecklenburg, Germany was palynologically investigated. The lake is situated in the rarely investigated Young moraine area at the transition from the Weichselian to the Saalian glaciation. The high-resolution pollen diagram contributes to the establishment of the north-eastern German Late Pleistocene pollen stratigraphy. The vegetation distribution pattern after the end of the Weichselian is in good agreement with other studies from North-eastern Germany, but also has its own characteristics. The Holocene vegetation development reveals features from the north-eastern and north-western German lowlands. A special focus was laid on the environmental history of the two settlements on an island within the lake (Late Neolithic and Younger Slavic period), which were preserved under moist conditions. Both settlements were constructed during a period of low lake level. Although there is evidence of agriculture in the area during the respective periods, the two island settlements seem to have served other purposes.

The federal Securities act manual : a treatise based on the federal Securities act of 1933 and the Corporation of foreign bondholders act, 1933, with forms, rules and regulations /

Double diagram mounted on front lining-paper.

Duties on land values. Being an examination of part I. of the Finance (1909-10 act, 1910; the other relevant sections of that act; the incorporated enactments; and the rules, regulations and forms made or issued under the act ...

With a supplement containing rules made by the Commissioners of inland revenue ... with table and diagram; additional forms issued under part I. of the act; rules as to appeals to the referee, high court, and county court, with observations thereon; and the relevant sections of the revenue act, 1911, with observations thereon.

General therapeutics and materia medica : adapted for a medical text book /

Includes index.

Old 83" diagram football trick play used by fielding Yost in 1907 Penn game

[photographic copy of original, on verso states diagram was made by Fielding Yost in his office for Earl Rathbun on Dec. 22nd 1934]