A homomorphism between link and XXZ modules over the periodic Temperley-Lieb algebra

We study finite loop models on a lattice wrapped around a cylinder. A section of the cylinder has N sites. We use a family of link modules over the periodic Temperley-Lieb algebra EPTL_N(\beta, \alpha) introduced by Martin and Saleur, and Graham and Lehrer. These are labeled by the numbers of sites N and of defects d, and extend the standard modules of the original Temperley-Lieb algebra. Beside the defining parameters \beta=u^2+u^{-2} with u=e^{i\lambda/2} (weight of contractible loops) and \alpha (weight of non-contractible loops), this family also depends on a twist parameter v that keeps track of how the defects wind around the cylinder. The transfer matrix T_N(\lambda, \nu) depends on the anisotropy \nu and the spectral parameter \lambda that fixes the model. (The thermodynamic limit of T_N is believed to describe a conformal field theory of central charge c=1-6\lambda^2/(\pi(\lambda-\pi)).) The family of periodic XXZ Hamiltonians is extended to depend on this new parameter v and the relationship between this family and the loop models is established. The Gram determinant for the natural bilinear form on these link modules is shown to factorize in terms of an intertwiner i_N^d between these link representations and the eigenspaces of S^z of the XXZ models. This map is shown to be an isomorphism for generic values of u and v and the critical curves in the plane of these parameters for which i_N^d fails to be an isomorphism are given.Comment: Replacement of "The Gram matrix as a connection between periodic loop models and XXZ Hamiltonians", 31 page

Using 21-cm absorption surveys to measure the average HI spin temperature in distant galaxies

We present a statistical method for measuring the average HI spin temperature in distant galaxies using the expected detection yields from future wide-field 21cm absorption surveys. As a demonstrative case study we consider a simulated all-southern-sky survey of 2-h per pointing with the Australian Square Kilometre Array Pathfinder for intervening HI absorbers at intermediate cosmological redshifts between $z = 0.4$ and $1$. For example, if such a survey yielded $1000$ absorbers we would infer a harmonic-mean spin temperature of $\overline{T}_\mathrm{spin} \sim 100$K for the population of damped Lyman $\alpha$ (DLAs) absorbers at these redshifts, indicating that more than $50$ per cent of the neutral gas in these systems is in a cold neutral medium (CNM). Conversely, a lower yield of only 100 detections would imply $\overline{T}_\mathrm{spin} \sim 1000$K and a CNM fraction less than $10$ per cent. We propose that this method can be used to provide independent verification of the spin temperature evolution reported in recent 21cm surveys of known DLAs at high redshift and for measuring the spin temperature at intermediate redshifts below $z \approx 1.7$, where the Lyman-$\alpha$ line is inaccessible using ground-based observatories. Increasingly more sensitive and larger surveys with the Square Kilometre Array should provide stronger statistical constraints on the average spin temperature. However, these will ultimately be limited by the accuracy to which we can determine the HI column density frequency distribution, the covering factor and the redshift distribution of the background radio source population.Comment: 11 pages, 9 figures, 1 table. Proof corrected versio

Validity of the Adiabatic Approximation

We analyze the validity of the adiabatic approximation, and in particular the reliability of what has been called the "standard criterion" for validity of this approximation. Recently, this criterion has been found to be insufficient. We will argue that the criterion is sufficient only when it agrees with the intuitive notion of slowness of evolution of the Hamiltonian. However, it can be insufficient in cases where the Hamiltonian varies rapidly but only by a small amount. We also emphasize the distinction between the adiabatic {\em theorem} and the adiabatic {\em approximation}, two quite different although closely related ideas.Comment: 4 pages, 1 figur

Découverte de mégadunes dans l’estuaire moyen du fleuve Saint-Laurent, Québec, Canada

Des levés régionaux de géologie marine effectués sur trois ans dans l’estuaire du Saint-Laurent permettent pour la première fois de caractériser en détail le relief sous-marin entre l’Ile aux Coudres et Pointe-des-Monts, Québec Canada. Les levés de bathymétrie multifaisceaux, couplés à des levés géophysiques à haute résolution (sismique et sonar à balayage latéral) et à l’échantillonnage du fond marin, ont permis d’imager et de documenter des champs de dunes décamétriques pouvant atteindre une dizaine de kilomètres de longueur et quelques kilomètres de largeur. La présence de ces mégadunes suggère un environnement très dynamique ainsi qu’une grande mobilité des sédiments. Deux de ces champs, localisés à l’intérieur des limites du Parc marin Saguenay‑Saint‑Laurent, font l’objet d’une description plus détaillée afin de comprendre l’environnement physique dans lequel ils ont été mis en place. Des ondes internes modernes dans l’estuaire moyen du Saint‑Laurent, phénomènes connus et documentés, sont peut-être un mécanisme important de la mise en place et de la mobilité des mégadunes. Toutefois, les profils sismiques dans ces champs de mégadunes montrent que certaines pourraient être un vestige d’une période où le régime hydraulique de l’estuaire était différent, avec un débit beaucoup plus fort vers l’aval et des courants de marée plus importants. Des mégadunes imagées sur le fond marin, d’une amplitude de 10 m et d’une longueur d’onde moyenne de 200 m, sont en effet observées sur un des profils sismiques en‑dessous de boues modernes. Les ondulations du fond marin sont identifiables à plusieurs échelles, les plus grosses étant surmontées de plus petites, qui elles pourraient représenter le régime hydrodynamique actuel. Il reste à évaluer l’activité moderne des mégadunes par le biais de levés multi‑annuels afin de quantifier le taux de déplacement, les changements morphologiques et d’établir une relation directe avec les conditions hydrodynamiques modernes.Three years of regional marine geology surveys in the St. Lawrence Estuary allow for the first time the detailed characterization of the seabed topography between Ile aux Coudres and Pointe-des-Monts, Québec, Canada. Multibeam bathymetric surveys complemented with high resolution geophysical surveys (seismic and side-scan sonar) and seabed sampling, are the basis for documenting megadune (10 m) fields up to 10 km in length and a few kilometers in width. The presence of these megadunes suggests a very dynamic environment as well as high sediment mobility. Two of these fields, located within the limits of the Saguenay‑St. Lawrence Marine Park, are described in detail in order to better understand the physical environment in which they were formed. The occurrence of internal waves in the upper St. Lawrence Estuary, a known and documented phenomenon, suggests that this may be an important factor in the development and mobility of the megadunes. However, seismic profiles over the megadune fields show that some of them may be a relict of a time when hydrodynamic conditions in the estuary were different, i.e. with a much stronger discharge and more important tidal currents. Some megadunes imaged on the seabed, with an amplitude of ten meters and an average wavelength of 200 m, have been observed on the seismic profiles under modern mud. Bedforms are observed at various scales, the largest being overridden by smaller ones, these ones perhaps representing modern hydrodynamic conditions. The modern activity of the megadunes needs to be evaluated with multi-year bathymetric surveys, which will allow quantifying their displacement characterization of changes in morphology associated with varying hydrodynamic conditions, and establish a direct relationship with modern hydrodynamic conditions

Ultra-violet photo-ionisation in far-infrared selected sources

It has been reported that there is a deficit of stellar heated dust, as evident from the lack of far-infrared (FIR) emission, in sources within the Herschel-SPIRE sample with X-ray luminosities exceeding a ``critical value'' of L~10^37 W. Such a scenario would be consistent with the suppression of star formation by the AGN, required by current theoretical models. Since absorption of the 21-cm transition of neutral hydrogen (HI), which traces the star-forming reservoir, also exhibits a critical value in the ultra-violet band (above ionising photon rates of Q ~ 3 x 10^56 s^-1), we test the SPIRE sample for the incidence of the detection of 250 micron emission with Q. The highest value at which FIR emission is detected above the SPIRE confusion limit is Q = 8.9 x 10^57 s^-1, which is ~30 times that for the HI, with no critical value apparent. Since complete ionisation of the neutral atomic gas is expected at Q > 3 x 10^56 s-1., this may suggest that much of the FIR must arise from heating of the dust by the AGN. However, integrating the ionising photon rate of each star over the initial mass function, we cannot rule out that the high observed ionising photon rates are due to a population of hot, massive stars.Comment: Accepted by A&

Refined conformal spectra in the dimer model

Working with Lieb's transfer matrix for the dimer model, we point out that the full set of dimer configurations may be partitioned into disjoint subsets (sectors) closed under the action of the transfer matrix. These sectors are labelled by an integer or half-integer quantum number we call the variation index. In the continuum scaling limit, each sector gives rise to a representation of the Virasoro algebra. We determine the corresponding conformal partition functions and their finitizations, and observe an intriguing link to the Ramond and Neveu-Schwarz sectors of the critical dense polymer model as described by a conformal field theory with central charge c=-2.Comment: 44 page

Detection of Heterodera avenae infestations on winter wheat by radiothermometry

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