Chern-Simons theory, exactly solvable models and free fermions at finite temperature

We show that matrix models in Chern-Simons theory admit an interpretation as 1D exactly solvable models, paralleling the relationship between the Gaussian matrix model and the Calogero model. We compute the corresponding Hamiltonians, ground-state wavefunctions and ground-state energies and point out that the models can be interpreted as quasi-1D Coulomb plasmas. We also study the relationship between Chern-Simons theory on $S^3$ and a system of N one-dimensional fermions at finite temperature with harmonic confinement. In particular we show that the Chern-Simons partition function can be described by the density matrix of the free fermions in a very particular, crystalline, configuration. For this, we both use the Brownian motion and the matrix model description of Chern-Simons theory and find several common features with c=1 theory at finite temperature. Finally, using the exactly solvable model result, we show that the finite temperature effect can be described with a specific two-body interaction term in the Hamiltonian, with 1D Coulombic behavior at large separations.Comment: 19 pages, v2: references adde

A note on the existence of standard splittings for conformally stationary spacetimes

Let $(M,g)$ be a spacetime which admits a complete timelike conformal Killing vector field $K$. We prove that $(M,g)$ splits globally as a standard conformastationary spacetime with respect to $K$ if and only if $(M,g)$ is distinguishing (and, thus causally continuous). Causal but non-distinguishing spacetimes with complete stationary vector fields are also exhibited. For the proof, the recently solved "folk problems" on smoothability of time functions (moreover, the existence of a {\em temporal} function) are used.Comment: Metadata updated, 6 page

Multiple Sources toward the High-mass Young Star S140 IRS1

S140 IRS1 is a remarkable source where the radio source at the center of the main bipolar molecular outflow in the region is elongated perpendicular to the axis of the outflow, an orientation opposite to that expected if the radio source is a thermal jet exciting the outflow. We present results of 1.3 cm continuum and H2O maser emission observations made with the VLA in its A configuration toward this region. In addition, we also present results of continuum observations at 7 mm and re-analyse observations at 2, 3.5 and 6 cm (previously published). IRS 1A is detected at all wavelengths, showing an elongated structure. Three water maser spots are detected along the major axis of the radio source IRS 1A. We have also detected a new continuum source at 3.5 cm (IRS 1C) located ~0.6'' northeast of IRS 1A. The presence of these two YSOs (IRS 1A and 1C) could explain the existence of the two bipolar molecular outflows observed in the region. In addition, we have also detected three continuum clumps (IRS 1B, 1D and 1E) located along the major axis of IRS 1A. We discuss two possible models to explain the nature of IRS 1A: a thermal jet and an equatorial wind.Comment: 17 pages, 4 figures, to be published in A

Structure of characteristic Lyapunov vectors in spatiotemporal chaos

We study Lyapunov vectors (LVs) corresponding to the largest Lyapunov exponents in systems with spatiotemporal chaos. We focus on characteristic LVs and compare the results with backward LVs obtained via successive Gram-Schmidt orthonormalizations. Systems of a very different nature such as coupled-map lattices and the (continuous-time) Lorenz `96 model exhibit the same features in quantitative and qualitative terms. Additionally we propose a minimal stochastic model that reproduces the results for chaotic systems. Our work supports the claims about universality of our earlier results [I. G. Szendro et al., Phys. Rev. E 76, 025202(R) (2007)] for a specific coupled-map lattice.Comment: 9 page

Finsler geodesics in the presence of a convex function and their applications

We obtain a result about the existence of only a finite number of geodesics between two fixed non-conjugate points in a Finsler manifold endowed with a convex function. We apply it to Randers and Zermelo metrics. As a by-product, we also get a result about the finiteness of the number of lightlike and timelike geodesics connecting an event to a line in a standard stationary spacetime.Comment: 16 pages, AMSLaTex. v2 is a minor revision: title changed, references updated, typos fixed; it matches the published version. This preprint and arXiv:math/0702323v3 [math.DG] substitute arXiv:math/0702323v2 [math.DG

Stress-free states of continuum dislocation fields: Rotations, grain boundaries, and the Nye dislocation density tensor

We derive general relations between grain boundaries, rotational deformations, and stress-free states for the mesoscale continuum Nye dislocation density tensor. Dislocations generally are associated with long-range stress fields. We provide the general form for dislocation density fields whose stress fields vanish. We explain that a grain boundary (a dislocation wall satisfying Frank's formula) has vanishing stress in the continuum limit. We show that the general stress-free state can be written explicitly as a (perhaps continuous) superposition of flat Frank walls. We show that the stress-free states are also naturally interpreted as configurations generated by a general spatially-dependent rotational deformation. Finally, we propose a least-squares definition for the spatially-dependent rotation field of a general (stressful) dislocation density field.Comment: 9 pages, 3 figure

Self-isospectrality, mirror symmetry, and exotic nonlinear supersymmetry

We study supersymmetry of a self-isospectral one-gap Poschl-Teller system in the light of a mirror symmetry that is based on spatial and shift reflections. The revealed exotic, partially broken nonlinear supersymmetry admits seven alternatives for a grading operator. One of its local, first order supercharges may be identified as a Hamiltonian of an associated one-gap, non-periodic Bogoliubov-de Gennes system. The latter possesses a nonlinear supersymmetric structure, in which any of the three non-local generators of a Clifford algebra may be chosen as the grading operator. We find that the supersymmetry generators for the both systems are the Darboux-dressed integrals of a free spin-1/2 particle in the Schrodinger picture, or of a free massive Dirac particle. Nonlocal Foldy- Wouthuysen transformations are shown to be involved in the supersymmetric structure.Comment: 20 pages, comment added. Published versio

The tribe Spermacoceae (Rubiaceae) in the State of Ceará, northeastern Brazil

Tribe Spermacoceae comprises more than 1000 species and about 80 genera, being the largest lineage of herbaceous plants within Rubiaceae. Historically, it is marked by taxonomic complexes. This study aims to investígate the diversity and geographical distribution o f the tribe Spermacoceae in Ceará, in the Northeast región of Brazil. This State covers an area o f 150,000 km2 within the Caatinga domain and is divided into 11 phytoecological units, where the Crystalline Caatinga predominates. Specimens collected from 1990 to 2023, and collections from the EAC, HCDAL, HUEFS, HUVA, and PEUFR herbaria were analysed. The tribe is represented in Ceará by 31 species, of which Borreria savannicola and Mitracarpus fernandesii are endemic to the State, and seven genera, with Borreria being the most diverse (13 spp.), followed by Mitracarpus (six spp.), Hexasepalum (four spp.), Richardia and Spermacoce (three spp. each), andEmmeorhiza and Staelia (one sp. each). In total, 605 collections were verified. Morphological characteristics of fruit, seed, pollen, and intemal indumentum o f the corolla were diagnostic for taxonomic delimitation, with new species having been described for Science in recent years (B. apodiensis, B. savannicola, and H. nordestinum). Borreria scabiosoides has the broadest geographic range, while B. cupularis, B. savannicola, H. nordestinum, and M. polygonifolius are the most restricted species. The northwest región of Ceará is the most diverse (with 22 to 26 species), followed by the south (with 17 to 21 species). The same pattem was verified for the distribution o f records, with the northwest región having the highest numbers (232 to 289 records), whereas the south presents fewer records (59 to 116). Therefore, despite the northwest región having the highest number of species, the greatest diversity relative to the number o f records is found in the Southern región of Ceará. Acknowledgements: FUNCAP (Process BP5-0197-00136.01.00/22); UVA

On the relation between virial coefficients and the close-packing of hard disks and hard spheres

The question of whether the known virial coefficients are enough to determine the packing fraction $\eta_\infty$ at which the fluid equation of state of a hard-sphere fluid diverges is addressed. It is found that the information derived from the direct Pad\'e approximants to the compressibility factor constructed with the virial coefficients is inconclusive. An alternative approach is proposed which makes use of the same virial coefficients and of the equation of state in a form where the packing fraction is explicitly given as a function of the pressure. The results of this approach both for hard-disk and hard-sphere fluids, which can straightforwardly accommodate higher virial coefficients when available, lends support to the conjecture that $\eta_\infty$ is equal to the maximum packing fraction corresponding to an ordered crystalline structure.Comment: 10 pages, 6 figures; v2: discussion about hard-square and hard-hexagon systems on a lattice added; five new reference