A Special Case Of A Conjecture By Widom With Implications To Fermionic Entanglement Entropy

We prove a special case of a conjecture in asymptotic analysis by Harold Widom. More precisely, we establish the leading and next-to-leading term of a semi-classical expansion of the trace of the square of certain integral operators on the Hilbert space $L^2(\R^d)$. As already observed by Gioev and Klich, this implies that the bi-partite entanglement entropy of the free Fermi gas in its ground state grows at least as fast as the surface area of the spatially bounded part times a logarithmic enhancement.Comment: 20 pages, 3 figures, improvement of the presentation, some references added or updated, proof of Theorem 12 (formerly Lemma 11) adde

Complexity of links in 3-manifolds

We introduce a natural-valued complexity c(X) for pairs X=(M,L), where M is a closed orientable 3-manifold and L is a link contained in M. The definition employs simple spines, but for well-behaved X's we show that c(X) equals the minimal number of tetrahedra in a triangulation of M containing L in its 1-skeleton. Slightly adapting Matveev's recent theory of roots for graphs, we carefully analyze the behaviour of c under connected sum away from and along the link. We show in particular that c is almost always additive, describing in detail the circumstances under which it is not. To do so we introduce a certain (0,2)-root for a pair X, we show that it is well-defined, and we prove that X has the same complexity as its (0,2)-root. We then consider, for links in the 3-sphere, the relations of c with the crossing number and with the hyperbolic volume of the exterior, establishing various upper and lower bounds. We also specialize our analysis to certain infinite families of links, providing rather accurate asymptotic estimates.Comment: 24 pages, 6 figure

Gas phase mean opacities for varying [M/H], N/O, and C/O

We present a set of gas-phase Planck mean and Rosseland mean opacity tables applicable for simulations of star and planet formation, stellar evolution, disk modelling at various metallicities in hydrogen-rich environments. The tables are calculated for gas temperatures between 1000K and 10000K and total hydrogen number densities between 10^2 cm^-3 and 10^17 cm^-3. The carbon-to-oxygen ratio is varied from 0.43 to well above 2.0, the nitrogen-to-oxygen ration between 0.14 and 100.0. The tables are calculated for a range of metallicities down to [M/H]'= log N_M/N_H=-7.0. We demonstrate how the mean opacities and the abundances of the opacity species vary with C/O, N/O, and [M/H]'. We use the element abundances from Grevesse, Asplund & Sauval (2007), and we provide additional tables for the oxygen-abundance value from Caffau et al.(2008). All tables will be available online under http://star-www.st-and.ac.uk/$\sim$ch80/datasources.htmlComment: 10 pages, accepted for publication in MNRA

A Review of Noncommutative Field Theories

We present a brief review of selected topics in noncommutative field theories ranging from its revival in string theory, its influence on quantum field theories, its possible experimental signatures and ending with some applications in gravity and emergent gravity.Comment: Talk presented at the XIV Mexican School on Particles and Fields, Morelia, Mexico, November 9-11, 2010; 8 pages. V2 reference adde

Detectability of dirty dust grains in brown dwarf atmospheres

Dust clouds influence the atmospheric structure of brown dwarfs, and they affect the heat transfer and change the gas-phase chemistry. However, the physics of their formation and evolution is not well understood. In this letter, we predict dust signatures and propose a potential observational test of the physics of dust formation in brown dwarf atmosphere based on the spectral features of the different solid components predicted by dust formation theory. A momentum method for the formation of dirty dust grains (nucleation, growth, evaporation, drift) is used in application to a static brown dwarf atmosphere structure to compute the dust grain properties, in particular the heterogeneous grain composition and the grain size. Effective medium and Mie theory are used to compute the extinction of these spherical grains. Dust formation results in grains whose composition differs from that of grains formed at equilibrium. Our kinetic model predicts that solid amorphous SiO2[s] (silica) is one of the most abundant solid component followed by amorphous MgSiO4[s] and MgSiO3[s], while SiO2[s] is absent in equilibrium models because it is a metastable solid. Solid amorphous SiO2[s] possesses a strong broad absorption feature centered at 8.7mum, while amorphous Mg2SiO4[s]/MgSiO3[s] absorb at 9.7mum beside other absorption features at longer wavelength. Those features at lambda < 15mum are detectable in absorption if grains are small (radius < 0.2mum) in the upper atmosphere as suggested by our model. We suggest that the detection of a feature at 8.7mum in deep infrared spectra could provide evidence for non-equilibrium dust formation that yields grains composed of metastable solids in brown dwarf atmospheres. This feature will shift towards 10mum and broaden if silicates (e.g. fosterite) are much more abundant.Comment: A&A Letter, accepte

M dwarf stars in the light of (future) exoplanet searches

We present a brief overview of a splinter session on M dwarf stars as planet hosts that was organized as part of the Cool Stars 17 conference. The session was devoted to reviewing our current knowledge of M dwarf stars and exoplanets in order to prepare for current and future exoplanet searches focusing in low mass stars. We review the observational and theoretical challenges to characterize M dwarf stars and the importance of accurate fundamental parameters for the proper characterization of their exoplanets and our understanding on planet formation.Comment: 4 pages, 1 figure. Summary of the splinter session "M dwarf stars in the light of (future) exoplanet searches" held at the 17th Cambridge Workshop on Cool Stars, Stellar Systems, and the Sun, June 28th 2012, Barcelona, Spain. Submitted for publication in Astronomische Nachrichten - Astronomical Notes (AN) 334, Issue 1-2, Eds Klaus Strassmeier and Mercedes L\'opez-Morale

Understanding the atmospheric properties and chemical composition of the ultra-hot Jupiter HAT-P-7b II. Mapping the effects of gas kinetics

Funding: Part of this work was supported by the German Deutsche Forschungsgemeinschaft, DFG project number Ts 17/2–1.Aims. The atmospheres of ultra-hot Jupiters (UHJs) are commonly considered to be at thermochemical equilibrium. We aim to provide disequilibrium chemistry maps for a global understanding of the chemistry in the atmosphere of HAT-P-7b and assess the importance of disequilibrium chemistry on UHJs. Methods. We applied a hierarchical modeling approach using 97 1D atmospheric profiles from a 3D general circulation model of HAT-P-7b. For each atmospheric 1D profile, we evaluated our kinetic cloud formation model consistently with the local gas-phase composition in chemical equilibrium. This served as input to study the quenching of dominating CHNO-binding molecules. We evaluated quenching results from a zeroth-order approximation in comparison to a kinetic gas-phase approach. Results. We find that the zeroth-order approach of estimating quenching points agrees well with the full gas-kinetic modeling results. However, it underestimates the quenching levels by about one order of magnitude at high temperatures. Chemical disequilibrium has the greatest effect on the nightside and morning abundance of species such as H, H2O, CH4, CO2, HCN, and all CnHm molecules; heavier CnHm molecules are more affected by disequilibrium processes. The CO abundance, however, is affected only marginally. While dayside abundances also notably change, those around the evening terminator of HAT-P-7b are the least affected by disequilibrium processes. The latter finding may partially explain the consistency of observed transmission spectra of UHJs with atmospheres in thermochemical equilibrium. Photochemistry only negligibly affects molecular abundances and quenching levels. Conclusions. In general, the quenching points of the atmosphere of HAT-P-7b are at much lower pressures than in the cooler hot-jupiters. We propose several avenues to determining the effect of disequilibrium processes on UHJs that are in general based on abundance and opacity measurements at different local times. It remains a challenge to completely disentangle this from the chemical effects of clouds and that of a primordial nonsolar abundance.Publisher PDFPeer reviewe

Transcranial magnetic stimulation-evoked electroencephalography responses as biomarkers for epilepsy: A review of study design and outcomes

Transcranial magnetic stimulation (TMS) with electroencephalography (EEG), that is TMS-EEG, may assist in managing epilepsy. We systematically reviewed the quality of reporting and findings in TMS-EEG studies on people with epilepsy and healthy controls, and on healthy individuals taking anti-seizure medication. We searched the Cochrane Library, Embase, PubMed and Web of Science databases for original TMS-EEG studies comparing people with epilepsy and healthy controls, and healthy subjects before and after taking anti-seizure medication. Studies should involve quantitative analyses of TMS-evoked EEG responses. We evaluated the reporting of study population characteristics and TMS-EEG protocols (TMS sessions and equipment, TMS trials and EEG protocol), assessed the variation between protocols, and recorded the main TMS-EEG findings. We identified 20 articles reporting 14 unique study populations and TMS methodologies. The median reporting rate for the group of people with epilepsy parameters was 3.5/7 studies and for the TMS parameters was 13/14 studies. TMS protocols varied between studies. Fifteen out of 28 anti-seizure medication trials in total were evaluated with time-domain analyses of single-pulse TMS-EEG data. Anti-seizure medication significantly increased N45, and decreased N100 and P180 component amplitudes but in marginal numbers (N45: 8/15, N100: 7/15, P180: 6/15). Eight articles compared people with epilepsy and controls using different analyses, thus limiting comparability. The reporting quality and methodological uniformity between studies evaluating TMS-EEG as an epilepsy biomarker is poor. The inconsistent findings question the validity of TMS-EEG as an epilepsy biomarker. To demonstrate TMS-EEG clinical applicability, methodology and reporting standards are required

On The Interaction Of D0-Brane Bound States And RR Photons

We consider the problem of the interaction between D0-brane bound state and 1-form RR photons by the world-line theory. Based on the fact that in the world-line theory the RR gauge fields depend on the matrix coordinates of D0-branes, the gauge fields also appear as matrices in the formulation. At the classical level, we derive the Lorentz-like equations of motion for D0-branes, and it is observed that the center-of-mass is colourless with respect to the SU(N) sector of the background. Using the path integral method, the perturbation theory for the interaction between the bound state and the RR background is developed. We discuss what kind of field theory may be corresponded to the amplitudes which are calculated by the perturbation expansion in world-line theory. Qualitative considerations show that the possibility of existence of a map between the world-line theory and the non-Abelian gauge theory is very considerable.Comment: LaTeX, 28 pages, 4 eps figures. v2 and v3: eqs. (3.18) and (B.2) are corrected, very small change

Sturmian morphisms, the braid group B_4, Christoffel words and bases of F_2

We give a presentation by generators and relations of a certain monoid generating a subgroup of index two in the group Aut(F_2) of automorphisms of the rank two free group F_2 and show that it can be realized as a monoid in the group B_4 of braids on four strings. In the second part we use Christoffel words to construct an explicit basis of F_2 lifting any given basis of the free abelian group Z^2. We further give an algorithm allowing to decide whether two elements of F_2 form a basis or not. We also show that, under suitable conditions, a basis has a unique conjugate consisting of two palindromes.Comment: 25 pages, 4 figure