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At least 325 records · Page 18

Monstrous entanglement

The Monster CFT plays an important role in moonshine and is also conjectured to be the holographic dual to pure gravity in AdS3. We investigate the entanglement and Rényi entropies of this theory along with other extremal CFTs. The Rényi entropies of a single interval on the torus are evaluated using the short interval expansion. Each order in the expansion contains closed form expressions in the modular parameter. The leading terms in the q-series are shown to precisely agree with the universal corrections to Rényi entropies at low temperatures. Furthermore, these results are shown to match with bulk computations of Rényi entropy using the one-loop partition function on handlebodies. We also explore some features of Rényi entropies of two intervals on the plane.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Charged structure constants from modularity

We derive a universal formula for the average heavy-heavy-light structure constants for 2d CFTs with non-vanishing u(1) charge. The derivation utilizes the modular properties of one-point functions on the torus. Refinements in N = 2 SCFTs, show that the resulting Cardy-like formula for the structure constants has precisely the same shifts in the central charge as that of the thermodynamic entropy found earlier. This analysis generalizes the recent results by Kraus and Maloney for CFTs with an additional global u(1) symmetry. Our results at large central charge are also shown to match with computations from the holographic dual, which suggest that the averaged CFT three-point coefficient also serves as a useful probe of detecting black hole hair.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Reparameterization invariant operator basis for NRQED and HQET

We provide a self-contained discussion of how reparameterization invariance connects a rotationally-invariant heavy particle effective theory with a single heavy fermion to a Lorentz-invariant theory. Furthermore, using Hilbert-series methods, a Lorentz- invariant operator basis is tabulated, up to and including operators of order $1/M^4$, when the fermion couples to an external U(1) or SU(3) gauge interaction.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Symmetry-resolved entanglement entropy, spectra & boundary conformal field theory

We perform a comprehensive analysis of the symmetry-resolved (SR) entanglement entropy (EE) for one single interval in the ground state of a 1 + 1D conformal field theory (CFT), that is invariant under an arbitrary finite or compact Lie group, G. We utilize the boundary CFT approach to study the total EE, which enables us to find the universal leading order behavior of the SREE and its first correction, which explicitly depends on the irreducible representation under consideration and breaks the equipartition of entanglement. We present two distinct schemes to carry out these computations. The first relies on the evaluation of the charged moments of the reduced density matrix. This involves studying the action of the defect-line, that generates the symmetry, on the boundary states of the theory. This perspective also paves the way for discussing the infeasibility of studying symmetry resolution when an anomalous symmetry is present. The second scheme draws a parallel between the SREE and the partition function of an orbifold CFT. This approach allows for the direct computation of the SREE without the need to use charged moments. From this standpoint, the infeasibility of defining the symmetry-resolved EE for an anomalous symmetry arises from the obstruction to gauging. Finally, we derive the symmetry-resolved entanglement spectra for a CFT invariant under a finite symmetry group. We revisit a similar problem for CFT with compact Lie group, explicitly deriving an improved formula for U(1) resolved entanglement spectra. Using the Tauberian formalism, we can estimate the aforementioned EE spectra rigorously by proving an optimal lower and upper bound on the same. In the abelian case, we perform numerical checks on the bound and find perfect agreement.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Angular fractals in thermal QFT

We show that thermal effective field theory controls the long-distance expansion of the partition function of a d-dimensional QFT, with an insertion of any finite-order spatial isometry. Consequently, the thermal partition function on a sphere displays a fractal-like structure as a function of angular twist, reminiscent of the behavior of a modular form near the real line. As an example application, we find that for CFTs, the effective free energy of even-spin minus odd-spin operators at high temperature is smaller than the usual free energy by a factor of 1/2 d . Near certain rational angles, the partition function receives subleading contributions from “Kaluza-Klein vortex defects” in the thermal EFT, which we classify. We illustrate our results with examples in free and holographic theories, and also discuss nonperturbative corrections from worldline instantons.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Weyl consistency conditions in non-relativistic quantum field theory

Weyl consistency conditions have been used in unitary relativistic quantum field theory to impose constraints on the renormalization group flow of certain quantities. We classify the Weyl anomalies and their renormalization scheme ambiguities for generic non-relativistic theories in 2 + 1 dimensions with anisotropic scaling exponent z = 2; the extension to other values of z are discussed as well. We give the consistency conditions among these anomalies. As an application we find several candidates for a C-theorem. Here, we comment on possible candidates for a C-theorem in higher dimensions.

74 ATOMIC AND MOLECULAR PHYSICS↗

Twist Accumulation in Conformal Field Theory: A Rigorous Approach to the Lightcone Bootstrap

We prove that in any unitary CFT, a twist gap in the spectrum of operator product expansion (OPE) of identical scalar quasiprimary operators (i.e. Φ x Φ) implies the existence of a family of quasiprimary operators O τ,l with spins l → ∞ and twists τ → 2Δ Φ in the same OPE spectrum. A similar twist-accumulation result is proven for any two-dimensional Virasoro-invariant, modular-invariant, unitary CFT with a normalizable vacuum and central charge c > 1, where we show that a twist gap in the spectrum of Virasoro primaries implies the existence of a family of Virasoro primaries Oh, $\overline{h}$ with h → ∞ and $\overline{h}$→ c-1/24 (the same is true with h and $\overline{h}$ interchanged). Here, we summarize the similarity of the two problems and propose a general formulation of the lightcone bootstrap.

97 MATHEMATICS AND COMPUTING↗

Spectral Bounds on Hyperbolic 3-Manifolds: Associativity and the Trace Formula

We constrain the low-energy spectra of Laplace operators on closed hyperbolic manifolds and orbifolds in three dimensions, including the standard Laplace--Beltrami operator on functions and the Laplacian on powers of the cotangent bundle. Our approach employs linear programming techniques to derive rigorous bounds by leveraging two types of spectral identities. The first type, inspired by the conformal bootstrap, arises from the consistency of the spectral decomposition of the product of Laplace eigensections, and involves the Laplacian spectra as well as integrals of triple products of eigensections. We formulate these conditions in the language of representation theory of PSL 2 (C) and use them to prove upper bounds on the first and second Laplacian eigenvalues. The second type of spectral identities follows from the Selberg trace formula. We use them to find upper bounds on the spectral gap of the Laplace--Beltrami operator on hyperbolic 3-orbifolds, as well as on the systole length of hyperbolic 3-manifolds, as a function of the volume. Further, we prove that the spectral gap λ 1 of the Laplace--Beltrami operator on all closed hyperbolic 3-manifolds satisfies λ 1 < 47.32. Along the way, we use the trace formula to estimate the low-energy spectra of a large set of example orbifolds and compare them with our general bounds, finding that the bounds are nearly sharp in several cases.

Bonifacio, James [University of Mississippi, MS (U↗

Universality of the Microcanonical Entropy at Large Spin

We consider rigorous consequences of modular invariance for two-dimensional unitary non-rational CFTs with c > 1. Simple estimates for the torus partition function can lead to remarkably strong results. We show in particular that the spectral density of spin-J operators must grow like exp (π√$\frac{2}{3}$$(c - 1)$J})/√2J in any twist interval at or above (c - 1)/12, with a known twist-dependent prefactor. This proves that the large J spectrum becomes dense even without averaging over spins. For twists below (c - 1)/12 we establish that the growth must be strictly slower. Finally, we estimate how fast the maximal gap between two spin-J operators must go to zero as J becomes large.

Pal, Sridip [California Institute of Technology (C↗

An Excursion-Theoretic Approach to Stability of Discrete-Time Stochastic Hybrid Systems

We address stability of a class of Markovian discrete-time stochastic hybrid systems. This class of systems is characterized by the state-space of the system being partitioned into a safe or target set and its exterior, and the dynamics of the system being different in each domain. We give conditions for L{sub 1}-boundedness of Lyapunov functions based on certain negative drift conditions outside the target set, together with some more minor assumptions. We then apply our results to a wide class of randomly switched systems (or iterated function systems), for which we give conditions for global asymptotic stability almost surely and in L{sub 1}. The systems need not be time-homogeneous, and our results apply to certain systems for which functional-analytic or martingale-based estimates are difficult or impossible to get.

97 MATHEMATICS AND COMPUTING↗

Risk-Sensitive Control of Pure Jump Process on Countable Space with Near Monotone Cost

In this article, we study risk-sensitive control problem with controlled continuous time pure jump process on a countable space as state dynamics. We prove multiplicative dynamic programming principle, elliptic and parabolic Harnack’s inequalities. Using the multiplicative dynamic programing principle and the Harnack’s inequalities, we prove the existence and a characterization of optimal risk-sensitive control under the near monotone condition.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

On the development of a coupled regional climate-vegetation model RCM-CLM-CN-DV and its validation in Tropical Africa

This paper presents a regional climate system model RCM-CLM-CN-DV and its validation over Tropical Africa. The model development involves the initial coupling between the ICTP regional climate model RegCM4.3.4 (RCM) and the Community Land Model version 4 (CLM4) including models of carbon-nitrogen dynamics (CN) and vegetation dynamics (DV), and further improvements of the models. Model improvements derive from the new parameterization from CLM4.5 that addresses the well documented overestimation of gross primary production (GPP), a refinement of stress deciduous phenology scheme in CN that addresses a spurious LAI fluctuation for drought-deciduous plants, and the incorporation of a survival rule into the DV model to prevent tropical broadleaf evergreens trees from growing in areas with a prolonged drought season. The impact of the modifications on model results is documented based on numerical experiments using various subcomponents of the model. The performance of the coupled model is then validated against observational data based on three configurations with increasing capacity: RCM-CLM with prescribed leaf area index and fractional coverage of different plant functional types (PFTs); RCM-CLM-CN with prescribed PFTs coverage but prognostic plant phenology; RCM-CLM-CN-DV in which both the plant phenology and PFTs coverage are simulated by the model. Results from these three models are compared against the FLUXNET up-scaled GPP and ET data, LAI and PFT coverages from remote sensing data including MODIS and GIMMS, University of Delaware precipitation and temperature data, and surface radiation data from MVIRI and SRB. Our results indicate that the models perform well in reproducing the physical climate and surface radiative budgets in the domain of interest. However, PFTs coverage is significantly underestimated by the model over arid and semi-arid regions of Tropical Africa, caused by an underestimation of LAI in these regions by the CN model that gets exacerbated through vegetation dynamics in RCM-CLM-CN-DV.

54 ENVIRONMENTAL SCIENCES↗

Comparative Approach of MRI-Based Brain Tumor Segmentation and Classification Using Genetic Algorithm

The detection of a brain tumor and its classification from modern imaging modalities is a primary concern, but a time-consuming and tedious work was performed by radiologists or clinical supervisors. The accuracy of detection and classification of tumor stages performed by radiologists is depended on their experience only, so the computer-aided technology is very important to aid with the diagnosis accuracy. In this study, to improve the performance of tumor detection, we investigated comparative approach of different segmentation techniques and selected the best one by comparing their segmentation score. Further, to improve the classification accuracy, the genetic algorithm is employed for the automatic classification of tumor stage. The decision of classification stage is supported by extracting relevant features and area calculation. The experimental results of proposed technique are evaluated and validated for performance and quality analysis on magnetic resonance brain images, based on segmentation score, accuracy, sensitivity, specificity, and dice similarity index coefficient. The experimental results achieved 92.03% accuracy, 91.42% specificity, 92.36% sensitivity, and an average segmentation score between 0.82 and 0.93 demonstrating the effectiveness of the proposed technique for identifying normal and abnormal tissues from brain MR images. The experimental results also obtained an average of 93.79% dice similarity index coefficient, which indicates better overlap between the automated extracted tumor regions with manually extracted tumor region by radiologists.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

Status of the ITER Electron Cyclotron Heating and Current Drive System

We present that the electron cyclotron (EC) heating and current drive (H&CD) system developed for the ITER is made of 12 sets of high-voltage power supplies feeding 24 gyrotrons connected through 24 transmission lines (TL), to five launchers, four located in upper ports and one at the equatorial level. Nearly all procurements are in-kind, following general ITER philosophy, and will come from Europe, India, Japan, Russia and the USA. The full system is designed to couple to the plasma 20 MW among the 24 MW generated power, at the frequency of 170 GHz, for various physics applications such as plasma start-up, central H&CD and magnetohydrodynamic (MHD) activity control. The design takes present day technology and extends toward high-power continuous operation, which represents a large step forward as compared to the present state of the art. The ITER EC system will be a stepping stone to future EC systems for DEMO and beyond.The development of the EC system is facing significant challenges, which includes not only an advanced microwave system but also compliance with stringent requirements associated with nuclear safety as ITER became the first fusion device licensed as basic nuclear installations as of 9 November 2012. Finally, since the conceptual design of the EC system was established in 2007, the EC system has progressed to a preliminary design stage in 2012 and is now moving forward toward a final design.

42 ENGINEERING↗

A Review on Biodegradable Polymeric Materials Striving Towards the Attainment of Green Environment

Polymers are a chain of repeating monomers that can be either non-biodegradable or biodegradable with technical properties for a wide range of applications. The present scenario drives industries to develop new and eco-friendly materials to replace non-biodegradable materials to attain a clean and green environment. Significant research work has been carried out on the development of biocomposites based on biodegradable polymers and natural fibers. The review article addresses the wide range of biodegradable composites that are capable of undergoing degradation by various routes. Our main emphasis has been on the preparation and characterization of biocomposites, using various biodegradable polymers and natural fibers for wide applications like biomedical, packaging, aerospace, agriculture etc. It is clear that blending of reinforcing fibers and fillers with biodegradable polymers significantly enhanced the physical, chemical, biological, mechanical, thermal and biodegradation properties of the base matrix.

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗

Conferring Antibacterial Properties on Sesbania Gum via Microwave-Assisted Graft Copolymerization of DADMAC

Microbial contamination, the consequences of both anthropogenic and geogenic activity, includes high health and environmental threats and may adversely affects the ecological niche. The present work is a successful attempt towards the fabrication of anti-bacterial agent by incorporation of cationic monomer, diallyldimethylammonium chloride (DADMAC) on sesbania gum through microwave assisted method. The grafted chains of poly (DADMAC) provide positive charge to sesbania gum which in turn confers antibacterial activity. The synthesized product was characterized through FTIR, SEM, TGA, DSC elemental and viscometric analysis. The inhibitory activity of the synthesized product has been evaluated in vitro against both Gram-positive (Staphylococcus aureus NCIM 2122 and Bacillus anthracis) as well as Gram-negative (Salmonella typhi NCIM 2501 and Escherichia coli NCIM 2832) bacteria through standard agar cup method. Optimum minimum inhibitory concentration for each grade of graft copolymer measured by calculating the zone of inhibition has been found at 750 µg/ml. Graphical Abstract: .

36 MATERIALS SCIENCE↗

Novel Biocide Based on Cationic Derivative of Psyllium: Surface Modification and Antibacterial Activity

To circumvent the problems (such as volatilization, photolytic decomposition, chemical instability, easy permeability through the skin) associated with low molecular weight antimicrobial agents, our strategy employed graft copolymerization of cationic monomer with the polymeric substrate viz. psyllium husk. The surface graft concentration of quaternary ammonium ion on psyllium was optimized by measuring the extent of grafting in the microwave-induced process. The surface modification of graft copolymers was evident by different physico–chemical techniques like {sup 13}C nuclear magnetic resonance (NMR), Fourier-transform infrared spectroscopy (FTIR), scanning electron microscope (SEM), X-ray diffractometer (XRD), differential scanning calorimetry (DSC), Thermo gravimeteric analysis (TGA), and viscometric study. The synthesized water soluble product resulted good antibacterial activity against Gram positive Staphylococcus aureus and Bacillus anthracis but failed to produce any antibacterial activity against Gram negative Salmonella typhi and Escherichia coli. The reason to failure has been explained on the basis of differences in the electrokinetic property between Gram-positive and Gram-negative bacteria. Optimum minimum inhibitory concentration (MIC) for the polymeric grade which showed good biocidal effect evaluated by both zone of inhibition and absorbance is found at 1000 µg/ml.

36 MATERIALS SCIENCE↗