ShantanuT01/DACTYL-Pretraining huggingface dataset:
AdS_4/CFT_3 duality relating IIA string theory on AdS_4 x CP^3 to N=6 superconformal Chern-Simons theory provides an arena for studying aspects of integrability in a new potentially exactly solvable system. In this paper we explore the tree-level worldsheet scattering for strings on AdS_4 x CP^3. We compute all bosonic four-, five- and six-point amplitudes in the gauge-fixed action and demonstrate the absence of particle production.
Observational and theoretical arguments support the idea that violent events connected with $AGN$ activity and/or intense star forming episodes have played a significant role in the early phases of galaxy formation at high red shifts. Being old stellar systems, globular clusters seem adequate candidates to search for the eventual signatures that might have been left by those energetic phenomena. The analysis of the colour distributions of several thousands of globular clusters in the Virgo and Fornax galaxy clusters reveals the existence of some interesting and previously undetected features. A simple pattern recognition technique, indicates the presence of "colour modulations", distinctive for each galaxy cluster. The results suggest that the globular cluster formation process has not been completely stochastic but, rather, included a significant fraction of globulars that formed in a synchronized way and over supra-galactic spatial scales.
To study exotic excitations described by parafermions in the possible spin liquid states of SU($n$) spin systems, we introduce a parafermion parton approach. The SU($n$) spin operators can be represented by clock and shift matrices, which are shown to be the polynomials of parafermion operators in the parafermion representation. We find that SU($n$) spins can be decomposed into $n$ parafermion matrices of degree one. In this decomposition, the spin has a $\{\bigotimes{\rm SU}(n)\}^{n-1}$ gauge symmetry. As an application, we study the one-dimensional three-state clock model and generalized Kitaev model by a mean-field theory, both of them have been proved to be related to parafermion excitations. We find that with the symmetries of translations, $6$-fold rotation and combination of parity and time reversal, there are $9$ types and $102$ solutions for two-dimensional $Z_3$ parafermion spin liquids on the honeycomb lattice. On the contrast, there are $9$ types and $36$ solutions if both parity and time-reversal symmetries are present. Our results provide a novel route for the systematic search of new types of spin liquids with exotic anyon excitations.
A signed bipartite (simple) graph $(G, \sigma)$ is said to be $C_{-4}$-critical if it admits no homomorphism to $C_{-4}$ (a negative 4-cycle) but every proper subgraph of it does. In this work, first of all we show that the notion of 4-coloring of graphs and signed graphs is captured, through simple graph operations, by the notion of homomorphism to $C_{-4}$. In particular, the 4-color theorem is equivalent to: Given a planar graph $G$, the signed bipartite graph obtained from $G$ by replacing each edge with a negative path of length 2 maps to $C_{-4}$.   We prove that, except for one particular signed bipartite graph on 7 vertices and 9 edges, any $C_{-4}$-critical signed graph on $n$ vertices must have at least $\lceil\frac{4n}{3}\rceil$ edges, and that this bound or $\lceil\frac{4n}{3}\rceil+1$ is attained for each value of $n\geq 9$. As an application, we conclude that all signed bipartite planar graphs of negative girth at least $8$ map to $C_{-4}$. Furthermore, we show that there exists an example of a signed bipartite planar graph of girth $6$ which does not map to $C_{-4}$, showing $8$ is the best possible and disproving a conjecture of Naserasr, Rollova and Sopena, in extension of the above mentioned restatement of the 4CT.
We report the results of low-temperature thermal and magnetic measurements on Ba$_3$CoNb$_2$O$_9$ powder, described as a uniform triangular-lattice antiferromagnet (TLAF) with a fictitious spin-1/2. Ba$_3$CoNb$_2$O$_9$ is found to undergo two-step antiferromagnetic transitions at $T_{\rm N1}=1.39~{\rm K}$ and $T_{\rm N2}=1.13~{\rm K}$. As the magnetic field is increased, both $T_{\rm N1}$ and $T_{\rm N2}$ monotonically decrease. The magnetic field vs temperature phase diagram indicates that the exchange interactions are nearly of the Heisenberg type with weak easy-axis anisotropy and that the exchange interaction between triangular lattices is crucial, in contrast to the case of the quasi-two-dimensional TLAF Ba$_3$CoSb$_2$O$_9$ [Susuki {\it et al}., Phys. Rev. Lett. \textbf{110}, 267201 (2013)].
We show that all zero energy eigenstates of an arbitrary $m$--state quantum spin chain Hamiltonian with nearest neighbor interaction in the bulk and single site boundary terms, which can also describe the dynamics of stochastic models, can be written as matrix product states. This means that the weights in these states can be expressed as expectation values in a Fock representation of an algebra generated by $2m$ operators fulfilling $m^2$ quadratic relations which are defined by the Hamiltonian.
We study general symmetric powers $S^k L^{[n]}$ of a tautological bundle $L^{[n]}$ on the Hilbert scheme $X^{[n]}$ of $n$ points over a smooth quasi-projective surface $X$, associated to a line bundle $L$ on $X$. Let $V_L$ be the $\mathfrak{S}_n$-vector bundle on $X^n$ defined as the exterior direct sum $L \boxplus \cdots \boxplus L$. We prove that the Bridgeland-King-Reid transform $\mathbf{\Phi}(S^k L^{[n]})$ of symmetric powers $S^k L^{[n]}$ is quasi isomorphic to the last term of a finite decreasing filtration on the natural vector bundle $S^k V_L$, defined by kernels of operators $D^l_L$, which operate locally as higher order restrictions to pairwise diagonals. We use this description and the natural filtration on $(S^k V_L)^{\mathfrak{S}_n}$ induced by the decomposition in direct sum, to obtain, for $n =2$ or $k \leq 4$, a finite decreasing filtration $\mathcal{W}^\bullet$ on the direct image $\mu_*(S^k L^{[n]})$ for the Hilbert-Chow morphism whose graded sheaves we control completely. As a consequence of this structural result, we obtain a chain of cohomological consequences, like a spectral sequence abutting to the cohomology of symmetric powers $S^k L^{[n]}$, an effective vanishing theorem for the cohomology of symmetric powers $S^k L^{[n]} \otimes \mathcal{D}_A$ twisted by the determinant, in presence of adequate positivity hypothesis on $L$ and $A$, as well as universal formulas for their Euler-Poincar\'e characteristic.
The dynamics of the solar wind depends intrinsically on the structure of the global solar magnetic field, which undergoes fundamental changes over the 11-yr solar cycle. For instance, the wind terminal velocity is thought to be anti-correlated with the expansion factor, a measure of how the magnetic field varies with height in the solar corona, usually computed at a fixed height ($\approx 2.5 R_{\odot}$, the source surface radius which approximates the distance at which all magnetic field lines become open). However, the magnetic field expansion affects the solar wind in a more detailed way, its influence on the solar wind properties remaining significant well beyond the source surface. We demonstrate this using 3D global MHD simulations of the solar corona, constrained by surface magnetograms over half a solar cycle (1989-2001). A self-consistent expansion beyond the solar wind critical point (even up to $10R_{\odot}$) makes our model comply with observed characteristics of the solar wind, namely, that the radial magnetic field intensity becomes latitude independent at some distance from the Sun, and that the mass flux is mostly independent of the terminal wind speed. We also show that near activity minimum, the expansion in the higher corona has more influence on the wind speed than the expansion below $2.5 R_{\odot}$.
A variational problem for three-dimensional (3D) classical lattice models is considered with trial state given by two-dimensional (2D) uniform product of local variational weights. This approach, the tensor product variational approach (TPVA), has been applied to 3D classical models (the Ising and the Potts models). We consider a way of estimating the magnetic critical exponent $\beta$ for the simple 3D Ising model assuming a functional form of the spontaneous magnetization in the off critical region, where the TPVA provides reliable data.
Recent experimental progress in coupling nanoscale conductors to superconducting microwave cavities has opened up for transport investigations of the deep quantum limit of light-matter interactions, with tunneling electrons strongly coupled to individual cavity photons. We have investigated theoretically the most basic cavity-conductor system with strong, single photon induced non-local transport effects; two spatially separated double quantum dots (DQD:s) resonantly coupled to the fundamental cavity mode. The system, described by a generalized Tavis-Cummings model, is investigated within a quantum master equation formalism, allowing us to account for both the electronic transport properties through the DQD:s as well as the coherent, non-equilibrium cavity photon state. We find sizeable non-locally induced current and current cross-correlations mediated by individual photons. From a full statistical description of the electron transport we further reveal a dynamical channel blockade in one DQD lifted by photon emission due to tunneling through the other DQD. Moreover, large entanglement between the orbital states of electrons in the two DQD:s is found for small DQD-lead temperatures.
We experimentally demonstrate that in magnetostrictive ferrimagnetic single crystal of CoFe2O4 there is clear correlation between magnetostriction and magnetoreflection of unpolarized light in the infrared range. The influence of magnetic field on specular reflection is likely to be indirect: application of a magnetic field results in strong strain and deformation of the crystal lattice, which leads to the change in electron energy structure and hence reflection spectrum.
Defining an efficient training set is one of the most delicate phases for the success of remote sensing image classification routines. The complexity of the problem, the limited temporal and financial resources, as well as the high intraclass variance can make an algorithm fail if it is trained with a suboptimal dataset. Active learning aims at building efficient training sets by iteratively improving the model performance through sampling. A user-defined heuristic ranks the unlabeled pixels according to a function of the uncertainty of their class membership and then the user is asked to provide labels for the most uncertain pixels. This paper reviews and tests the main families of active learning algorithms: committee, large margin and posterior probability-based. For each of them, the most recent advances in the remote sensing community are discussed and some heuristics are detailed and tested. Several challenging remote sensing scenarios are considered, including very high spatial resolution and hyperspectral image classification. Finally, guidelines for choosing the good architecture are provided for new and/or unexperienced user.
In this paper, we consider the state-dependent reflecting random walk on a half-strip. We provide explicit criteria for (positive) recurrence, and an explicit expression for the stationary distribution. As a consequence, the light-tailed behavior of the stationary distribution is proved under appropriate conditions. The key idea of the method employed here is the decomposition of the trajectory of the random walk and the main tool is the intrinsic branching structure buried in the random walk on a strip, which is different from the matrix-analytic method.
We report on results of N-body simulations aimed at testing the hypothesis that galaxies in X-ray emitting (i.e., virialized) Compact Groups are not tidally stripped when they are embedded in a common, massive, quiescent dark matter halo. To disentangle the effects of interactions from spurious effects due to an incorrect choice of the initial galaxy model configurations, these have been chosen to be tidally-limited King spheres, representing systems in quasi-equilibrium within the tidal field of the halo. The potential of the halo has been assumed to be frozen and the braking due to dynamical friction neglected. Our results confirm the hypothesis of low rates of tidal stripping and suggest a scenario for virialized Compact Group evolution in their quiescent phases with only very moderate tidally induced galaxy evolution can be generally expected. This implies the group stability, provided that the dynamical friction timescales in these systems are not much shorter than the Hubble time. We discuss briefly this possibility, in particular taking account of the similarity between the velocity dispersions of a typical virialized Compact Groups and the internal velocity dispersion of typical member galaxies. A number of puzzling observational data on Compact Groups can be easily explained in this framework. Other observations would be better understood as the result of enhanced merging activity in the proto-group environment, leading to virialized Compact Group formation through mergers of lower mass halos, as predicted by hierarchical scenarios of structure formation.
We introduce a new coarse grain model capable of describing the phase behavior of two dimensional ferromagnetic systems with competing exchange and dipolar interactions, as well as an external magnetic field. An improved expression for the mean field entropic contribution allows to compute the phase diagram in the whole temperature versus external field plane. We find that the topology of the phase diagram may be qualitatively different depending on the ratio between the strength of the competing interactions. In the regime relevant for ultrathin ferromagnetic films with perpendicular anisotropy we confirm the presence of inverse symmetry breaking from a modulated phase to a homogenous one as the temperature is lowered at constant magnetic field, as reported in experiments. For other values of the competing interactions we show that reentrance may be absent. Comparing thermodynamic quantities in both cases, as well as the evolution of magnetization profiles in the modulated phases, we conclude that the reentrant behavior is a consequence of the suppression of domain wall degrees of freedom at low temperatures at constant fields.
A black hole holographic model is used to mimic the behavior of the quark gluon plasma at finite temperature and density. This model reproduces lattice data at $\mu_B\!=\!0$ and displays critical behavior at large densities. High order baryon susceptibilities are used to extract freeze-out points by comparing those susceptibilities with the corresponding net-protons distribution measured by STAR. Possible experimental signatures of the critical end point are discussed.
We study the Bak-Sneppen model in the probabilistic framework of the Run Time Statistics (RTS). This model has attracted a large interest for its simplicity being a prototype for the whole class of models showing Self-Organized Criticality. The dynamics is characterized by a self-organization of almost all the species fitnesses above a non-trivial threshold value, and by a lack of spatial and temporal characteristic scales. This results in {\em avalanches} of activity power law distributed. In this letter we use the RTS approach to compute the value of $x_c$, the value of the avalanche exponent $\tau$ and the asymptotic distribution of minimal fitnesses.
We present structural measurements for the galaxies in the 0.05<z<0.0585 groups of the Zurich Environmental Study, aimed at establishing how galaxy properties depend on four environmental parameters: group halo mass M_GROUP, group-centric distance R/R_200, ranking into central or satellite, and large-scale structure density delta_LSS. Global galaxy structure is quantified both parametrically and non-parametrically. We correct all these measurements for observational biases due to PSF blurring and surface brightness effects as a function of galaxy size, magnitude, steepness of light profile and ellipticity. Structural parameters are derived also for bulges, disks and bars. We use the galaxy bulge-to-total ratios (B/T), together with the calibrated non-parametric structural estimators, to implement a quantitative morphological classification that maximizes purity in the resulting morphological samples. We investigate how the concentration C of satellite galaxies depends on galaxy mass for each Hubble type, and on M_GROUP, R/R_200 and delta_LSS. At galaxy masses M>10^10 M_sun, the concentration of disk satellites increases with increasing stellar mass, separately within each morphological bin of B/T. The known increase in concentration with stellar mass for disk satellites is thus due, at least in part, to an increase in galaxy central stellar density at constant B/T. The correlation between concentration and galaxy stellar mass becomes progressively steeper for later morphological types. The concentration of disk satellites shows a barely significant dependence on delta_LSS or R/R_200. The strongest environmental effect is found with group mass for M>10^10 M_sun disk-dominated satellites, which are ~10% more concentrated in high mass groups than in lower mass groups.
We identify the category Shv_{Nilp}(Bun_G) of automorphic sheaves with nilpotent singular support with its own dual, and relate this structure to the Serre functor on Shv_{Nilp}(Bun_G) and miraculous duality.
Sound propagation in a Fermi liquid with impurities is studied using the Landau-Boltzmann equation and the result is compared with a recent experiment in liquid ${}^3$He in aerogel by Northwestern University group. The sound absorption calculated using the fixed impurity model is a few orders of magnitude larger than the experiment. We take into account the simultaneous motion of aerogel molecules and propose a model in which the momentum loss of ${}^3$He quasi-particles during the collisions with the aerogel is converted to a drag force that acts on the aerogel molecules. This collision drag model gives a reasonable description for the temperature and the pressure dependence of observed sound velocity and absorption.
We propose a conformal field theory description of a solitonic heterotic string in type $IIA$ superstring theory compactified on $K3$, generalizing previous work by J. Harvey, A. Strominger and A. Sen. In ten dimensions the construction gives a fivebrane which is related to the fundamental type $II$ string by electric -- magnetic duality, and to the Dirichlet fivebrane of type $IIB$ string theory by $SL(2, Z)$.
Physicists are engaged in vigorous debate on the nature of the quantum critical points (QCP) governing the low-temperature properties of heavy-fermion (HF) metals. Recent experimental observations of the much-studied compound YbRh2Si2 in the regime of vanishing temperature incisively probe the nature of its magnetic-field-tuned QCP. The jumps revealed both in the residual resistivity rho_0 and the Hall resistivity R_H, along with violation of the Wiedemann-Franz law, provide vital clues to the origin of such non-Fermi-liquid behavior. The empirical facts point unambiguously to association of the observed QCP with a fermion-condensation phase transition. Based on this insight, the resistivities rho_0 and R_H are predicted to show jumps at the crossing of the QCP produced by application of a magnetic field, with attendant violation of the Wiedemann-Franz law. It is further demonstrated that experimentally identifiable multiple energy scales are related to the scaling behavior of the effective mass of the quasiparticles responsible for the low-temperature properties of such HF metals.
We develop a simple $O((\log n)^2)$ test as an extension of Proth's test for the primality for $p2^n+1$, $p>2^n$. This allows for the determination of large, non-Sierpinski primes $p$ and the smallest $n$ such that $p2^n+1$ is prime. If $p$ is a non-Sierpinski prime, then for all $n$ where $p2^n+1$ passes the initial test, $p2^n+1$ is prime with $3$ as a primitive root or is primover and divides the base $3$ Fermat Number, $GF(3,n-1)$. We determine the form the factors of any composite overpseudoprime that passes the initial test take by determining the form that factors of $GF(3,n-1)$ take.
In this paper we present a large-scale sensitivity study of reaction rates in the main component of the $s$ process. The aim of this study is to identify all rates, which have a global effect on the $s$ process abundance distribution and the three most important rates for the production of each isotope. We have performed a sensitivity study on the radiative $^{13}$C-pocket and on the convective thermal pulse, sites of the $s$ process in AGB stars. We identified 22 rates, which have the highest impact on the $s$-process abundances in AGB stars.
We show that any weak solution to the full Navier-Stokes-Fourier system emanating from the data belonging to the Sobolev space W^{3,2} remains regular as long as the velocity gradient is bounded. The proof is based on the weak-strong uniqueness property and parabolic a priori estimates for the local strong solutions.
We present a Neutrino-Factory-based setup with three detectors of different kind in principle capable to solve the eightfold-degeneracy in the simultaneous measurement of $\theta_{13}$ and $\delta$, for $\theta_{13} \geq 1^\circ (\sin^2 (2 \theta_{13}) \geq 10^{-3})$. Our setup includes a Superbeam-driven water Cherenkov (the Superbeam conceived as the first stage of the Neutrino Factory); two muon-storage-ring-driven detectors (namely, a large magnetized iron calorimeter and an emulsion cloud chamber) to take advantage of both the so-called "golden" ($\nu_e \to \nu_\mu$) and "silver" ($\nu_e \to \nu_\tau$) channels.
There is general agreement that the MiSaTaQuWa equations should describe the motion of a "small body" in general relativity, taking into account the leading order self-force effects. However, previous derivations of these equations have made a number of ad hoc assumptions and/or contain a number of unsatisfactory features. For example, all previous derivations have invoked, without proper justification, the step of "Lorenz gauge relaxation", wherein the linearized Einstein equation is written down in the form appropriate to the Lorenz gauge, but the Lorenz gauge condition is then not imposed--thereby making the resulting equations for the metric perturbation inequivalent to the linearized Einstein equations. In this paper, we analyze the issue of "particle motion" in general relativity in a systematic and rigorous way by considering a one-parameter family of metrics, $g_{ab} (\lambda)$, corresponding to having a body (or black hole) that is "scaled down" to zero size and mass in an appropriate manner. We prove that the limiting worldline of such a one-parameter family must be a geodesic of the background metric, $g_{ab} (\lambda=0)$. Gravitational self-force--as well as the force due to coupling of the spin of the body to curvature--then arises as a first-order perturbative correction in $\lambda$ to this worldline. No assumptions are made in our analysis apart from the smoothness and limit properties of the one-parameter family of metrics. Our approach should provide a framework for systematically calculating higher order corrections to gravitational self-force, including higher multipole effects, although we do not attempt to go beyond first order calculations here. The status of the MiSaTaQuWa equations is explained.
We checked Eling-Oz formula [1] for the bulk viscosity of the holographic fluid dual to the exotic black holes [2]. Initially, Eling and Oz argued that the formula is valid in the high temperature and adiabatic limits. In [3] the validity of the formula for $\caln=2^*$ plasma and cascading gauge theory was pushed forward for arbitrary temperatures. We successfully verified the formula with the computations of the bulk viscosity [4,5] for a wide range of the temperatures. Moreover, it correctly reproduces the critical behavior in the vicinity of the critical point, where the bulk-to-shear viscosity diverges.