ShantanuT01/DACTYL-Pretraining huggingface dataset:
Let $(X,B)$ be a complex projective klt pair, and let $f\colon X\to Z$ be a surjective morphism onto a normal projective variety with maximal albanese dimension such that $K_X+B$ is relatively big over $Z$. We show that such pairs have good log minimal models.
We show that energy deposited into an expanding supernova remnant by a highly magnetic (B ~ 5 x 10^14 G) neutron star spinning at an initial period of P ~ 2-20 ms can substantially brighten the light curve. For magnetars with parameters in this range, the rotational energy is released on a timescale of days to weeks, which is comparable to the effective diffusion time through the supernova remnant. The late time energy injection can then be radiated without suffering overwhelming adiabatic expansion losses. The magnetar input also produces a central bubble which sweeps ejecta into an internal dense shell, resulting in a prolonged period of nearly constant photospheric velocity in the observed spectra. We derive analytic expressions for the light curve rise time and peak luminosity as a function of B, P and the properties of the supernova ejecta that allow for direct inferences about the underlying magnetar in bright supernovae. We perform numerical radiation hydrodynamical calculations of a few specific instances and compare the resulting light curves to observed events. Magnetar activity is likely to impact more than a few percent of all core collapse supernovae, and may naturally explain some of the brightest events ever seen (e.g., SN 2005ap and SN 2008es) at L > 10^44 ergs/s.
Single Fe atoms on Au(111) surfaces were hydrogenated and dehydrogenated with the Au tip of a low-temperature scanning tunneling microscope (STM). Fe and FeH$_2$ were contacted with the tip of the microscope and show distinctly different evolutions of the conductance with the tip-substrate distance. The current shot noise of these contacts has been measured and indicates a single relevant conductance channel with the spin-polarized transmission. For FeH$_2$ the spin polarization reaches values up to 80\% for low conductances and is reduced if the tip-surface distance is decreased. These observations are partially reproduced using density functional theory (DFT) based transport calculations. We suggest that the quantum motion of the hydrogen atoms, which is not taken into account in our DFT modeling, may have a significant effect on the results.
Topological phases are unique states of matter which support non-local excitations which behave as particles with fractional statistics. A universal characterization of gapped topological phases is provided by the topological entanglement entropy (TEE). We study the finite size corrections to the TEE by focusing on systems with $Z_2$ topological ordered state using density-matrix renormalization group (DMRG) and perturbative series expansions. We find that extrapolations of the TEE based on the Renyi entropies with Renyi index $n\geq 2$ suffer from much larger finite size corrections than do extrapolations based on the von Neumann entropy. In particular, when the circumference of the cylinder is about ten times the correlation length, the TEE obtained using von Neumann entropy has an error of order $10^{-3}$, while for Renyi entropies it can even exceed 40%. We discuss the relevance of these findings to previous and future searches for topological ordered phases, including quantum spin liquids.
We analyze plasma dispersion and scattering of fast radio bursts (FRBs) to identify the dominant locations of free electrons along their lines of sight and thus constrain the distances of the burst sources themselves. We establish the average $\tau$-DM relation for Galactic pulsars and use it as a benchmark for discussing FRB scattering. Though scattering times $\tau$ for FRBs are large in the majority of the 17 events we analyze, they are systematically smaller than those of Galactic pulsars that have similar dispersion measures (DMs). The lack of any correlation between $\tau$ and DM for FRBs suggests that the intergalactic medium (IGM) cannot account for both $\tau$ and DM. We therefore consider mixed models involving the IGM and host galaxies. If the IGM contributes significantly to DM while host galaxies dominate $\tau$, the scattering deficit with respect to the mean Galactic trend can be explained with a $\tau$-DM relation in the host that matches that for the Milky Way. However, it is possible that hosts dominate both $\tau$ and DM, in which case the observed scattering deficits require free electrons in the host to be less turbulent than in the Galaxy, such as if they are in hot rather than warm ionized regions. Our results imply that distances or redshifts of FRB sources can be significantly overestimated if they are based on the assumption that the extragalactic portion of DM is dominated by the IGM.
Research on 2D materials has been one of the fastest-growing fields in condensed matter physics and materials science in the past 10 years. The low dimensionality and strong correlations of 2D systems give rise to electronic and structural properties, in the form of collective excitations, that do not have counterparts in ordinary 3D materials used in modern technology. These 2D materials present extraordinary opportunities for new technologies, such as in flexible electronics. In this Review, we focus on plasmons, excitons, phonons and magnons in 2D materials. We discuss the theoretical formalism of these collective excitations and elucidate how they differ from their 3D counterparts.
We have a very limited knowledge about how the confinement mechanism works in processes like $\epea\epe\ra\epq\epqa\ggn\ldots\ggn$, when there are identical colour charges. In this case the partons can be connected by a string or a cluster chain in several different ways. We do not know if in such a situation Nature chooses a particular configuration at random, or if some configuration is dynamically favoured. Also in the perturbative parton cascade we have no well founded recipe for describing the interference effects, which correspond to non planar diagrams and are caused by identical colour charges. We have studied two different models, and are in particular interested in the possibility that a colour singlet gluon system hadronizes isolated from the remainder of the state. Using double tagged events with heavy $\epc\epca$ or $\epb\epba$ quarks, it appears to be possible to find a significant signal, if such events appear in Nature.   If this type of (re)connected states appear in Z decays it may also be an indication that reconnection might appear between the decay products of two W's in the reaction $\epea\epe\ra\gwp\gwm\ra\epq_1\epqa_2\epQ_1\epQa_2$ at LEP2. This would be important e.g. for a precision measurement of the W mass.
We use the random phase approximation to describe the muon capture rate on ${}^{44}$Ca,${}^{48}$Ca, ${}^{56}$Fe, ${}^{90}$Zr, and ${}^{208}$Pb. With ${}^{40}$Ca as a test case, we show that the Continuum Random Phase Approximation (CRPA) and the standard RPA give essentially equivalent descriptions of the muon capture process. Using the standard RPA with the free nucleon weak form factors we reproduce the experimental total capture rates on these nuclei quite well. Confirming our previous CRPA result for the $N = Z$ nuclei, we find that the calculated rates would be significantly lower than the data if the in-medium quenching of the axial-vector coupling constant were employed.
In statistical mechanics Gibbs' paradox is avoided if the particles of a gas are assumed to be indistinguishable. The resulting entropy then agrees with the empirically tested thermodynamic entropy up to a term proportional to the logarithm of the particle number. We discuss here how analogous situations arise in the statistical foundation of black-hole entropy. Depending on the underlying approach to quantum gravity, the fundamental objects to be counted have to be assumed indistinguishable or not in order to arrive at the Bekenstein--Hawking entropy. We also show that the logarithmic corrections to this entropy, including their signs, can be understood along the lines of standard statistical mechanics. We illustrate the general concepts within the area quantization model of Bekenstein and Mukhanov.
Extracting reliable low-energy information from string compactifications notoriously requires a detailed understanding of the UV sensitivity of the corresponding effective field theories. Despite past efforts in computing perturbative string corrections to the tree-level action, neither a systematic approach nor a unified framework has emerged yet. We make progress in this direction, focusing on the moduli dependence of perturbative corrections to the 4D scalar potential of type IIB Calabi-Yau orientifold compactifications. We proceed by employing two strategies. First, we use two rescaling symmetries of type IIB string theory to infer the dependence of any perturbative correction on both the dilaton and the Calabi-Yau volume. Second, we use F/M-theory duality to conclude that KK reductions on elliptically-fibred Calabi-Yau fourfolds of the M-theory action at any order in the derivative expansion can only generate $(\alpha')^{\rm even}$ corrections to the 4D scalar potential, which, moreover, all vanish for trivial fibrations. We finally give evidence that $(\alpha')^{\rm odd}$ effects arise from integrating out KK and winding modes on the elliptic fibration and argue that the leading no-scale breaking effects at string tree-level arise from $(\alpha')^3$ effects, modulo potential logarithmic corrections.
Let J be an abelian surface with a generic ample line bundle O(1). For n>0, the moduli space M(2, 0, 2n) of O(1)-semistable sheaves F of rank 2 with Chern classes c_1(F) = 0, c_2(F) = 2n is a singular projective variety, endowed with a holomorphic symplectic structure on the smooth locus. In this paper, we show that there does not exist a crepant resolution of M(2; 0; 2n) for n>1. This certainly implies that there is no symplectic desingularization of M(2, 0, 2n) for n>1.
In previous works, the authors investigated the relationships between linear stability of a generated linear series $|V|$ on a curve $C$, and slope stabillity of the vector bundle $M_{V,L} := \ker (V \otimes \mathcal{O}_C \to L)$. In particular, the second named author and L. Stoppino conjecture that, for a complete linear system $|L|$, linear (semi)stability is equivalent to slope (semi)stability of $M_V$, and the first and third named authors proved that this conjecture holds for hyperelliptic and for generic curves.   In this work we provide a counterexample to this conjecture on any smooth plane curve of degree $7$.
The randomly oriented graph $G_{n,p}^{\sigma}$ is an Erd\H{o}s-R\'enyi random graph $G_{n,p}$ with a random orientation $\sigma$, which assigns to each edge a direction so that $G_{n,p}^{\sigma}$ becomes a directed graph. Denote by $S_n$ the skew-adjacency matrix of $G_{n,p}^{\sigma}$. Under some mild assumptions, it is proved in this paper that, the spectral distribution of $S_n$ (under some normalization) converges to the standard semicircular law almost surely as $n\rightarrow\infty$. It is worth mentioning that our result does not require finite moments of the entries of the underlying random matrix.
In the last decade, the viscous decretion disk model has emerged as the new paradigm for Be star disks. In this contribution, we propose a simple analytical model to estimate the continuum infrared excess arising from these circumstellar disks, in the light of the currently accepted scenario. We demonstrate that the disk can be satisfactorily described by a two component system: an inner optically thick region, which we call the pseudo-photosphere, and a diffuse outer part. In particular, a direct connexion between the disk brightness profile and the thermal structure is derived, and then confronted to realistic numerical simulations. This result quantifies how the non-isothermality of the disk ultimately affects both infrared measured fluxes and visibilities.
In this paper, we prove the existence of a weak solution for the Dirichlet boundary value problem related to the $p(x)-$Laplacian $$ -\mbox{div}(|\nabla u|^{p(x)-2}\nabla u)+u\in -[\underline{g}(x,u),\overline{g}(x,u)], $$ by using the degree theory after turning the problem into a Hammerstein equation. The right hand side $g$ is a possibly discontinuous function in the second variable satisfying some non-standard growth conditions..
New simulations demonstrate that low-mode, nonradial hydrodynamic instabilities of the accretion shock help starting hot-bubble convection in supernovae and thus support explosions by the neutrino-heating mechanism. The prevailing conditions depend on the high-density equation of state which governs stellar core collapse, core bounce, and neutron star formation. Tests of this sensitivity to nuclear physics variations are shown for spherically symmetric models. Implications of current explosion models for r-process nucleosynthesis are addressed.
Based directly on the microscopic lattice dynamics, a simple high temperature expansion can be devised for non-equilibrium steady states. We apply this technique to investigate the disordered phase and the phase diagram for a driven bilayer lattice gas at half filling. Our approximation captures the phases first observed in simulations, provides estimates for the transition lines, and allows us to compute signature observables of non-equilibrium dynamics, namely, particle and energy currents. Its focus on non-universal quantities offers a useful analytic complement to field-theoretic approaches.
We propose an approach to compute the boundary crossing probabilities for a class of diffusion processes which can be expressed as piecewise monotone (not necessarily one-to-one) functionals of a standard Brownian motion. This class includes many interesting processes in real applications, e.g., Ornstein-Uhlenbeck, growth processes and geometric Brownian motion with time dependent drift. This method applies to both one-sided and two-sided general nonlinear boundaries, which may be discontinuous. Using this approach explicit formulas for boundary crossing probabilities for certain nonlinear boundaries are obtained, which are useful in evaluation and comparison of various omputational algorithms. Moreover, numerical computation can be easily done by Monte Carlo integration and the approximation errors for general boundaries are automatically calculated. Some numerical examples are presented.
Electronic screening renormalizes the linear bands of graphene and in the vicinity of the Dirac point, creates a diamond shaped structure in the quasiparticle spectral density. This is a result of electron-plasmon scattering processes which produce a finite momentum feature referred to as the `plasmaron ring'. In this work we explore the effects of uniaxial strain on these spectral features with the aim of understanding how strain modifies correlations. We derive and calculate the spectral density to the G$_0$W-RPA level which allows us to identify the dispersive behaviour of the diamond geometry, and thus electron-plasmon scattering, for variation in electron-electron coupling strength and magnitude of applied strain. We find that the application of strain changes the geometry (in momentum) of the electron-plasmon scattering and that renormalizations beyond simple geometrical scalings further enhance this effect. These results suggest that the properties of the plasmaron ring can be tuned through the application of uniaxial strain, effectively producing a larger fine structure constant without the need to change the sample substrate.
We calculate the electroweak corrections to the production of WWZ and ZZZ at the linear collider in the Standard Model. These processes are important for the extraction of the quartic couplings of the massive gauge bosons which can be a window on the mechanism of spontaneous symmetry breaking. We find that the weak corrections to some kinematic distributions show new features and hence cannot be explained by an overall scale factor.
We study the environmental dependence of color, stellar mass, and morphology by comparing galaxies in a forming cluster to those in the field at z = 1:6 with Hubble Space Telescope near-infrared imaging in the CANDELS/UDS field. We quantify the morphology of the galaxies using the effective radius, reff, and S\'ersic index, n. In both the cluster and field, approximately half of the bulge-dominated galaxies (n > 2) reside on the red sequence of the color-magnitude diagram, and most disk-dominated galaxies (n < 2) have colors expected for star-forming galaxies. There is weak evidence that cluster galaxies have redder rest-frame U - B colors and higher stellar masses compared to the field. Star-forming galaxies in both the cluster and field show no significant differences in their morphologies. In contrast, there is evidence that quiescent galaxies in the cluster have larger median effective radii and smaller S\'ersic indices compared to the field with a significance of 2?. These differences are most pronounced for galaxies at clustercentric distances 1 Mpc < Rproj < 1.5 Mpc, which have low S\'ersic indices and possibly larger effective radii, more consistent with star-forming galaxies at this epoch and in contrast to other quiescent galaxies. We argue that star-forming galaxies are processed under the influence of the cluster environment at distances greater than the cluster-halo virial radius. Our results are consistent with models where gas accretion onto these galaxies is suppressed from processes associated with the cluster environment.
The X9.3 flare of September 6, 2017, was the most powerful flare of Solar Cycle 24. It generated strong white-light emission and multiple helioseismic waves (sunquakes). By using data from Helioseismic and Magnetic Imager (HMI) onboard the Solar Dynamics Observatory (SDO) as well as hard X-ray data from KONUS instrument onboard WIND spacecraft, and Anti-Coincidence System (ACS) onboard the INTERGRAL space observatory, we investigate spatio-temporal dynamics of photospheric emission sources, identify sources of helioseismic waves and compare the flare photospheric dynamics with the hard X-ray (HXR) temporal profiles. The results show that the photospheric flare impacts started to develop in compact regions in close vicinity of the magnetic polarity inversion line (PIL) in the pre-impulsive phase before detection of the HXR emission. The initial photospheric disturbances were localized in the region of strong horizontal magnetic field of the PIL, and, thus, are likely associated with a compact sheared magnetic structure elongated along the PIL. The acoustic egression power maps revealed two primary sources of generation of sunquakes, which were associated with places of the strongest photospheric impacts in the pre-impulsive phase and the early impulsive phase. This can explain the two types of helioseismic waves observed in this flare. Analysis of the high-cadence HMI filtergrams suggests that the flare energy release developed in the form of sequential involvement of compact low-lying magnetic loops that were sheared along the PIL.
The "slope-number" of a graph $G$ is the minimum number of distinct edge slopes in a straight-line drawing of $G$ in the plane. We prove that for $\Delta\geq5$ and all large $n$, there is a $\Delta$-regular $n$-vertex graph with slope-number at least $n^{1-\frac{8+\epsilon}{\Delta+4}}$. This is the best known lower bound on the slope-number of a graph with bounded degree. We prove upper and lower bounds on the slope-number of complete bipartite graphs. We prove a general upper bound on the slope-number of an arbitrary graph in terms of its bandwidth. It follows that the slope-number of interval graphs, cocomparability graphs, and AT-free graphs is at most a function of the maximum degree. We prove that graphs of bounded degree and bounded treewidth have slope-number at most $O(\log n)$. Finally we prove that every graph has a drawing with one bend per edge, in which the number of slopes is at most one more than the maximum degree. In a companion paper (http://arxiv.org/abs/math/0606450), planar drawings of graphs with few slopes are also considered.
Hankel tensors are generalizations of Hankel matrices. This article studies the relations among various ranks of Hankel tensors. We give an algorithm that can compute the Vandermonde ranks and decompositions for all Hankel tensors. For a generic $n$-dimensional Hankel tensor of even order or order three, we prove that the the cp rank, symmetric rank, border rank, symmetric border rank, and Vandermonde rank all coincide with each other. In particular, this implies that the Comon's conjecture is true for generic Hankel tensors when the order is even or three. Some open questions are also posed.
It is shown that the experimental results reported in cond-mat/0010412 do not invalidate the well-known expression for the Kelvin force density in ferrofluids.
The optimal discrimination of non-orthogonal quantum states with minimum error probability is a fundamental task in quantum measurement theory as well as an important primitive in optical communication. In this work, we propose and experimentally realize a new and simple quantum measurement strategy capable of discriminating two coherent states with smaller error probabilities than can be obtained using the standard measurement devices; the Kennedy receiver and the homodyne receiver.
Monolayer transition metal dichalcogenides (TMDs) offer new opportunities for realizing quantum dots (QDs) in the ultimate two-dimensional (2D) limit. Given the rich control possibilities of electron valley pseudospin discovered in the monolayers, this quantum degree of freedom can be a promising carrier of information for potential quantum spintronics exploiting single electrons in TMD QDs. An outstanding issue is to identify the degree of valley hybridization, due to the QD confinement, which may significantly change the valley physics in QDs from its form in the 2D bulk. Here we perform a systematic study of the intervalley coupling by QD confinement potentials on extended TMD monolayers. We find that the intervalley coupling in such geometry is generically weak due to the vanishing amplitude of the electron wavefunction at the QD boundary, and hence valley hybridization shall be well quenched by the much stronger spin-valley coupling in monolayer TMDs and the QDs can well inherit the valley physics of the 2D bulk. We also discover sensitive dependence of intervalley coupling strength on the central position and the lateral length scales of the confinement potentials, which may possibly allow tuning of intervalley coupling by external controls
In our theoretical study where we combine a nonequilibrium Green's function (NEGF) approach with density functional theory (DFT) we investigate branched compounds containing ferrocene moieties in both branches which due to their metal centers are designed to allow for asymmetry induced by local charging. In these compounds the ferrocene moieties are connected to pyridyl anchor groups either directly or via acetylenic spacers in a meta-connection where we also compare our results with those obtained for the respective single-branched molecules with both meta- and para-connections between the metal center and the anchors. We find a destructive quantum interference (DQI) feature in the transmission function slightly below the lowest unoccupied molecular orbital (LUMO) which dominates the conductance even for the uncharged branched compound with spacer groups inserted. In an analysis based on mapping the structural characteristics of the range of molecules in our article onto tight-binding models, we identify the structural source of the DQI minimum as the through-space coupling between the pyridyl anchor groups. We also find that local charging on one of the branches only changes the conductance by about one order of magnitude which we explain in terms of the spatial distributions of the relevant molecular orbitals for the branched compounds.