ShantanuT01/DACTYL-Pretraining huggingface dataset:
We prove a logarithmic convexity result for exponentially weighted $L^2$-norms of solutions to electromagnetic Schr\"odinger equation, without needing to assume smallness of the magnetic potential. As a consequence, we can prove a unique continuation result in the style of the Hardy uncertainty principle, which generalizes the analogous theorems which have been recently proved by Escauriaza, Kenig, Ponce and Vega.
The nature of the hard X-ray source XSSJ12270-4859 is still unclear though it was claimed to be a magnetic Cataclysmic Variable. We here present a broad-band X-ray and gamma ray study based on a recent XMM-Newton observation and archival INTEGRAL and RXTE data. From the Fermi/LAT 1-year point source catalogue, we tentatively associate XSSJ12270-4859 with 1FGLJ1227.9-4852, a source of high energy gamma rays with emission up to 10GeV. We complement the study with UV photometry from XMM-Newton and ground-based optical and near-IR photometry. The X-ray emission is highly variable showing flares and intensity dips. The X-ray flares consist of flare-dip pairs. Flares are also detected in the UV range but not the dips. Aperiodic dipping behaviour is also observed during X-ray quiescence but not in the UV. The 0.2-100keV spectrum is featureless and described by a power law model with Gamma=1.7. The 100MeV-10GeV spectrum is instead represented by a power law index of 2.45. The luminosity ratio between 0.1-100GeV and 0.2--100keV is ~0.8, hence the GeV emission is a significant component of the total energy output. Furthermore, the X-ray spectrum does not greatly change during flares, quiescence and the dips seen in quiescence but it hardens during the post-flare dips. Optical photometry reveals a period of 4.32hr likely related to the binary orbit. Near-IR, possibly ellipsoidal, variations are detected. Large amplitude variability on shorter (tens mins) timescales are found to be non-periodic. The observed variability at all wavelengths and the spectral characteristics strongly favour a low-mass atypical low-luminosity X-ray binary and are against a Cataclysmic Variable nature. The association with a Fermi/LAT high energy gamma ray source further strengths this interpretation.
We have used neutron diffraction measurements to study the zero-field magnetic structure of the intermetallic compound Yb3Pt4, which was earlier found to order antiferromagnetically at the Neel temperature TN=2.4 K, and displays a field-driven quantum critical point at 1.6 T. In Yb3Pt4, the Yb moments sit on a single low-symmetry site in the rhombohedral lattice with space group R-3. The Yb ions form octahedra with edges that are twisted with respect to the hexagonal unit cell, a twisting that results in every Yb ion having exactly one Yb nearest neighbor. Below TN, we found new diffracted intensity due to a k=0 magnetic structure. This magnetic structure was compared to all symmetry-allowed magnetic structures, and was subsequently refined. The best fitting magnetic structure model is antiferromagnetic, and involves pairs of Yb nearest neighbors on which the moments point almost exactly towards each other. This structure has moment components within the ab-plane as well as parallel to the c-axis, although the easy magnetization direction lies in the ab-plane. Our magnetization results suggest that besides the crystal-electric field anisotropy, anisotropic exchange favoring alignment along the c-axis is responsible for the overall direction of the ordered moments. The magnitude of the ordered Yb moments in Yb3Pt4 is 0.81 uB/Yb at 1.4 K. The analysis of the bulk properties, the size of the ordered moment, and the observation of well-defined crystal-field levels argue that the Yb moments are spatially localized in zero field.
We investigate the ground state of the system of N bosons enclosed in a hard-wall trap interacting via a repulsive or attractive $\delta$-function potential. Based on the Bethe ansatz method, the explicit ground state wave function is derived and the corresponding Bethe ansatz equations are solved numerically for the full physical regime from the Tonks limit to the strongly attractive limit. It is shown that the solution takes different form in different regime. We also evaluate the one body density matrix and second-order correlation function of the ground state for finite systems. In the Tonks limit the density profiles display the Fermi-like behavior, while in the strongly attractive limit the Bosons form a bound state of N atoms corresponding to the N-string solution. The density profiles show the continuous crossover behavior in the entire regime. Further the correlation function indicates that the Bose atoms bunch closer as the interaction constant decreases.
The status of the Standard Model (SM) is reviewed. We emphazize the fact that in spite of the success of the SM for the descrition of the fermionic sector, the status of the bosonic sector (gauge and scalar) suffers from many theoretical deficiencies and from the lack of empirical support. This situation, which leaves room for several types of extensions or alternatives to SM, strongly motivates the pursue of intense efforts for finding hints of New Physics (NP) effects. We present a phenomenological description valid for energies lying below the NP scale. We discuss the indirect constraints established from high precision tests at LEP1, as well as the direct tests that could be performed at future machines
In the standard model of cosmology, Cosmic Microwave Background (CMB) sky is expected to show no symmetry preferences. Following our previous studies, we explore the presence of any particular parity preference in the latest full-mission CMB temperature maps from ESA's Planck probe. Specifically, in this work, we will probe (a)symmetry in power between even and odd multipoles of CMB via it's angular power spectrum from Planck 2015 data. Further we also assess any specific preference for mirror parity (a)symmetry, by analysing the power contained in $l+m$=even or odd mode combinations.
In the decay chain B(d) --> Psi + K --> Psi + (pi l nu), neutral K mixing follows on the heels of neutral B mixing. This "cascade mixing" leads to an interference which probes cos(2*beta), where beta is one of the three CP-violating phase angles which characterize CP violation in the Standard Model. Widely-discussed future B-system experiments will determine trigonometric functions of these three phase angles, leaving the underlying angles themselves discretely ambiguous. A determination of cos(2*beta) through cascade mixing would eliminate all the discrete ambiguities entirely.
In quantum Shannon theory, the way information is encoded and decoded takes advantage of the laws of quantum mechanics, while the way communication channels are interlinked is assumed to be classical. In this Letter we relax the assumption that quantum channels are combined classically, showing that a quantum communication network where quantum channels are combined in a superposition of different orders can achieve tasks that are impossible in conventional quantum Shannon theory. In particular, we show that two identical copies of a completely depolarizing channel become able to transmit information when they are combined in a quantum superposition of two alternative orders. This finding runs counter to the intuition that if two communication channels are identical, using them in different orders should not make any difference. The failure of such intuition stems from the fact that a single noisy channel can be a random mixture of elementary, non-commuting processes, whose order (or lack thereof) can affect the ability to transmit information.
Neutrino-matter interactions play an important role in core-collapse supernova (CCSN) explosions as they contribute to both lepton number and/or four-momentum exchange between neutrinos and matter, and thus act as the agent for neutrino-driven explosions. Due to the multiscale nature of neutrino transport in CCSN simulations, an implicit treatment of neutrino-matter interactions is desired, which requires solutions of coupled nonlinear systems in each step of the time integration scheme. In this paper we design and compare nonlinear iterative solvers for implicit systems with energy coupling neutrino-matter interactions commonly used in CCSN simulations. Specifically, we consider electron neutrinos and antineutrinos, which interact with static matter configurations through the Bruenn~85 opacity set. The implicit systems arise from the discretization of a non-relativistic two-moment model for neutrino transport, which employs the discontinuous Galerkin (DG) method for phase-space discretization and an implicit-explicit (IMEX) time integration scheme. In the context of this DG-IMEX scheme, we propose two approaches to formulate the nonlinear systems -- a coupled approach and a nested approach. For each approach, the resulting systems are solved with Anderson-accelerated fixed-point iteration and Newton's method. The performance of these four iterative solvers has been compared on relaxation problems with various degree of collisionality, as well as proto-neutron star deleptonization problems with several matter profiles adopted from spherically symmetric CCSN simulations. Numerical results suggest that the nested Anderson-accelerated fixed-point solver is more efficient than other tested solvers for solving implicit nonlinear systems with energy coupling neutrino-matter interactions.
Let $f(x,y), g(x,y)$ denote either a pair of holomorphic function germs, or a pair of monic polynomials in $x$ whose coefficients are Laurent series in $y$. A relative polar arc is a Newton-Puiseux root, $x=\gamma(y)$, of the Jacobian $J=f_yg_x-f_xg_y$. We define the tree-model, $T(f,g)$, for the pair, using the contact orders of the Newton-Puiseux roots of $f$ and $g$. We then describe how the $\gamma$'s climb, and where they leave, the tree. We shall also show by two examples that the way the $\gamma$'s leave the tree is not an invariant of the tree; this phenomenon is in sharp contrast to that in the one function case where the tree completely determines how the polar roots split away. Our result yield a factorisation of the Jacobian determinant.
Most existing action quality assessment methods rely on the deep features of an entire video to predict the score, which is less reliable due to the non-transparent inference process and poor interpretability. We argue that understanding both high-level semantics and internal temporal structures of actions in competitive sports videos is the key to making predictions accurate and interpretable. Towards this goal, we construct a new fine-grained dataset, called FineDiving, developed on diverse diving events with detailed annotations on action procedures. We also propose a procedure-aware approach for action quality assessment, learned by a new Temporal Segmentation Attention module. Specifically, we propose to parse pairwise query and exemplar action instances into consecutive steps with diverse semantic and temporal correspondences. The procedure-aware cross-attention is proposed to learn embeddings between query and exemplar steps to discover their semantic, spatial, and temporal correspondences, and further serve for fine-grained contrastive regression to derive a reliable scoring mechanism. Extensive experiments demonstrate that our approach achieves substantial improvements over state-of-the-art methods with better interpretability. The dataset and code are available at \url{https://github.com/xujinglin/FineDiving}.
New high resolution, high sensitivity WSRT HI synthesis observations of the spiral galaxy NGC 3631 are presented. In the total atomic hydrogen map, the spiral arms are well distinguished from the interarm regions, while the sensitivity allows detection of HI in all but a few isolated regions of the areas between the spiral arms. Most of the atomic hydrogen is located within the optical disc, but the HI extends to some 1.5R_opt. The HI follows the spiral arms, and streaming motions of up to ~15 kms (projected) can be identified from the velocity field. Assuming a constant inclination angle of 17 deg, a rotation curve is derived which is slightly falling in the outer parts of the disc. Analysis of a residual velocity field, obtained after subtraction of an axisymmetric model based on the rotation curve, confirms the existence of streaming motions near the spiral arms in an otherwise undisturbed disc.
We give an exposition of recent results on regularity and Fredholm properties for first-order one-dimensional hyperbolic PDEs. We show that large classes of boundary operators cause an effect that smoothness increases with time. This property is the key in finding regularizers (parametrices) for hyperbolic problems. We construct regularizers for periodic problems for dissipative first-order linear hyperbolic PDEs and show that these problems are modeled by Fredholm operators of index zero.
When waves propagate through a complex or heterogeneous medium the wave field is corrupted by the heterogeneities. Such corruption limits the performance of imaging or communication schemes. One may then ask the question: is there an optimal way of encoding a signal so as to counteract the corruption by the medium? In the ideal situation the answer is given by time reversal: for a given target or focusing point, in a first step let the target emit a signal and then record the signal transmitted to the source antenna, time reverse this and use it as the source trace at the source antenna in a second step. This source will give a sharply focused wave at the target location if the source aperture is large enough. Here we address this scheme in the more practical situation with a limited aperture, time-harmonic signal, and finite-sized elements in the source array. Central questions are then the focusing resolution and signal-to-noise ratio at the target, their dependence on the physical parameters, and the capacity to focus selectively in the neighborhood of the target point and therefore to transmit images. Sharp results are presented for these questions.
Pseudo-$C_\ell$ quadratic estimators for CMB temperature and polarization power spectra have been used in the analysis pipelines of many CMB experiments, such as WMAP and Boomerang. In the polarization case, these estimators mix E and B modes, in the sense that the estimated B-mode power is nonzero for a noiseless CMB realization which contains only E-modes. Recently, Challinor & Chon showed that for moderately sized surveys ($f_{sky} \sim 0.01$), this mixing limits the gravity wave B-mode signal which can be detected using pseudo-$C_\ell$ estimators to $T/S \sim 0.05$. We modify the pseudo-$C_\ell$ construction, defining ``pure'' pseudo-$C_\ell$ estimators, which do not mix E and B modes in this sense. We study these estimators in detail for a survey geometry similar to that which has been proposed for the QUIET experiment, for a variety of noise levels, and both homogeneous and inhomogeneous noise. For noise levels $\simle 20$ $\mu$K-arcmin, our modification significantly improves the B-mode power spectrum errors obtained using pseudo-$C_\ell$ estimators. In the homogeneous case, we compute optimal power spectrum errors using a Fisher matrix approach, and show that our pure pseudo-$C_\ell$ estimators are roughly 80% of optimal, across a wide range of noise levels. There is no limit, imposed by the estimators alone, to the value of $T/S$ which can be detected.
A classification of the maximally extended solutions for 1+1 gravity models (comprising e.g. generalized dilaton gravity as well as models with non-trivial torsion) is presented. No restrictions are placed on the topology of the arising solutions, and indeed it is found that for generic models solutions on non-compact surfaces of arbitrary genus with an arbitrary non-zero number of holes can be obtained. The moduli space of classical solutions (solutions of the field equations with fixed topology modulo gauge transformations) is parametrized explicitly.
The effect of finite control beam on the transverse spatial profile of the slow light propagation in an electromagnetically induced transparency medium is studied. We arrive at a general criterion in terms of eigenequation, and demonstrate the existence of a set of localized, stationary transverse modes for the negative detuning of the probe signal field. Each of these diffraction-free transverse modes has its own characteristic group velocity, smaller than the conventional theoretical result without considering the transverse spatial effect.
We consider the distribution of the sum and the maximum of a collection of independent exponentially distributed random variables. The focus is laid on the explicit form of the density functions (pdf) of non-i.i.d. sequences. Those are recovered in a simple and direct way based on conditioning. A connection between the pdf and a representation of the convolution characteristic function as a linear combination of the single characteristic functions is drawn. It is demonstrated how the results on the pdf of order statistics and the convolution merge.
The current work shows the efficacy of Dzyaloshinshkii-Moriya (DM) interaction to free the bound entanglement. Based on the work [Sharma, K.K., Pandey, S.N., Quant. Info. Proc. 15, 1539 (2016)], we present further results in two qutrits bound entangled state proposed by Jurkovaski et al. We consider a closed system of two qutrits and an auxiliary qutrit which interacts with either one of the two qutrits in a closed system. We erase the auxiliary qutrit from the system by doing partial trace operation and open system dynamics has been studied. We have found, the probability amplitude of auxiliary qutrit does not affect the system, while DM interaction plays a major role to govern the dynamics. The realignment and CCNR criteria have been used to detect the bound entanglement in the state, while for quantification of entanglement the negativity has been used. We explored the dynamics with all the possible cases of Jurkowski et al. bound entangled state.
Raman spectra obtained by the inelastic scattering of light by crystalline solids contain contributions from first-order vibrational processes (e.g. the emission or absorption of one phonon, a quantum of vibration) as well as higher-order processes with at least two phonons being involved. At second order, coupling with the entire phonon spectrum induces a response that may strongly depend on the excitation energy, and reflects complex processes more difficult to interpret. In particular, excitons (i.e. bound electron-hole pairs) may enhance the absorption and emission of light, and couple strongly with phonons in resonance conditions. We design and implement a first-principles methodology to compute second-order Raman scattering, incorporating dielectric responses and phonon eigenstates obtained from density-functional theory and many-body theory. We demonstrate our approach for the case of silicon, relating frequency-dependent relative Raman intensities, that are in excellent agreement with experiment, to different vibrations and regions of the Brillouin zone. We show that exciton-phonon coupling, computed from first principles, indeed strongly affect the spectrum in resonance conditions. The ability to analyze second-order Raman spectra thus provides direct insight into this interaction.
We explicitly evaluate the principal eigenvalue of the extremal Pucci's sup--operator for a class of special plane domains, and we prove that, for fixed area, the eigenvalue is minimal for the most symmetric set.
Recent research on disorder effects in topological phases in quasicrystalline systems has received much attention. In this work, by numerically computing the (spin) Bott index and the thermal conductance, we reveal the effects of disorder on a class D chiral topological superconductor and a class DIII time-reversal-invariant topological superconductor in a two-dimensional Ammann-Beenker tiling quasicrystalline lattice. We demonstrate that both the topologically protected chiral and helical Majorana edge modes are robust against weak disorder in the quasicrystalline lattice. More fascinating is the discovery of disorder-induced topologically nontrivial phases exhibiting chiral and helical Majorana edge modes in class D and DIII topological superconductor systems, respectively. Our findings open the door for the research on disorder-induced Majorana edge modes in quasicrystalline systems.
A geometric derivation of $W_\infty$ Gravity based on Fedosov's deformation quantization of symplectic manifolds is presented. To lowest order in Planck's constant it agrees with Hull's geometric formulation of classical nonchiral $W_\infty$ Gravity. The fundamental object is a ${\cal W}$-valued connection one form belonging to the exterior algebra of the Weyl algebra bundle associated with the symplectic manifold. The ${\cal W} $-valued analogs of the Self Dual Yang Mills equations, obtained from a zero curvature condition, naturally lead to the Moyal Plebanski equations, furnishing Moyal deformations of self dual gravitational backgrounds associated with the complexified cotangent space of a two dimensional Riemann surface. Deformation quantization of $W_\infty$ Gravity is retrieved upon the inclusion of all the $\hbar$ terms appearing in the Moyal bracket. Brief comments on Non Commutative Geometry and M(atrix)theory are made.
Observations performed with the Fermi-LAT telescope have revealed the presence of a spectral break in the GeV spectrum of flat-spectrum radio quasars (FSRQs) and other low- and intermediate-synchrotron peaked blazars. We propose that this feature can be explained by Compton scattering of broad-line region (BLR) photons by a non-thermal population of electrons described by a log-parabolic function. We consider in particular a scenario in which the energy densities of particles, magnetic field, and soft photons in the emitting region are close to equipartition. We show that this model can satisfactorily account for the overall spectral energy distribution of the FSRQ 3C 454.3, reproducing the GeV spectal cutoff due to Klein-Nishina effects and a curving electron distribution.
We construct and study global solutions for the 3-dimensional incompressible MHD systems with arbitrary small viscosity. In particular, we provide a rigorous justification for the following dynamical phenomenon observed in many contexts: the solution initially behaves like non-dispersive waves and the shape of the solution persists for a very long time (proportional to the Reynolds number), thereafter, the solution will be damped due to the long-time accumulation of the diffusive effects, eventually, the total energy of the system becomes extremely small compared to the viscosity so that the diffusion takes over and the solution afterwards decays fast in time.   We do not assume any condition on the symmetry or on the vorticity. The size of data and the a priori estimates do not depend on viscosity. The proof is builded upon a novel use of the basic energy identity and a geometric study of the characteristic hypersurfaces. The approach is partly inspired by Christodoulou-Klainerman's proof of the nonlinear stability of Minkowski space in general relativity.
Spatial fluctuations of the local electric field induced by a constant applied electric field in composite media are studied analytically and numerically. It is found that the density of states for the fields exhibit sharp peaks and abrupt changes in the slope at certain critical points which are analogous to van Hove singularities in the density of states for phonons and electrons in solids. As in solids, these singularities are generally related to saddle and inflection points in the field spectra and are of considerable value in the characterization of the field fluctuations. The critical points are very prominent in dispersions with a regular, ``crystal-like'', structure. However, they broaden and eventually disappear as the disorder increases.