ShantanuT01/DACTYL-Pretraining huggingface dataset:
We analyze the impact of the recently released CDF-II measurement of $W$ mass on the SMEFT analyses of the electroweak precision data as well as Higgs and electroweak diboson productions. We work in the Hagiwara, Ishihara, Szalapski, and Zeppenfeld basis in which eight generation-independent operators enter in the electroweak precision data at tree level and, unlike in the Warsaw basis, the analysis of that set of data constrains all the eight Wilson coefficients, without the need of combination with Higgs or electroweak diboson data results. We show that in the global analysis the determination of the coefficients of all operators which do not enter the electroweak precision data are barely affected by the new $M_W$ determination.
In the quasi-one-dimensional cuprate PrBa$_2$Cu$_4$O$_8$, the Pr cations order antiferromagnetically at 17 K in zero field. Through a combination of magnetic susceptibility, torque magnetometry, specific heat and interchain transport measurements, the anisotropic temperature-magnetic field phase diagram associated with this ordering has been mapped out. A low-temperature spin-flop transition in the Pr sub-lattice is found to occur at the same magnetic field strength and orientation as a dimensional crossover in the ground state of the metallic CuO chains. This coincidence suggests that the spin reorientation is driven by a change in the anisotropic Rudermann-Kittel-Kasuya-Yosida (RKKY) interaction induced by a corresponding change in effective dimensionality of the conduction electrons.
We show how methods of algebraic geometry can produce criteria for the identifiability of specific tensors that reach beyond the range of applicability of the celebrated Kruskal criterion. More specifically, we deal with the symmetric identifiability of symmetric tensors in Sym$^4(\mathbb{C}^{n+1})$, i.e., quartic hypersurfaces in a projective space $\mathbb{P}^n$, that have a decomposition in 2n+1 summands of rank 1. This is the first case where the reshaped Kruskal criterion no longer applies. We present an effective algorithm, based on efficient linear algebra computations, that checks if the given decomposition is minimal and unique. The criterion is based on the application of advanced geometric tools, like Castelnuovo's lemma for the existence of rational normal curves passing through a finite set of points, and the Cayley-Bacharach condition on the postulation of finite sets. In order to apply these tools to our situation, we prove a reformulation of these results, hereby extending classical results such as Castelnuovo's lemma and the analysis of Geramita, Kreuzer, and Robbiano, "Cayley-Bacharach schemes and their canonical modules", Trans. Amer. Math. Soc. 339:443-452, 1993.
In this paper, we study the qualitative behaviour of approximation schemes for Backward Stochastic Differential Equations (BSDEs) by introducing a new notion of numerical stability. For the Euler scheme, we provide sufficient conditions in the one-dimensional and multidimensional case to guarantee the numerical stability. We then perform a classical Von Neumann stability analysis in the case of a linear driver $f$ and exhibit necessary conditions to get stability in this case. Finally, we illustrate our results with numerical applications.
We present a theoretical and experimental study of the peak effect in the surface pinning of vortices. It is associated with a sharp transition in the vortex slippage length which we relate to a crossover from a weakly disordered crystal to a surface glass state. Experiments are performed on ion-beam etched Nb crystals. The slippage length is deduced from 1kHz-1MHz linear AC penetration depth measurements.
Context: Molecular data of extreme environments, such as Arp 220, but also NGC 253, show evidence for extremely high cosmic ray (CR) rates (10^3-10^4 * Milky Way) and mechanical heating from supernova driven turbulence.   Aims: The consequences of high CR rates and mechanical heating on the chemistry in clouds are explored.   Methods: PDR model predictions are made for low, n=10^3, and high, n=10^5.5 cm^-3, density clouds using well-tested chemistry and radiation transfer codes. Column densities of relevant species are discussed, and special attention is given to water related species. Fluxes are shown for fine-structure lines of O, C+, C, and N+, and molecular lines of CO, HCN, HNC, and HCO+. A comparison is made to an X-ray dominated region model.   Results: Fine-structure lines of [CII], [CI], and [OI] are remarkably similar for different mechanical heating and CR rates, when already exposed to large amounts of UV. HCN and H2O abundances are boosted for very high mechanical heating rates, while ionized species are relatively unaffected. OH+ and H2O+ are enhanced for very high CR rates zeta > 5 * 10^-14 s^-1. A combination of OH+, OH, H2O+, H2O, and H3O+ trace the CR rates, and are able to distinguish between enhanced cosmic rays and X-rays.
The cobalt and iron clusters CoN, FeN (20 < N < 150) measured in a cryogenic molecular beam are found to be bistable with magnetic moments per atom both {\mu}N/N 2{\mu}B in the ground states and {\mu}N */N {\mu}B in the metastable excited states (for iron clusters, {\mu}N ~3N{\mu}B and {\mu}N* N{\mu}B). This energy gap between the two states vanish for large clusters, which explains the rapid convergence of the magnetic moments to the bulk value and suggests that ground state for the bulk involves a superposition of the two, in line with the fluctuating local orders in the bulk itinerant ferromagnetism.
We construct a gauge mediation model of dynamical supersymmetry breaking (DSB) based on a vector-like gauge theory, in which there is a unique color-preserving true vacuum. The DSB scale $\Lambda/4\pi$ turns out to be as high as $\Lambda/4\pi \simeq 10^{8-9} GeV$, since the transmission of the DSB effects to the standard model sector is completed through much higher loops. This model is perfectly natural and phenomenologically consistent. We also stress that the dangerous D-term problem for the messenger U(1)_m is automatically solved by a charge conjugation symmetry in the vector-like gauge theory.
In my lecture I consider integrals over moduli spaces of supersymmetric gauge field configurations (instantons, Higgs bundles, torsion free sheaves).   The applications are twofold: physical and mathematical; they involve supersymmetric quantum mechanics of D-particles in various dimensions, direct computation of the celebrated Seiberg-Witten prepotential, sum rules for the solutions of the Bethe ansatz equations and their relation to the Laumon's nilpotent cone. As a by-product we derive some combinatoric identities involving the sums over Young tableaux.
We investigate the computational power of passive and active linear optical elements and photo-detectors. We show that single photon sources, passive linear optics and photo-detectors are sufficient for implementing reliable quantum algorithms. Feedback from the detectors to the optical elements is required for this implementation. Without feedback, non-deterministic quantum computation is possible. A single photon source sufficient for quantum computation can be built with an active linear optical element (squeezer) and a photo-detector. The overheads associated with using only linear optics appear to be sufficiently low to make quantum computation based on our proposal a viable alternative.
In this article, we classify connected commutative (locally) Nash groups, which is a continuation of our previous work on the classification of abelian Nash manifolds. Our results generalize the classification of the one-dimensional case by Madden-Stanton and the two-dimensional case by Baro-Vicente-Otero. Moreover, we determine the affineness and toroidal affinenese of a connected commutative Nash group.
We study the optical appearance of a thin accretion disk around the strongly naked static Janis-Newman-Winicour singularity. The solution does not possess a photon sphere, which results in the formation of a complex structure of bright rings in the central region of the disk image. Such structure is absent in the case of the Schwarzschild black hole with a thin accretion disk, where instead of the image we observe the black hole shadow. Some of the rings emit with the maximal observable radiation flux from the accretion disk, and should be experimentally detectable. Thus, this qualitatively new feature can be used to distinguish observationally black holes from naked singularities. We elucidate the appearance of the ring structure by revealing the physical mechanism of its formation, and explaining the nature of each of the ring images. We make the conjecture that a similar structure would also appear for other solutions without a photon sphere and it can serve as a general observational signature for distinguishing compact objects possessing no photon sphere from black holes.
The existence of charge density wave (CDW) correlations in cuprate superconductors has now been established. However, the nature of the ground state order has remained uncertain because disorder and the presence of superconductivity typically limit the CDW correlation lengths to a dozen unit cells or less. Here we explore the CDW correlations in YBa2Cu3Ox (YBCO) ortho-II and ortho-VIII crystals, which belong to the cleanest available cuprate family, at magnetic fields in excess of the resistive upper critical field (Hc2) where the superconductivity is heavily suppressed. We find an incommensurate, unidirectional CDW with a well-defined onset at a critical field strength that is proportional to Hc2. It is related to but distinct from the short-range bidirectional CDW that exists at zero magnetic field. The unidirectional CDW possesses a long inplane correlation length as well as significant correlations between neighboring CuO2 planes, yielding a correlation volume that is at least 2 - 3 orders of magnitude larger than that of the zero-field CDW. This is by far the largest CDW correlation volume observed in any cuprate crystal and so is presumably representative of the high-field ground-state of an "ideal" disorder-free cuprate.
We study the clustering of galaxies, as a function of their colour, from Data Release Ten (DR10) of the SDSS-III Baryon Oscillation Spectroscopic Survey. We select 122,967 galaxies with 0.43 < z < 0.7 into a "Blue" sample and 131,969 into a "Red" sample based on k+e corrected (to z=0.55) r-i colours and i band magnitudes. The samples are chosen to each contain more than 100,000 galaxies, have similar redshift distributions, and maximize the difference in clustering amplitude. The Red sample has a 40% larger bias than the Blue (b_Red/b_Blue = 1.39+-0.04), implying the Red galaxies occupy dark matter halos with an average mass that is 0.5 log Mo greater. Spherically averaged measurements of the correlation function, \xi 0, and the power spectrum are used to locate the position of the baryon acoustic oscillation (BAO) feature of both samples. Using \xi 0, we obtain distance scales, relative to our reference LCDM cosmology, of 1.010+-0.027 for the Red sample and 1.005+-0.031 for the Blue. After applying reconstruction, these measurements improve to 1.013+/-0.020 for the Red sample and 1.008+-0.026 for the Blue. For each sample, measurements of \xi 0 and the second multipole moment, \xi 2, of the anisotropic correlation function are used to determine the rate of structure growth, parameterized by f\sigma 8. We find f\sigma 8,Red = 0.511+-0.083, f\sigma 8,Blue = 0.509+/-0.085, and f\sigma 8,Cross = 0.423+-0.061 (from the cross-correlation between the Red and Blue samples). We use the covariance between the bias and growth measurements obtained from each sample and their cross-correlation to produce an optimally-combined measurement of f\sigma 8,comb = 0.443+-0.055. In no instance do we detect significant differences in distance scale or structure growth measurements obtained from the Blue and Red samples.
This work investigates the impact of cosmic flows and density perturbations on Hubble constant $H_0$ measurements using nonlinear phase-space reconstructions of the Local Universe (LU). In particular, we rely on 25 constrained N-body simulations of the LU using the 2MRS galaxy sample within distances of 90 Mpc/h. These have been randomly extended up to volumes enclosing 360 Mpc/h with augmented Lagrangian perturbation theory (750 simulations in total), accounting in this way for gravitational mode coupling from larger scales, correcting for periodic boundary effects, and estimating systematics of missing attractors ($\sigma_{\rm large}=134$ km/s). We report on Local Group speed reconstructions, which are compatible with CMB-dipole measurements: $|v_{\rm LG}|=685\pm137$ km/s. The direction $(l,b)=(260.5\pm 13.3,39.1\pm 10.4)^\circ$ is compatible with observations after considering the variance of large scales. Accounting for large scales, our local bulk flow estimations assuming a $\Lambda$CDM model are compatible with estimates based on velocity data derived from the Tully-Fisher relation.   We focus on low redshift supernova measurements ($0.01<z<0.025$), which have been found to disagree with probes at larger distances. Our analysis indicates that there are two effects contributing to this tension. First, the anisotropic distribution of supernovae aligns with the velocity dipole and induces a systematic boost in $H_0$. Second, a divergent region surrounding the Virgo Supercluster is responsible for an additional positive bias in $H_0$. Taking these effects into account yields a correction of $\Delta H_0=-1.76 \pm 0.21 $ km/s/Mpc, thereby reducing the tension between local probes and more distant probes. Effectively $H_0$ is lower by about $2\%$.
Based on the concepts of a generalized critical point and the corresponding generalized P.S. condition introduced by Duong Minh Duc[1], we have proved a new $Z_2$ index theorem and get a result on multiplicity of generalized critical points. Using the result and a quite standard variational method, it is found that the equation $$ -\Delta_{H^n} u=|u|^{p-1} u ~ x\in H^n $$ has infinite positive solutions. Our approach can also be applied to study more general nonlinear problems.
We have studied the phase diagram and entanglement of the one dimensional Ising model with Dzyaloshinskii-Moriya (DM) interaction. We have applied the quantum renormalization group (QRG) approach to get the stable fixed points, critical point and the scaling of coupling constants. This model has two phases, antiferromagnetic and saturated chiral ones. We have shown that the staggered magnetization is the order parameter of the system and DM interaction produces the chiral order in both phases. We have also implemented the exact diagonalization (Lanczos) method to calculate the static structure factors. The divergence of structure factor at the ordering momentum as the size of systems goes to infinity defines the critical point of the model. Moreover, we have analyzed the relevance of the entanglement in the model which allows us to shed insight on how the critical point is touched as the size of the system becomes large. Nonanalytic behavior of entanglement and finite size scaling have been analyzed which is tightly connected to the critical properties of the model. It is also suggested that a spin-fluid phase has a chiral order in terms of new spin operators which are defined by a nonlocal transformation.
Extremely low-mass white dwarfs (ELM WDs) are helium WDs with a mass less than $\sim$$0.3\rm\;M_\odot$. Most ELM WDs are found in double degenerates (DDs) in the ELM Survey led by Brown and Kilic. These systems are supposed to be significant gravitational-wave sources in the mHz frequency. In this paper, we firstly analyzed the observational characteristics of ELM WDs and found that there are two distinct groups in the ELM WD mass and orbital period plane, indicating two different formation scenarios of such objects, i.e. a stable Roche lobe overflow channel (RL channel) and common envelope ejection channel (CE channel). We then systematically investigated the formation of ELM WDs in DDs by a combination of detailed binary evolution calculation and binary population synthesis. Our study shows that the majority of ELM WDs with mass less than $0.22\rm\;M_\odot$ are formed from the RL channel. The most common progenitor mass in this way is in the range of $1.15-1.45\rm\;M_\odot$ and the resulting ELM WDs have a peak around $0.18\rm\;M_\odot$ when selection effects are taken into account, consistent with observations. The ELM WDs with a mass larger than $0.22\rm\;M_\odot$ are more likely to be from the CE channel and have a peak of ELM WD mass around $0.25\rm\;M_\odot$ which needs to be confirmed by future observations. By assuming a constant star formation rate of 2$\rm\;M_\odot yr^{-1}$ for a Milky Way-like galaxy, the birth rate and local density are $5\times10^{-4}\rm\;yr^{-1}$ and $1500\rm\;kpc^{-3}$, respectively, for DDs with an ELM WD mass less than $0.25\rm\;M_\odot$.
A magnetic domain boundary on the surface of a three-dimensional topological insulator is predicted to host a chiral edge state, but direct demonstration is challenging. Here, we used a scanning superconducting quantum interference device to show that current in a magnetized EuS/Bi2Se3 heterostructure flows at the edge when the Fermi level is gate-tuned to the surface band gap. We further induced micron-scale magnetic structures on the heterostructure, and detected a chiral edge current at the magnetic domain boundary. The chirality of the current was determined by magnetization of the surrounding domain and its magnitude by the local chemical potential rather than the applied current. Such magnetic structures, provide a platform for detecting topological magnetoelectric effects and may enable progress in quantum information processing and spintronics.
For integer $k\geq2,$ a graph $G$ is called $k$-leaf-connected if $|V(G)|\geq k+1$ and given any subset $S\subseteq V(G)$ with $|S|=k,$ $G$ always has a spanning tree $T$ such that $S$ is precisely the set of leaves of $T.$ Thus a graph is $2$-leaf-connected if and only if it is Hamilton-connected. In this paper, we present a best possible condition based upon the size to guarantee a graph to be $k$-leaf-connected, which not only improves the results of Gurgel and Wakabayashi [On $k$-leaf-connected graphs, J. Combin. Theory Ser. B 41 (1986) 1-16] and Ao, Liu, Yuan and Li [Improved sufficient conditions for $k$-leaf-connected graphs, Discrete Appl. Math. 314 (2022) 17-30], but also extends the result of Xu, Zhai and Wang [An improvement of spectral conditions for Hamilton-connected graphs, Linear Multilinear Algebra, 2021]. Our key approach is showing that an $(n+k-1)$-closed non-$k$-leaf-connected graph must contain a large clique if its size is large enough. As applications, sufficient conditions for a graph to be $k$-leaf-connected in terms of the (signless Laplacian) spectral radius of $G$ or its complement are also presented.
Methods for calculating lower bounds to the exact energy using the variance of the upper bound energy are discussed and explored. All the matrix elements of the Hamiltonian squared are collected and considered, and those for which no known solutions could be found in the literature are derived for an explicitly correlated Gaussian (ECG) basis set. Analytical Solutions are determined for two-electron, mono-nuclear systems, in addition to a one-dimensional integral expression which has use in polyatomic calculations. The newly derived integral expressions have been implemented in the integral library of the QUANTEN computer program.
It has long been speculated that the Dirac or, more generally, the Dirac-Pauli spinor in the Foldy-Wouthuysen (FW) representation should behave like a classical relativistic spinor in the low-energy limit when the probability of particle-antiparticle pair creation and annihilation is negligible. In the weak-field limit of static and homogeneous electromagnetic fields, by applying the method of direct perturbation theory inductively on the orders of $1/c$ in the power series, we rigorously prove that it is indeed the case: the FW transformation of the Dirac-Pauli Hamiltonian is in full agreement with the classical counterpart, which is the sum of the orbital Hamiltonian for the Lorentz force equation and the spin Hamiltonian for the Thomas-Bargmann-Michel-Telegdi equation.
In this paper we introduce a precise definition of algebraic traveling wave solution for general n-th order partial differential equations. All examples of explicit traveling waves known by the authors fall in this category. Our main result proves that algebraic traveling waves exist if and only if an associated n- dimensional first order ordinary differential system has some invariant algebraic curve. As a paradigmatic application we prove that, for the celebrated Fisher- Kolmogorov equation, the only algebraic traveling waves solutions are the ones found in 1979 by Ablowitz and Zeppetella. To the best of our knowledge, this is the first time that this type of results have been obtained.
In this paper we make steps in a new direction by considering fluids with EoS of more general form $F(\rho,P)=0$. It is thought that there should be interaction between cosmic fluids, but this assumption for this stage carries only phenomenological character opening a room for different kind of manipulations. In this article we will consider a modification of an interaction $Q$, where we accept that interaction parameter $b_{1}$ (order of unity) in $Q=3Hb_{1}\rho$ is time dependent and presented as a linear function of Hubble parameter $H$ of the form $b_{0}+btH$, where $b$ and $b_{0}$ are constants. We consider two different models include modified Chaplygin gas and palotropic gas which have bulk viscosity. Then, we investigate problem numerically and analyze behavior of different cosmological parameters concerning to fluids and behavior of Universe.
In this paper we deal with linear systems of P^3 through fat points. We consider the behavior of these systems under a cubo-cubic Cremona transformation that allows us to produce a class of special systems which we conjecture to be the only ones.
A random matrix with rows distributed as a function of their length is said to be isotropic. When these distributions are Gaussian, beta type I, or beta type II, previous work has, from the viewpoint of integral geometry, obtained the explicit form of the distribution of the determinant. We use these result to evaluate the sum of the Lyapunov spectrum of the corresponding random matrix product, and we further give explicit expressions for the largest Lyapunov exponent. Generalisations to the case of complex or quaternion entries are also given. For standard Gaussian matrices $X$, the full Lyapunov spectrum for products of random matrices $I_N + {1 \over c} X$ is computed in terms of a generalised hypergeometric function in general, and in terms of a single single integral involving a modified Bessel function for the largest Lyapunov exponent.
We study the occurrence of multipartite entanglement in spin chains. We show that certain genuine multipartite entangled states, namely W states, can be obtained as ground states of simple XX type ferromagnetic spin chains in a transverse magnetic field, for any number of sites. Moreover, multipartite entanglement is proven to exist even at finite temperatures. A transition from a product state to a multipartite entangled state occurs when decreasing the magnetic field to a critical value. Adiabatic passage through this point can thus lead to the generation of multipartite entanglement.
We consider a gradient flow modeling the epitaxial growth of thin films with slope selection. The surface height profile satisfies a nonlinear diffusion equation with biharmonic dissipation. We establish optimal local and global wellposedness for initial data with critical regularity. To understand the mechanism of slope selection and the dependence on the dissipation coefficient, we exhibit several lower and upper bounds for the gradient of the solution in physical dimensions $d\le 3$.