ShantanuT01/DACTYL-Pretraining huggingface dataset:
For the time being isotropic three-body exchange interactions are scarcely explored and mostly used as a tool for constructing various exactly solvable one-dimensional models, although, generally speaking, such competing terms in generic Heisenberg spin systems can be expected to support specific quantum effects and phases. The Heisenberg chain constructed from alternating S=1 and sigma=1/2 site spins defines a realistic prototype model admitting extra three-body exchange terms. Based on numerical density-matrix renormalization group (DMRG) and exact diagonalization (ED) calculations, we demonstrate that the additional isotropic three-body terms stabilize a variety of partially-polarized states as well as two specific non-magnetic states including a critical spin-liquid phase controlled by two Gaussinal conformal theories as well as a critical nematic-like phase characterized by dominant quadrupolar S-spin fluctuations. Most of the established effects are related to some specific features of the three-body interaction such as the promotion of local collinear spin configurations and the enhanced tendency towards nearest-neighbor clustering of the spins. It may be expected that most of the predicted effects of the isotropic three-body interaction persist in higher space dimensions.
The Taylor coefficients of flavor diagonal and off-diagonal susceptibilities as well as baryon number, isovector and electric charge susceptibilities are considered within a phenomenological quasiparticle model of the quark-gluon plasma and successfully compared with lattice QCD data for two degenerate quark flavors. These susceptibility coefficients represent sensible probes of baryon density effects in the equation of state. The baryon charge is carried, in our model, by quark-quasiparticle excitations for hard momenta.
Teleportation of a pure two particle entangled state of continuous variables by triplet of the Greenberger-Horne-Zeilinger form is considered.   The three-particle basis needed for a joint measurement is found. It describes a measurement of momentum one of single particle and total moment and relative position of the two others. Optical realization using squeezed state of the light is discussed.
In general, solutions $u$ to \[ \Delta u(\mathbf{x})=f(\mathbf{x})\chi_{\{u>\psi\}} \] are not $C^{1,1}$, even for $f$ smooth and $\psi(\mathbf{x})\equiv0$. Points around which $u$ is not $C^{1,1}$ are called singular points, and the set of all such points, the singular set. In this article we analyze blow-ups, the free boundary $\partial\{u>\psi\}$, and the singular set close to singular points $\mathbf{x}^{0}=(x^{0},y^{0},z^{0})$ in $\mathbb{R}^{3}$. We show that blow-ups of the form \[ \lim_{j\to\infty}\frac{u(r_{j}\cdot+\mathbf{x}^{0})}{\|u\|_{L^{\infty}(B_{r_{j}}(\mathbf{x}^{0}))}}, \] $r_{j}\to0^{+}$ are unique, the free boundary $\partial\{u>\psi\}$ is up to rotations close to the surfaces $(x-x^{0})^{2}+(y-y^{0})^{2}=2(z-z^{0})^{2}$ or $(x-x^{0})^{2}=(z-z^{0})^{2}$, and that singular points are either isolated or contained in a $C^{1}$ curve. The methods of the proofs are based on projecting the solutions $u$ on the space of harmonic two-homogeneous polynomials.
We measure the statistical polarization of quadrupolar nuclear spins in a sub-micrometer (0.6 um^3) particle of GaAs using magnetic resonance force microscopy. The crystalline sample is cut out of a GaAs wafer and attached to a micro-mechanical cantilever force sensor using a focused ion beam technique. Nuclear magnetic resonance is demonstrated on ensembles containing less than 5 x 10^8 nuclear spins and occupying a volume of around (300 nm)^3 in GaAs with reduced volumes possible in future experiments. We discuss how the further reduction of this detection volume will bring the spin ensemble into a regime where random spin fluctuations, rather than Boltzmann polarization, dominate its dynamics. The detection of statistical polarization in GaAs therefore represents an important first step toward 3D magnetic resonance imaging of III-V materials on the nanometer-scale.
Photo-excited state in correlated electron system with spin-state degree of freedom is studied. We start from the two-orbital extended Hubbard model where energy difference between the two orbitals is introduced. Photo-excited metastable state is examined based on the effective model Hamiltonian derived by the two-orbital Hubbard model. Spin-state change is induced by photo-irradiation in the low-spin band insulator near the phase boundary. High-spin state is stabilized by creating a ferromagnetic bound state with photo-doped hole carriers. An optical absorption occurs between the bonding and antibonding orbitals inside of the bound state. Time-evolution for photo-excited states is simulated in the time-dependent mean-field scheme. Pair-annihilations of the photo-doped electron and hole generate the high-spin state in a low-spin band insulator. We propose that this process is directly observed by the time-resolved photoemission experiments.
We study low-lying zeros of $L$-functions attached to holomorphic cusp forms of level $1$ and large weight. In this family, the Katz--Sarnak heuristic with orthogonal symmetry type was established in the work of Iwaniec, Luo and Sarnak for test functions $\phi$ satisfying the condition supp$(\widehat \phi) \subset(-2,2)$. We refine their density result by uncovering lower-order terms that exhibit a sharp transition when the support of $\widehat \phi$ reaches the point $1$. In particular the first of these terms involves the quantity $\widehat \phi(1)$ which appeared in previous work of Fouvry--Iwaniec and Rudnick in symplectic families. Our approach involves a careful analysis of the Petersson formula and circumvents the assumption of GRH for $\text{GL}(2)$ automorphic $L$-functions. Finally, when supp$(\widehat \phi)\subset (-1,1)$ we obtain an unconditional estimate which is significantly more precise than the prediction of the $L$-functions Ratios Conjecture.
Let $\rho$ be a mod $\ell$ Galois representation attached to a newform $f$. Explicit methods are sometimes able to determine the image of $\rho$, or even the number field cut out by $\rho$, provided that $\ell$ and the level $N$ of $f$ are small enough; however these methods are not amenable to the case where $\ell$ or $N$ are large. The purpose of this short note is to establish a sufficient condition for the image of $\rho$ to be large and which remains easy to test for moderately large $\ell$ and $N$.
We show that the low temperature electron transport properties of chemically functionalized graphene can be explained as sequential tunneling of charges through a two dimensional array of graphene quantum dots (GQD). Below 15 K, a total suppression of current due to Coulomb blockade through GQD array was observed. Temperature dependent current-gate voltage characteristics show Coulomb oscillations with energy scales of 6.2-10 meV corresponding to GQD sizes of 5-8 nm while resistance data exhibit an Efros-Shklovskii variable range hopping arising from structural and size induced disorder.
We study in this paper the problem of novel human-object interaction (HOI) detection, aiming at improving the generalization ability of the model to unseen scenarios. The challenge mainly stems from the large compositional space of objects and predicates, which leads to the lack of sufficient training data for all the object-predicate combinations. As a result, most existing HOI methods heavily rely on object priors and can hardly generalize to unseen combinations. To tackle this problem, we propose a unified framework of adversarial domain generalization to learn object-invariant features for predicate prediction. To measure the performance improvement, we create a new split of the HICO-DET dataset, where the HOIs in the test set are all unseen triplet categories in the training set. Our experiments show that the proposed framework significantly increases the performance by up to 50% on the new split of HICO-DET dataset and up to 125% on the UnRel dataset for auxiliary evaluation in detecting novel HOIs.
Consider a graph $G = (V, E)$ and, for each vertex $v \in V$, a subset $\Sigma(v)$ of neighbors of $v$. A $\Sigma$-coloring is a coloring of the elements of $V$ so that vertices appearing together in some $\Sigma(v)$ receive pairwise distinct colors. An obvious lower bound for the minimum number of colors in such a coloring is the maximum size of a set $\Sigma(v)$, denoted by $\rho(\Sigma)$. In this paper we study graph classes $F$ for which there is a function $f$, such that for any graph $G \in F$ and any $\Sigma$, there is a $\Sigma$-coloring using at most $f(\rho(\Sigma))$ colors. It is proved that if such a function exists for a class $F$, then $f$ can be taken to be a linear function. It is also shown that such classes are precisely the classes having bounded star chromatic number. We also investigate the list version and the clique version of this problem, and relate the existence of functions bounding those parameters to the recently introduced concepts of classes of bounded expansion and nowhere-dense classes.
Quantum power corrections to the gravitational spin-orbit and spin-spin interactions, as well as to the Lense-Thirring effect, were found for particles of spin 1/2. These corrections arise from diagrams of second order in Newton gravitational constant G with two massless particles in the unitary cut in the t-channel. The corrections obtained differ from the previous calculation of the corrections to spin effects for rotating compound bodies with spinless constituents.
We consider a probe linearly coupled to the center of mass of a nonequilibrium bath. We study the induced motion on the probe for a model where a resetting mechanism is added to an overdamped bath dynamics with quadratic potentials. The fact that each bath-particle is at random times being reset to a fixed position is known for optimizing diffusive search strategies, but here stands for the nonequilibrium aspect of the bath. In the large bath scaling limit the probe is governed by an effective Langevin equation. Depending on the value of the parameters, there appear three regimes: (i) an equilibrium-like regime but with a reduced friction and an increased effective temperature; (ii) a regime where the noise felt by the probe is continuous but nonGaussian and exhibits fat-tails; (iii) a regime with a nonGaussian noise exhibiting power-law distributed jumps. The model thus represents an exactly solvable case for the origin of nonequilibrium probe dynamics.
We have investigated the dynamics of quantum discord and entanglement for two qubits subject to independent global transverse and/or longitudinal memoryless noisy classical fields. Global transverse and/or longitudinal random fields are found to drive the system to maximally discordant mixed separable steady states for suitable initial conditions. Moreover, two independent noises in the system are found to enhance both the steady state randomness and quantum discord in the absence of entanglement for some initial states.
We present the formulation for finding the distribution of eigenstrains, i.e. the sources of residual stress, from a set of measurements of residual elastic strain (e.g. by diffraction), or residual stress, or stress redistribution, or distortion. The variational formulation employed seeks to achieve the best agreement between the model prediction and some measured parameters in the sense of a minimum of a functional given by a sum over the entire set of measurements. The advantage of this approach lies in its flexibility: different sets of measurements and information about different components of the stress-strain state can be incorporated. We demonstrate the power of the technique by analysing experimental data for welds in thin sheet of a nickel superalloy aerospace material. Very good agreement can be achieved between the prediction and the measurement results without the necessity of using iterative solution. In practice complete characterisation of residual stress states is often very difficult, due to limitations of facility access, measurement time or specimen dimensions. Implications of the new technique for experimental analysis are all the more significant, since it allows the reconstruction of the entire stress state from incomplete sets of data.
We present a construction of quantum states in dimension $d$ that has at least 1 dit of ideal key, called private dits (pdits), which covers most of the known examples of private bits (pbits) $d=2$. We examine properties of this class of states, focusing mostly on its distance to the set of separable states $\mathcal{SEP}$, showing that for a fixed dimension of key part $d_k$ the distance increases with $d_s$. We provide explicit examples of PPT states (in $d$ dimensions) which are nearly as far from separable ones as possible. Precisely, the distance from the set of $\mathcal{SEP}$ is $2 - \epsilon$, where $d$ scales with $\epsilon$ as $d \propto 1/\epsilon^3$, as opposed to $d \propto 2^{(log(4/\epsilon))^2}$ obtained in [Badzi\c{a}g et al., Phys. Rev. A 90, 012301 (2014)]. We do not use boosting (taking many copies of pdits to boost the distance) as in Badzi\c{a}g et al. paper.
We argue that the fundamental solution corresponding to a maximal rank differential operator, where the symbol is regarded as a vector valued distribution, is not necessarily very regular. Thus, for a fundamental solution, the property of being very regular, is not invariant to change of local coordinates.
Recent studies of the molecular medium in nearby galaxies have provided mounting evidence that the molecular gas can exist in two phases: one that is clumpy and organized as molecular clouds and another one that is more diffuse. This last component has a higher velocity dispersion than the clumpy one. In order to investigate these two molecular components further, we compare the fluxes and line widths of CO in NGC 4736 and NGC 5055, two nearby spiral galaxies for which high-quality interferometric as well as single-dish data sets are available. Our analysis leads to two main results: 1) Employing three different methods, we determine the flux recovery of the interferometer as compared to the single-dish to be within a range of 35-74% for NGC4736 and 81-92% for NGC5055, and 2) when focusing on high (SNR>5) lines of sight, the single-dish line widths are larger by ~(40+-20)% than the ones derived from interferometric data; which is in agreement with stacking all lines of sight. These results point to a molecular gas component that is distributed over spatial scales larger than 30"(~1kpc), and is therefore filtered out by the interferometer. The available observations do not allow us to distinguish between a truly diffuse gas morphology and a uniform distribution of small clouds that are separated by less than the synthesized beam size (~3" or ~100pc), as they would both be invisible for the interferometer. This high velocity dispersion component has a dispersion similar to what is found in the atomic medium, as traced through observations of the HI line.
The interplay between frustration and quantum fluctuation in magnetic systems is known to be the origin of many exotic states in condensed matter physics. In this paper, we consider a frustrated four-leg spin tube under a magnetic field. This system is a prototype to study the emergence of a nonmagnetic ground state factorizable into local states and the associated order parameter without quantum fluctuation, that appears in a wide variety of frustrated systems. The one-dimensional nature of the system allows us to apply various techniques: a path-integral formulation based on the notion of order by disorder, strong-coupling analysis where magnetic excitations are gapped, and density-matrix renormalization group. All methods point toward an interesting property of the ground state in the magnetization plateaus, namely, a quantized value of relative magnetizations between different sublattices (spin imbalance) and an almost perfect factorization of the ground state.
We have characterized the spectroscopic orbit of the TWA 3A binary and provide preliminary families of probable solutions for the TWA 3A visual orbit as well as for the wide TWA 3A--B orbit. TWA 3 is a hierarchical triple located at 34 pc in the $\sim$10 Myr old TW Hya association. The wide component separation is 1."55; the close pair was first identified as a possible binary almost 20 years ago. We initially identified the 35-day period orbital solution using high-resolution infrared spectroscopy which angularly resolved the A and B components. We then refined the preliminary orbit by combining the infrared data with a re-analysis of our high-resolution optical spectroscopy. The orbital period from the combined spectroscopic solution is $\sim$35 days, the eccentricity is $\sim$0.63, and the mass ratio is $\sim$0.84; although this high mass ratio would suggest that optical spectroscopy alone should be sufficient to identify the orbital solution, the presence of the tertiary B component likely introduced confusion in the blended optical spectra. Using millimeter imaging from the literature, we also estimate the inclinations of the stellar orbital planes with respect to the TWA 3A circumbinary disk inclination and find that all three planes are likely misaligned by at least $\sim$30 degrees. The TWA 3A spectroscopic binary components have spectral types of M4.0 and M4.5; TWA 3B is an M3. We speculate that the system formed as a triple, is bound, and that its properties were shaped by dynamical interactions between the inclined orbits and disk.
We consider central extensions of two dimensional abelian current algebra and Virasoro algebra and see that the sign of the Schwinger term changes if we arrange the Fourier modes of the fermion in the commutator in the order opposite to the normal. We argue that this is permissible in the case of fermions, but not in the case of bosons.
The EAS Cherenkov light array Tunka-133, with $\sim$ 3 km$^2$ geometric area, is taking data since 2009.The array permits a detailed study of energy spectrum and mass composition of cosmic rays in the energy range from $6\cdot 10^{15}$ to $10^{18}$ eV. We describe the methods of time and amplitude calibration of the array and the methods of EAS parameters reconstruction. We present the all-particle energy spectrum, based on 7 seasons of operation.
We report on the first demonstration of generating a spin current and spin transport in a highly doped Si channel at room temperature (RT) using a four-terminal lateral device with a spin injector and a detector consisting of an Fe/MgO tunnel barrier. Spin current was generated using a nonlocal technique, and spin injection signals and Hanle-type spin precession were successfully detected at 300 K, thus proving spin injection with the elimination of spurious signals. The spin diffusion length and its lifetime at RT were estimated to be 0.6 \"im and 1.3 ns by the Hanle-type spin precession, respectively.
We discuss the Randall-Sundrum (RS) choice for $h_{MN}$ in the brane-world. We begin with the de Donder gauge (transverse-tracefree) including scalar($h_{55}$), vector($h_{5\mu}$) and tensor($h_{\mu\nu}$) in five dimensions for comparison. One finds that $h_{55}=0$ and $h_{5\mu}=0$. This leads to the RS choice. It appears that the RS choice is so restrictive for the five massless states, whereas it is unique for describing the massive states. Furthermore, one can establish the stability of the RS solution with the RS choice only.
In this paper we will construct the Schrodinger representation for the linearly polarized Gowdy $S^1\times S^2$ and $S^3$ models coupled to massless scalar fields. Here the quantum states belong to a $L^2$-space for a suitable quantum configuration space endowed with a Gaussian measure, whose support is analyzed. This study completes the quantization of these systems previously performed in the Fock scheme, and provides a specially useful framework to address physically relevant questions.
The quantum error threshold is the highest (model-dependent) noise rate which we can tolerate and still quantum-compute to arbitrary accuracy. Although noise thresholds are frequently estimated for the Steane seven-qubit, distance-three quantum code, there has been no proof that a constant threshold even exists for distance-three codes. We prove the existence of a constant threshold. The proven threshold is well below estimates, based on simulations and analytic models, of the true threshold, but at least it is now known to be positive.
We compute the prepotential for gauge theories descending from ${\cal N}=4$ SYM via quiver projections and mass deformations.   This accounts for gauge theories with product gauge groups and bifundamental matter. The case of massive orientifold gauge theories with gauge group SO/Sp is also described. In the case with no gravitational corrections the results are shown to be in agreement with Seiberg-Witten analysis and previous results in the literature.
The effect of H$_2$ ro-vibrational excitation on the chemistry of protoplanetary disks is studied using a framework that solves for the disk physical and chemical structure and includes a detailed calculation of H$_2$ level populations. Chemistry with ro-vibrationally excited H$_2$ is found to be important for the formation of several commonly observed species in disks and this work demonstrates the need to accurately treat PDR chemistry in disks if we are to make inferences on the chemical state of the disk during planet formation epochs. This is found to be even more critical for molecules like C$_2$H, CN or HCN that are commonly used to infer changes in the elemental disk C/O and N/O ratios, with implications for planetesimal formation and the composition of exoplanet atmospheres. Computed vertical column densities with the full H$_2$ population calculation are increased by $\sim1-2$ orders of magnitude for molecules such as CN, HCN/HNC compared to calculations with no treatment of excited H$_2$. For the commonly used pseudo-level approximation, the computed columns of these molecules are overestimated by a factor of $\sim3-5$ when compared to the full model. We further note that the computed abundance for these molecules strongly depends on the strength of the FUV photons at energies that pump H$_2$ (i.e. 11-13.6 eV), which is not well constrained in disks, and that rate constants as a function of H$_2$ ro-vibrational levels for the key reaction N + H$_2\rightarrow $ NH are needed for a more accurate assessment of CN/HCN chemistry but are currently unavailable.
A model of the universe as a very large white hole provides a useful alternative inhomogeneous theory to pit against the homogeneous standard FLRW big bang models. The white hole would have to be sufficiently large that we can fit comfortably inside the event horizon at the present time, so that the inhomogeneities of space-time are not in contradiction with current observational limits. A specific Lemaitre-Tolman model of a spherically symmetric non-rotating white hole with a few adjustable parameters is investigated. Comparison of calculated anisotropy in the Hubble flow and the CMB against observational limits constrain the parameter space. A Copernican principle would require that we are not too near the centre of the white hole. As an additional constraint this predicts a value of Omega between 0.9999 and 1.