ShantanuT01/DACTYL-Pretraining huggingface dataset:
Regularity and singularity of the solutions according to the shape of domains is a challenging research theme in the Boltzmann theory (\cite{Kim11,GKTT1}). In this paper, we prove an H\"older regularity in $C^{0,\frac{1}{2}-}_{x,v}$ for the Boltzmann equation of the hard-sphere molecule, which undergoes the elastic reflection in the intermolecular collision and the contact with the boundary of a convex obstacle. In particular, this H\"older regularity result is a stark contrast to the case of other physical boundary conditions (such as the diffuse reflection boundary condition and in-flow boundary condition), for which the solutions of the Boltzmann equation develop discontinuity in a codimension 1 subset (\cite{Kim11}), and therefore the best possible regularity is BV, which has been proved in \cite{GKTT2}.
We present the results of our recent calculation of $\epsilon^{\prime}/ \epsilon$ at the Next-to-Leading (NLO) order in QCD and QED, in the framework of $\DSone$ Effective Hamiltonians. The operator matrix elements are taken from lattice QCD, at a scale $\mu=2\,\,\mbox{GeV}$. NLO corrections seem to lower the value of $\epsilon^{\prime}/\epsilon$, favouring the experimental result of E731. Contributions from different operators are analyzed and dependence on $\mt$, $\mu$ and $\Lambda_{\sss QCD}$ discussed. (Talk given at the XXVIIIth Rencontres de Moriond, ``Electro-Weak Interactions and Unified Theories'', March 13-19 1993).
Using spin density functional theory we have carried out a comparative study of chemical bonding and magnetism in Fe_4N, Fe_3N and Fe_2N. All of these compounds form close packed Fe lattices, while N occupies octahedral interstitial positions. High spin fcc Fe and hypothetical FeN with rock salt structure have been included in our study as reference systems. We find strong, covalent Fe-N bonds as a result of a substantial \sigma-type p-d hybridisation, with some charge transfer to N. Those Fe d orbitals which contribute to the p-d bonds, do no longer participate in the exchange splitting of the Fe d bands. Because of the large exchange fields, the majority spin d bands are always fully occupied, while the minority spin d bands are close to half-filling, thus optimizing the Fe d-d covalent bonding. As a consequence, in good approximation the individual Fe moments decrease in steps of 0.5 \mu_B from fcc iron (2.7 \mu_B) via Fe_4N (2.7 and 1.97 mu_B}), \chem{Fe_3N} (1.99 \mu_B) to \zeta - Fe_2N (1.43 \mu_B).
Cosmic voids gravitationally lens the cosmic microwave background (CMB) radiation, resulting in a distinct imprint on degree scales. We use the simulated CMB lensing convergence map from the MICE N-body simulation to calibrate our detection strategy for a given void definition and galaxy tracer density. We then identify cosmic voids in DES Year 1 data and stack the Planck 2015 lensing convergence map on their locations, probing the consistency of simulated and observed void lensing signals. When fixing the shape of the stacked convergence profile to that calibrated from simulations, we find imprints at the $3{\sigma}$ significance level for various analysis choices. The best measurement strategies based on the MICE calibration process yield $S/N \sim 4$ for DES Y1, and the best-fit amplitude recovered from the data is consistent with expectations from MICE ($A \sim 1$). Given these results as well as the agreement between them and N-body simulations, we conclude that the previously reported excess integrated Sachs-Wolfe (ISW) signal associated with cosmic voids in DES Y1 has no counterpart in the Planck CMB lensing map.
The Sun's outer atmosphere is heated to temperatures of millions of degrees, and solar plasma flows out into interplanetary space at supersonic speeds. This paper reviews our current understanding of these interrelated problems: coronal heating and the acceleration of the ambient solar wind. We also discuss where the community stands in its ability to forecast how variations in the solar wind (i.e., fast and slow wind streams) impact the Earth. Although the last few decades have seen significant progress in observations and modeling, we still do not have a complete understanding of the relevant physical processes, nor do we have a quantitatively precise census of which coronal structures contribute to specific types of solar wind. Fast streams are known to be connected to the central regions of large coronal holes. Slow streams, however, appear to come from a wide range of sources, including streamers, pseudostreamers, coronal loops, active regions, and coronal hole boundaries. Complicating our understanding even more is the fact that processes such as turbulence, stream-stream interactions, and Coulomb collisions can make it difficult to unambiguously map a parcel measured at 1 AU back down to its coronal source. We also review recent progress -- in theoretical modeling, observational data analysis, and forecasting techniques that sit at the interface between data and theory -- that gives us hope that the above problems are indeed solvable.
We show that if a multigraph $G$ with maximum edge-multiplicity of at most $\frac{\sqrt{n}}{\log^2 n}$, is edge-coloured by $n$ colours such that each colour class is a disjoint union of cliques with at least $2n + o(n)$ vertices, then it has a full rainbow matching, that is, a matching where each colour appears exactly once. This asymptotically solves a question raised by Clemens, Ehrenm\"uller and Pokrovskiy, and is related to problems on algebras of sets studied by Grinblat in [Grinblat 2002].
We introduce a novel method for calculating the size of the critical nucleus and the value of the surface tension in systems with first order phase transition. The method is based on classical nucleation theory, and it consists in studying the thermodynamics of a sphere of given radius embedded in a frozen metastable surrounding. The frozen configuration creates a pinning field on the surface of the free sphere. The pinning field forces the sphere to stay in the metastable phase as long as its size is smaller than the critical nucleus. We test our method in two first-order systems, both on a two-dimensional lattice: a system where the parameter tuning the transition is the magnetic field, and a second system where the tuning parameter is the temperature. In both cases the results are satisfying. Unlike previous techniques, our method does not require an infinite volume limit to compute the surface tension, and it therefore gives reliable estimates even by using relatively small systems. However, our method cannot be used at, or close to, the critical point, i.e. at coexistence, where the critical nucleus becomes infinitely large.
The recently discovered layered kagome metals AV3Sb5 (A=K, Rb, and Cs) attract intensive interest due to their intertwining with superconductivity, charge-density-wave state, and nontrivial band topology. In this work, we show by first-principles calculations and symmetry arguments that unconventional type-II Dirac nodal line fermions close to the fermi level are present in another latest class of experimentally synthesized kagome compounds AV6Sb6 (A=K, Rb, and Cs). These compounds possess a unique kagome (V3Sb)2 bilayer that dominates their electronic and topological properties, instead of the kagome V3Sb monolayer in AV3Sb5. Crystal symmetry guarantees that the type-II Dirac nodal lines with quantized Berry phase lie in reflection-invariant planes of the Brillouin zone. We further reveal that the type-II Dirac nodal lines remain nearly intact in the presence of spin-orbital coupling and can be categorized as a Z2 classification. The findings establish AV6Sb6 as a class of new fascinating prototypes, which will extend the knowledge of interplay between unconventionally topological fermions and exotic quantum ordered states in kagome systems.
We investigate the detection of entanglement in $n$-partite quantum states. We obtain practical separability criteria to identify genuinely entangled and non-separable mixed quantum states. No numerical optimization or eigenvalue evaluation is needed, and our criteria can be evaluated by simple computations involving components of the density matrix. We provide examples in which our criteria perform better than all known separability criteria. Specifically, we are able to detect genuine $n$-partite entanglement which has previously not been identified. In addition, our criteria can be used in today's experiment.
For the Su-Schrieffer-Heeger (SSH) model on the two-dimensional square lattice, two third nearest neighbor hoppings which preserve chiral symmetry are introduced. Like the case of one dimension, the longer-range hopping can drive topological transitions and leads to the larger topological invariant (vectored Berry phase for the two dimensional SSH model). We obtain the phase boundaries and topological phase diagrams from the winding pattern of $\rho(k_l)$ of the Bloch Hamiltonian. Effects of correlations on the extended two dimensional SSH model are also investigated. The correlation shifts the phase boundaries and leads to topological transitions. Several special points in non-interacting phase diagrams are chosen to illustrate the different phase transitions and a correlations-driven topologically non-trivial phase from the trivial one is found. In this work, the slave-rotor mean field method is applied to the interacting model and we focus on the case of physical electrons, i.e. the Mott transition of charge degree of freedom is avoided in our investigations.
Quantum spin Hall insulators (QSHIs) based on HgTe and three-layer InAs/GaSb quantum wells (QWs) have comparable bulk band-gaps of about 10--18~meV. The former however features a band-gap vanishing with temperature, while the gap in InAs/GaSb QSHIs is rather temperature-independent.Here, we report on the realization of large inverted band-gap in strained three-layer InAs/GaInSb QWs. By temperature-dependent magnetotransport measurements of gated Hall bar devices, we extract a gap as high as 45 meV. Combining local and non-local measurements, we attribute the edge conductivity observed at temperatures up to 40 K to the topological edge channels with equilibration lengths of a few micrometers. Our findings pave the way toward manipulating edge transport at high temperatures in QW heterostructures.
In their constructions of system of quantum stochastic differential equations, mathematicians and/or several physicists interpret that the function of random force operator is to preserve the canonical commutation relation in time, i.e., to secure the unitarity of time evolution generator even for dissipative systems. If this is the case, it means physically that the origin of dissipation is attributed to quantum non-commutativity ({\it quantumness}). The mechanism that the mathematician's approaches rest on will be investigated from the unified view point of Non-Equilibrium Thermo Field Dynamics (NETFD) which is a canonical operator formalism of quantum systems in far-from-equilibrium state including the system of quantum {\it stochastic} equations.
We report resistivity measurements of a CrAs single crystal in a wide temperature range, with the specific aim to assess the applicability of the Bloch-Gruneisen formula for electron-phonon resistivity. We find that the resistance reaches a residual value at Tc=4.2 K and its temperature dependence cannot be fitted only with a suitable Bloch-Gruneisen formula in the whole temperature range, even though we are able to calculate a well defined transport Debye temperature. The observed temperature dependent resistivity seems to suggest a non phonon-mediated superconducting pairing, supporting a magnetic fluctuation mechanism as the likely glue for the superconducting coupling.
The inverse Radon transform allows to obtain partonic double distributions from (extended) generalized parton distributions. We express the extension of generalized parton distributions by their dual parts, generalized distribution amplitudes and study some aspects of the filtered backprojection (inverse Radon transform). We also show that single integral transforms, previously obtained in the context of wave function overlap representation, are valid for generalized parton distributions that do not possess such a representation. Utilizing Radyushkin`s double distribution ansatz, we study and compare the numerical evaluation of double distributions within the filtered backprojection and single integral transforms along the imaginary and real axes.
We compute the one-loop gluon amplitude for the open twistor string model of Berkovits, using a symmetric form of the vertex operators. We discuss the classical solutions in various topologies and instanton sectors and the canonical quantization of the world sheet Lagrangian. We derive the N-point functions for the gluon tree and one-loop amplitudes, and calculate a general one-loop expression for the current algebra.
In this paper, we study the torsion subgroup of $J_0(N)$ over the field generated by those points in the cuspidal group, where $N$ is an odd positive integer. We prove that, considered as Hecke modules, this group and the cuspidal subgroup are both supported at the maximal Eisenstein ideals.
The electronic band structure-controlled ultrafast demagnetization mechanism in Co2FexMn1-xSi Heusler alloy is underpinned by systematic variation of composition. We find the spin-flip scattering rate controlled by spin density of states at Fermi level is responsible for non-monotonic variation of ultrafast demagnetization time ({\tau}M) with x with a maximum at x = 0.4. Furthermore, Gilbert damping constant exhibits an inverse relationship with {\tau}M due to the dominance of inter-band scattering mechanism. This establishes a unified mechanism of ultrafast spin dynamics based on Fermi level position.
In this work, we present a conceptually simple yet effective framework for cross-modality 3D object detection, named voxel field fusion. The proposed approach aims to maintain cross-modality consistency by representing and fusing augmented image features as a ray in the voxel field. To this end, the learnable sampler is first designed to sample vital features from the image plane that are projected to the voxel grid in a point-to-ray manner, which maintains the consistency in feature representation with spatial context. In addition, ray-wise fusion is conducted to fuse features with the supplemental context in the constructed voxel field. We further develop mixed augmentor to align feature-variant transformations, which bridges the modality gap in data augmentation. The proposed framework is demonstrated to achieve consistent gains in various benchmarks and outperforms previous fusion-based methods on KITTI and nuScenes datasets. Code is made available at https://github.com/dvlab-research/VFF.
We have discovered an excess of extremely red objects (EROs) surrounding the z=2.69 quasar QSO 1213-0017 (UM 485). Optical/IR colors for these galaxies are consistent with z=1-2 ellipticals, and there are at least 5 galaxies with spectroscopic redshifts at <z>=1.31. Keck optical spectra for 3 of the red galaxies show rest-frame UV breaks resembling local elliptical galaxies. Our initial results suggest a coherent structure in redshift, possibly arising from a massive galaxy cluster.
We explore with exact diagonalization the propagation of a single hole in four magnetic phases of the t-J-like Kitaev-Heisenberg model on a honeycomb lattice: the Neel antiferromagnetic, stripe, zigzag and Kitaev spin-liquid phase. We find coherent propagation of spin-polaron quasiparticles in the antiferromagnetic phase by a similar mechanism as in the $t$-$J$ model for high-$T_c$ cuprates. In the stripe and zigzag phases clear quasiparticles features appear in spectral functions of those propagators where holes are created and annihilated on one sublattice, while they remain largely {\it hidden} in those spectral functions that correspond to photoemission experiments. As the most surprising result, we find a totally incoherent spectral weight distribution for the spectral function of a hole moving in the Kitaev spin-liquid phase in the strong coupling regime relevant for iridates. At intermediate coupling the finite systems calculation reveals a well defined quasiparticle at the $\Gamma$ point, however, we find that the gapless spin excitations wipe out quasiparticles at finite momenta. Also for this more subtle case we conclude that in the thermodynamic limit the lightly doped Kitaev liquid phase does not support quasiparticle states in the neighborhood of $\Gamma$, and therefore yields a {\it non-Fermi liquid}, contrary to earlier suggestions based on slave-boson studies. These observations are supported by the presented study of the dynamic spin-structure factor for the Kitaev spin liquid regime.
WMAP5 and related data have greatly restricted the range of acceptable cosmologies, by providing precise likelihood ellypses on the the w_0-w_a plane. We discuss first how such ellypses can be numerically rebuilt, and present then a map of constant-w models whose spectra, at various redshift, are expected to coincide with acceptable models within ~1%.
We address the microscopic origin of the current-induced forces by analyzing results of first principles density functional calculations of atomic gold wires connected to two gold electrodes with different electrochemical potentials. We find that current induced forces are closely related to the chemical bonding, and arise from the rearrangement of bond charge due to the current flow. We explain the current induced bond weakening/strengthening by introducing bond charges decomposed into electrode components.
In this letter we propose the design and simulation study of a novel transistor, called HFinFET, which is a hybrid of a HEMT and a FinFET, to obtain excellent performance and good off state control. Followed by the description of the design, 3D device simulation has been performed to predict the characteristics of the device. The device has been benchmarked against published state of the art HEMT as well as planar and non-planar Si NMOSFET data of comparable gate length using standard benchmarking techniques.
We consider the problem of calculating the logical error probability for a stabilizer quantum code subject to random Pauli errors. To access the regime of large code distances where logical errors are extremely unlikely we adopt the splitting method widely used in Monte Carlo simulations of rare events and Bennett's acceptance ratio method for estimating the free energy difference between two canonical ensembles. To illustrate the power of these methods in the context of error correction, we calculate the logical error probability $P_L$ for the 2D surface code on a square lattice with a pair of holes for all code distances $d\le 20$ and all error rates $p$ below the fault-tolerance threshold. Our numerical results confirm the expected exponential decay $P_L\sim \exp{[-\alpha(p)d]}$ and provide a simple fitting formula for the decay rate $\alpha(p)$. Both noiseless and noisy syndrome readout circuits are considered.
In this paper, we present a theoretical description to the quantum coherence and decoherence phenomena of energy transfer in photosynthesis observed in a recent experiment [see Science 316, 1462 (2007)]. As a successive two-color laser pulses with selected frequencies cast on a sample of the photosynthetic purple bacterium Rb. sphaeroides two resonant excitations of electrons in chromophores can be generated. However, this effective two-level subsystem will interact with its protein environment and decoherence is inevitable. We describe this subsystem coupled with its environment as a dynamical spin-boson model. The non-Markovian decoherence dynamics is described using a quasi-adiabatic propagator path integral (QUAPI) approach. With the photon-induced effective time-dependent level splitting energy and level flip coupling coefficient between the two excited states and the environment-induced non-Markovian decoherence dynamics, our theoretical result is in good agreement with the experimental data.
Let $\mathbb{F}_q$ be a finite field with $q$ elements, $\psi$ a non-zero element of $\mathbb{F}_q$, and $n$ an integer $\geq 3$ prime to $q$. The aim of this article is to show that the zeta function of the projective variety over $\mathbb{F}_q$ defined by $X_\psi \colon x_1^n+...+x_n^n - n \psi x_1... x_n=0$ has, when $n$ is prime and $X_\psi$ is non singular (i.e. when $\psi^n \neq 1$), an explicit decomposition in factors coming from affine varieties of odd dimension $\leq n-4$ which are of hypergeometric type. The method we use consists in counting separately the number of points of $X_\psi$ and of some varieties of the preceding type and then compare them. This article answers, at least when $n$ is prime, a question asked by D. Wan in his article "Mirror Symmetry for Zeta Functions".
We investigate through high resolution 3D simulations the nonlinear evolution of compressible magnetohydrodynamic flows subject to the Kelvin-Helmholtz instability. We confirm in 3D flows the conclusion from our 2D work that even apparently weak magnetic fields embedded in Kelvin-Helmholtz unstable plasma flows can be fundamentally important to nonlinear evolution of the instability. In fact, that statement is strengthened in 3D by this work, because it shows how field line bundles can be stretched and twisted in 3D as the quasi-2D Cat's Eye vortex forms out of the hydrodynamical motions. In our simulations twisting of the field may increase the maximum field strength by more than a factor of two over the 2D effect. If, by these developments, the Alfv\'en Mach number of flows around the Cat's Eye drops to unity or less, our simulations suggest magnetic stresses will eventually destroy the Cat's Eye and cause the plasma flow to self-organize into a relatively smooth and apparently stable flow that retains memory of the original shear. For our flow configurations the regime in 3D for such reorganization is $4\lesssim M_{Ax} \lesssim 50$, expressed in terms of the Alfv\'en Mach number of the original velocity transition and the initial Alfv\'en speed projected to the flow plan. For weaker fields the instability remains essentially hydrodynamic in early stages, and the Cat's Eye is destroyed by the hydrodynamic secondary instabilities of a 3D nature. Then, the flows evolve into chaotic structures that approach decaying isotropic turbulence. In this stage, there is considerable enhancement to the magnetic energy due to stretching, twisting, and turbulent amplification, which is retained long afterwards. The magnetic energy eventually catches up to the kinetic energy, and the nature of flows become magnetohydrodynamic.
Dependence on the gauge parameters is an important issue in gauge theories: physical quantities have to be independent. Extending BRS transformations by variation of the gauge parameter into a Grassmann variable one can control gauge parameter dependence algebraically. As application we discuss the anomaly coefficient in the Slavnov-Taylor identity, $S$-matrix elements, the vector two-point-function and the coefficients of renormalization group and Callan-Symanzik equation.