ShantanuT01/DACTYL-Pretraining huggingface dataset:
We aim to study the solutions of a fractional mesoscopic model of phase transitions in a periodic medium. After investigating the geometric properties of the interface of the associated minimal solutions, we construct minimal interfaces lying to a strip of prescribed direction and universal width.
The purpose of this paper is to prove a conjecture on reciprocity sheaves by Kahn-Saito-Yamazaki. This is accomplished by extending Voevodsky's fundamental results on homotopy invariant (pre)sheaves with transfers to its generalizations, reciprocity sheaves and cube-invariant sheaves in the context of theory of modulus (pre)sheave with transfers. The main results of this paper is expected to play a crucial role in deducing the main properties of the triangulated category of motives with modulus, which is a new triangulated category enlarging Voevodsky's triangulated category of motives to encompass non homotopy invariant motivic phenomena.
We estimate the mass of the Milky Way (MW) within 21.1 kpc using the kinematics of halo globular clusters (GCs) determined by Gaia. The second Gaia data release (DR2) contained a catalogue of absolute proper motions (PMs) for a set of Galactic GCs and satellite galaxies measured using Gaia DR2 data. We select from the catalogue only halo GCs, identifying a total of 34 GCs spanning $2.0 < r < 21.1$ kpc, and use their 3D kinematics to estimate the anisotropy over this range to be $\beta = 0.46^{+0.15}_{-0.19}$, in good agreement, though slightly lower than, a recent estimate for a sample of halo GCs using HST PM measurements further out in the halo. We then use the Gaia kinematics to estimate the mass of the MW inside the outermost GC to be $M(< 21.1 \mathrm{kpc}) = 0.21^{+0.04}_{-0.03} 10^{12} \mathrm{M_\odot}$, which corresponds to a circular velocity of $v_\mathrm{circ}(21.1 \mathrm{kpc}) = 206^{+19}_{-16}$ km/s. The implied virial mass is $M_\mathrm{virial} = 1.28^{+0.97}_{-0.48} 10^{12} \mathrm{M_\odot}$. The error bars encompass the uncertainties on the anisotropy and on the density profile of the MW dark halo, and the scatter inherent in the mass estimator we use. We get improved estimates when we combine the Gaia and HST samples to provide kinematics for 46 GCs out to 39.5 kpc: $\beta = 0.52^{+0.11}_{-0.14}$, $M(< 39.5 \mathrm{kpc}) = 0.42^{+0.07}_{-0.06} 10^{12} \mathrm{M_\odot}$, and $M_\mathrm{virial} = 1.54^{+0.75}_{-0.44} 10^{12} \mathrm{M_\odot}$. We show that these results are robust to potential substructure in the halo GC distribution. While a wide range of MW virial masses have been advocated in the literature, from below $10^{12} \mathrm{M_\odot}$ to above $2 \times 10^{12}\mathrm{M_\odot}$, these new data imply that an intermediate mass is most likely.
Temperature and angular momentum dependence of the quadrupole deformation is studied in the middle of the sd-shell for 28Si and 27Si isotopes using the spherical shell model approach. The shell model calculations have been performed using the standard USD interaction and the canonical partition function constructed from the calculated eigen-solutions. It is shown that the extracted average quadrupole moments show a transitional behavior as a function of temperature and the inferred transitional temperature is shown to vary with angular-momentum. The quadrupole deformation of the individual eigen-states is also analyzed.
We consider a scenario where we wish to bring a closed system of known Hilbert space dimension $d_S$ (the target), subject to an unknown Hamiltonian evolution, back to its quantum state at a past time $t_0$. The target is out of our control: this means that we ignore both its free Hamiltonian and how the system interacts with other quantum systems we may use to influence it. Under these conditions, we prove that there exist protocols within the framework of non-relativistic quantum physics which reset the target system to its exact quantum state at $t_0$. Each "resetting protocol" is successful with non-zero probability for all possible free Hamiltonians and interaction unitaries, save a subset of zero measure. When the target is a qubit and the interaction is sampled from the Haar measure, the simplest resetting circuits have a significant average probability of success and their implementation is within reach of current quantum technologies. Finally, we find that, in case the resetting protocol fails, it is possible to run a further protocol that, if successful, undoes both the natural evolution of the target and the effects of the failed protocol over the latter. By chaining in this fashion several such protocols, one can substantially increase the overall probability of a successful resetting.
We investigate various mean value problems involving order three primitive Dirichlet characters. In particular, we obtain an asymptotic formula for the first moment of central values of the Dirichlet L-functions associated to this family, with a power saving in the error term. We also obtain a large-sieve type result for order three (and six) Dirichlet characters.
Let A be a finite nonempty subset of an additive abelian group G, and let \Sigma(A) denote the set of all group elements representable as a sum of some subset of A. We prove that |\Sigma(A)| >= |H| + 1/64 |A H|^2 where H is the stabilizer of \Sigma(A). Our result implies that \Sigma(A) = Z/nZ for every set A of units of Z/nZ with |A| >= 8 \sqrt{n}. This consequence was first proved by Erd\H{o}s and Heilbronn for n prime, and by Vu (with a weaker constant) for general n.
We study relativistic gyratons which carry an electric charge. The Einstein-Maxwell equations in arbitrary dimensions are solved exactly in the case of a charged gyraton propagating in an asymptotically flat metric.
In this work, we study a model for monolayer molybdenum disulfide with including the intravalley and intervalley electron-electron interaction. We solve the model at a self-consistent mean-field level and get three solutions $L_{0}$, $L_{+}$ and $L_{-}$. As for $L_{0}$, the spin polarizations are opposite at $\textbf{K}$ and $\textbf{K}^{\prime}$ valley and the total magnetization is zero. $L_{\pm}$ describe two degenerate spin-polarized states, and the directions of polarization are opposite for the states of $L_{+}$ and $L_{-}$. Based on these results, the ground state can be deduced to be spin polarized in domains in which their particular states can be randomly described by $L_{+}$ or $L_{-}$. Therefore, a zero net magnetization is induced for zero external magnetic field $\mathbf{B}$, but a global ferromagnetic ground state for a nonzero $\mathbf{B}$. We estimate the size of domains as several nanometers. As the increase of the chemical potential, the ground state changes between $L_{0}$ and $L_{\pm}$, indicating first order phase transitions at the borders, which is coincident with the observation of photoluminescence experiments in the absence of the external magnetic field [J. G. Roch $\it{et}$ $\it{al.}$, Phys. Rev. Lett. ${\bf 124}$, 187602 (2020)].
We present an ALMA study of the ~180 brightest sources in the SCUBA-2 map of the COSMOS field from the S2COSMOS survey, as a pilot study for AS2COSMOS - a full survey of the ~1,000 sources in this field. In this pilot we have obtained 870-um continuum maps of an essentially complete sample of the brightest 182 sub-millimetre sources (S_850um=6.2mJy) in COSMOS. Our ALMA maps detect 260 sub-millimetre galaxies (SMGs) spanning a range in flux density of S_870um=0.7-19.2mJy. We detect more than one SMG counterpart in 34+/-2 per cent of sub-millimetre sources, increasing to 53+/-8 per cent for SCUBA-2 sources brighter than S_850um>12mJy. We estimate that approximately one-third of these SMG-SMG pairs are physically associated (with a higher rate for the brighter secondary SMGs, S_870um>3mJy), and illustrate this with the serendipitous detection of bright [CII] 157.74um line emission in two SMGs, AS2COS0001.1 & 0001.2 at z=4.63, associated with the highest significance single-dish source. Using our source catalogue we construct the interferometric 870um number counts at S_870um>6.2mJy. We use the extensive archival data of this field to construct the multiwavelength spectral energy distribution of each AS2COSMOS SMG, and subsequently model this emission with MAGPHYS to estimate their photometric redshifts. We find a median photometric redshift for the S_870um>6.2mJy AS2COSMOS sample of z=2.87+/-0.08, and clear evidence for an increase in the median redshift with 870-um flux density suggesting strong evolution in the bright-end of the 870um luminosity function.
P. Clarke describes mirror symmetry as a duality between Landau--Ginzburg models, so that the dual of an LG model is another LG model. We describe examples in which the underlying space is a total space of a vector bundle on the projective line, and we show that self-duality occurs in precisely two cases: the cotangent bundle and the resolved conifold.
In many applications to finite Fermi-systems, the pairing problem has to be treated exactly. We suggest a numerical method of exact solution based on SU(2) quasispin algebras and demonstrate its simplicity and practicality. We show that the treatment of binding energies with the use of the exact pairing and uncorrelated monopole contribution of other residual interactions can serve as an effective alternative to the full shell-model diagonalization in spherical nuclei. A self-consistent combination of the exactly treated pairing and Hartree-Fock method is discussed. Results for Sn isotopes indicate a good agreement with experimental data.
We systematically explore zero impact parameter collisions of white dwarfs with the Eulerian adaptive grid code FLASH for 0.64+0.64 M$_{\odot}$ and 0.81+0.81 M$_{\odot}$ mass pairings. Our models span a range of effective linear spatial resolutions from 5.2$\times10^{7}$ to 1.2$\times10^{7}$ cm. However, even the highest resolution models do not quite achieve strict numerical convergence, due to the challenge of properly resolving small-scale burning and energy transport. The lack of strict numerical convergence from these idealized configurations suggest that quantitative predictions of the ejected elemental abundances that are generated by binary white dwarf collision and merger simulations should be viewed with caution. Nevertheless, the convergence trends do allow some patterns to be discerned. We find that the 0.64+0.64 M$_{\odot}$ head-on collision model produces 0.32 M$_{\odot}$ of \nickel[56] and 0.38 M$_{\odot}$ of \silicon[28], while the 0.81+0.81 M$_{\odot}$ head-on collision model produces 0.39 M$_{\odot}$ of \nickel[56] and 0.55 M$_{\odot}$ of \silicon[28] at the highest spatial resolutions. Both mass pairings produce $\sim$0.2 M$_{\odot}$ of unburned \carbon[12]+\oxygen[16]. We also find the 0.64+0.64 M$_{\odot}$ head-on collision begins carbon burning in the central region of the stalled shock between the two white dwarfs, while the more energetic \hbox{0.81+0.81 M$_{\odot}$} head-on collision raises the initial post-shock temperature enough to burn the entire stalled shock region to nuclear statistical equilibrium.
Bounded weak solutions to a particular class of degenerate parabolic cross-diffusion systems are shown to coincide with the unique strong solution determined by the same initial condition on the maximal existence interval of the latter. The proof relies on an estimate established for a relative entropy associated to the system.
Recently, pure transformer-based models have shown great potentials for vision tasks such as image classification and detection. However, the design of transformer networks is challenging. It has been observed that the depth, embedding dimension, and number of heads can largely affect the performance of vision transformers. Previous models configure these dimensions based upon manual crafting. In this work, we propose a new one-shot architecture search framework, namely AutoFormer, dedicated to vision transformer search. AutoFormer entangles the weights of different blocks in the same layers during supernet training. Benefiting from the strategy, the trained supernet allows thousands of subnets to be very well-trained. Specifically, the performance of these subnets with weights inherited from the supernet is comparable to those retrained from scratch. Besides, the searched models, which we refer to AutoFormers, surpass the recent state-of-the-arts such as ViT and DeiT. In particular, AutoFormer-tiny/small/base achieve 74.7%/81.7%/82.4% top-1 accuracy on ImageNet with 5.7M/22.9M/53.7M parameters, respectively. Lastly, we verify the transferability of AutoFormer by providing the performance on downstream benchmarks and distillation experiments. Code and models are available at https://github.com/microsoft/AutoML.
Given an edge colouring of a graph with a set of $m$ colours, we say that the graph is (exactly) $m$-coloured if each of the colours is used. In 1999, Stacey and Weidl, partially resolving a conjecture of Erickson from 1994, showed that for a fixed natural number $m>2$ and for all sufficiently large $k$, there is a $k$-colouring of the complete graph on $\mathbb{N}$ such that no complete infinite subgraph is exactly $m$-coloured. In the light of this result, we consider the question of how close we can come to finding an exactly $m$-coloured complete infinite subgraph. We show that for a natural number $m$ and any finite colouring of the edges of the complete graph on $\mathbb{N}$ with $m$ or more colours, there is an exactly ${\hat m}$-coloured complete infinite subgraph for some ${\hat m}$ satisfying $|m-{\hat m}|\le \sqrt{m/2} + 1/2$; this is best-possible up to the additive constant. We also obtain analogous results for this problem in the setting of $r$-uniform hypergraphs. Along the way, we also prove a recent conjecture of the second author and investigate generalisations of this conjecture to $r$-uniform hypergraphs.
A platform for constructing microscopic Hamiltonians describing bosonic symmetry-protected topological (SPT) states is presented. The Hamiltonians we consider are examples of frustration-free Rokhsar-Kivelson models, which are known to be in one-to-one correspondence with classical stochastic systems in the same spatial dimensionality. By exploring this classical-quantum mapping, we are able to construct a large class of microscopic models which, in a closed manifold, have a non-degenerate gapped symmetric ground state describing the universal properties of SPT states. Examples of one and two dimensional SPT states which illustrate our approach are discussed.
We consider a voltage-biased Normal metal-Insulator-Superconductor (NIS) tunnel junction, connected to a high-temperature external electromagnetic environment. This model system features the commonly observed subgap leakage current in NIS junctions through photon-assisted tunneling which is detrimental for applications. We first consider a NIS junction directly coupled to the environment and analyze the subgap leakage current both analytically and numerically; we discuss the link with the phenomenological Dynes parameter. Then we focus on a circuit where a low-temperature lossy transmission line is inserted between the NIS junction and the environment. We show that the subgap leakage current is exponentially suppressed as the length, $\ell$, and the resistance per unit length, $R_0$, of the line are increased. We finally discuss our results in view of the performance of NIS junctions in applications.
Starting from microscopic and symmetry considerations, we derive the Hamiltonian describing the exchange interaction between the localized Mn spins and the valence band holes in $Ga_{1-x}Mn_x As$. We find that due to the strong spin-orbit coupling in the valence band, this exchange interaction has a rather complex structure and generates a highly anisotropic effective interaction between the Mn spins. The corresponding ground state has a finite ferromagnetic magnetization but is intrinsically spin-disordered even at zero temperature.
We present a 20-pc, volume-limited sample of M7-L8 dwarfs created through spectroscopic follow-up of sources selected from the Two Micron All Sky Survey (2MASS) Second Incremental Release Point Source Catalog. In this paper, we present optical spectroscopy of 198 candidate nearby ultracool dwarfs, including 12 late-M and L dwarfs likely to be within 20 pc of the Sun and 94 more distant late-type dwarfs. We have also identified five ultracool dwarfs with spectral signatures of low-gravity. Combining these data with previous results, we define a sample of 99 ultracool dwarfs in 91 systems within 20 pc. These are used to estimate the J- and K-band luminosity functions for dwarfs with optical spectral types between M7 and L8 (10.5<M_J<15, 9.5<M_K<13). We find a space density of 4.9 x 10^-3 pc^-3 for late-M dwarfs (M7-M9.5) and a lower limit of 3.8 x 10^-3 pc^-3 for L dwarfs.
The covariant kinetic approach for the radiative plasma, a mixture of a relativistic moving gas plus radiation quanta (photons, neutrinos, or gravitons) is generalized to D spatial dimensions. The operational and physical meaning of Eckart's temperature is reexamined and the D-dimensional expressions for the transport coefficients (heat conduction, bulk and shear viscosity) are explicitly evaluated to first order in the mean free time of the radiation quanta. Weinberg's conclusion that the mixture behaves like a relativistic imperfect simple fluid (in Eckart's formulation) depends neither on the number of spatial dimensions nor on the details of the collisional term. The case of Thomson scaterring is studied in detail, and some consequences for higher dimensional cosmologies are also discussed.
Here we propose that the excess flux of particle events of energy near 1 EeV from the direction of the Galactic Center region is due to the production of cosmic rays by the last few Gamma Ray Bursts in our Galaxy. The basic idea is that protons get accelerated inside Gamma Ray Bursts, then get ejected as neutrons, decay and so turn back into protons, meander around the inner Galaxy for some time, and then interact again, turning back to neutrons to be observed at our distance from the Galactic Center region, where most star formation is happening in our Galaxy. We demonstrate that this suggestion leads to a successful interpretation of the data, within the uncertainties of cosmic ray transport time scales in the inner Galaxy, and in conjunction with many arguments in the literature.
We present an investigation of partial filament eruption on 2012 June 17 in the active region NOAA 11504. For the first time, we observed the vertical splitting process during the partial eruption with high resolution narrow band images at 10830 . The active filament was rooted in a small sunspot of the active region. Particularly, it underwent the partial eruption in three steps, i.e. the precursor, the first eruption, and the second eruption, while the later two were associated with a C1.0 flare and a C3.9 flare, respectively. During the precursor, slow magnetic reconnection took place between the filament and the adjoining loops that also rooted in the sunspot. The continuous reconnection not only caused the filament to split into three groups of threads vertically but also formed a new filament, which was growing and accompanied brightening took place around the site. Subsequently, the growing filament erupted together with one group splitted threads, resulted in the first eruption. At the beginning of the first eruption, a subsequent magnetic reconnection occurred between the erupting splitted threads and another ambient magnetic loop. After about three minutes, the second eruption occurred as a result of the eruption of two larger unstable filaments induced by the magnetic reconnection. The high-resolution observation provides a direct evidence that magnetic reconnection between filament and its ambient magnetic fields could induce the vertical splitting of the filament, resulting in partial eruption.
We use transient absorption spectroscopy with circularly polarized x-rays to detect laser-excited hole states below the Fermi level and compare their dynamics with that of unoccupied states above the Fermi level in ferromagnetic [Co/Pd] multilayers. While below the Fermi level an instantaneous and significantly stronger demagnetization is observed, above the Fermi level the demagnetization is delayed by 35+/-10 fs. This provides a direct visualization of how ultrafast demagnetization proceeds via initial spin-flip scattering of laser-excited holes to the subsequent formation of spin waves.
The quantum ferromagnetic transition of itinerant electrons is considered. We give a pedagogical review of recent results which show that zero-temperature soft modes that are commonly neglected, invalidate the standard Landau-Ginzburg-Wilson description of this transition. If these modes are taken into account, then the resulting order parameter field theory is nonlocal in space and time. Nevertheless, for both disordered and clean systems the critical behavior has been exactly determined for spatial dimensions d>2 and d>1, respectively. The critical exponents characterizing the paramagnetic-to-ferromagnetic transition are dimensionality dependent, and substantially different from both mean-field critical exponents, and from the classical Heisenberg exponents that characterize the transition at finite temperatures. Our results should be easily observable, particularly those for the disordered case, and experiments to check our predictions are proposed.
This paper presents a study of the galactic environment of a chemically-pristine (<0.6% solar metallicity) Lyman Limit system (LLS) discovered along the sightline toward QSO SDSSJ135726.27+043541.4 (zQSO=1.233) at projected distance d=126 physical kpc (pkpc) from a luminous red galaxy (LRG) at z=0.33. Combining deep Hubble Space Telescope images, MUSE integral field spectroscopic data, and wide-field redshift survey data has enabled an unprecedented, ultra-deep view of the environment around this LRG-LLS pair. A total of 12 galaxies, including the LRG, are found at d<~400 pkpc and line-of-sight velocity dv<600 km/s of the LLS, with intrinsic luminosity ranging from 0.001L* to 2L* and a corresponding stellar mass range of Mstar=10^{7-11} Msun. All 12 galaxies contribute to a total mass of Mstar=1.6e11 Msun with ~80% contained in the LRG. The line-of-sight velocity dispersion of these galaxies is found to be {\sigma}_group=230 km/s with the center of mass at d_group=118 pkpc and line-of-sight velocity offset of {\Delta}v_group=181 km/s from the LLS. Three of these are located at d<~100 pkpc from the LLS, and they are all faint with intrinsic luminosity <0.02 L* and gas phase metallicity of ~10% solar in their interstellar medium. The disparity in the chemical enrichment level between the LLS and the group members suggests that the LLS originates in infalling intergalactic medium and that parts of the intergalactic gas near old and massive galaxies can still remain chemically pristine through the not too distant past.
We develop a real-space extension of the dual fermion approach. This method is formulated in terms of real-space Green's functions and local vertex functions, which enables us to discuss local and nonlocal correlations in inhomogeneous systems with an arbitrary geometric structure. We first demonstrate that the approach gives us reasonable results for a homogenous periodic system by taking into account onsite and nearest-neighbor intersite correlations. Moreover, we study the half-filled Hubbard model on the quasiperiodic Penrose lattice and clarify the role of intersite correlations for the Mott transition. The intersite correlations lead to a rich structure in local observables which is inherited from the quasiperiodic structure of the lattice.