ShantanuT01/DACTYL-Pretraining huggingface dataset:
The validity of dilute gas approximation is explored by making use of the large-sized instanton in quantum mechanical model. It is shown that the Euclidean probability amplitude derived through a dilute gas approximation not only cannot explain the result of the linear combination of atomic orbitals approximation, but also does not exhibit a proper limiting case when the size of instanton is very large.
Based on recent X-ray observations, ultra-fast outflows from supermassive black holes are expected to have enough energy to dramatically affect their host galaxy but their launch and acceleration mechanisms are not well understood. We perform two-dimensional radiation hydrodynamics simulations of UV line-driven disc winds in order to calculate the mass loss rates and kinetic power in these models. We develop a new iterative technique which reduces the mass accretion rate through the inner disc in response to the wind mass loss. This makes the inner disc is less UV bright, reducing the wind power compared to previous simulations which assumed a constant accretion rate with radius. The line-driven winds in our simulations are still extremely powerful, with around half the supplied mass accretion rate being ejected in the wind for black holes with mass $10^8-$$10^{10}\, M_\odot$ accreting at $L/L_{\rm Edd}=0.5-$$0.9$. Our results open up the way for estimating the growth rate of supermassive black hole and evaluating the kinetic energy ejected into the inter stellar medium (active galactic nuclei feedback) based on a physical model of line-driven disc winds.
We consider random energy landscapes constructed from d-dimensional lattices or trees. The distribution of the number of local minima in such landscapes follows a large deviation principle and we derive the associated law exactly for dimension 1. Also of interest is the probability of the maximum possible number of minima; this probability scales exponentially with the number of sites. We calculate analytically the corresponding exponent for the Cayley tree and the two-leg ladder; for 2 to 5 dimensional hypercubic lattices, we compute the exponent numerically and compare to the Cayley tree case.
We show that Maxwell's electromagnetism can be mapped into the Born-Infeld theory in a curved space-time, which depends only on the electromagnetic field in a specific way. This map is valid for any value of the two lorentz invariants $F$ and $G$ confirming that we have included all possible solutions of Maxwell's equations. Our result seems to show that specifying the dynamics and the space-time structure of a given theory can be viewed merely as a choice of representation to describe the physical system.
An integral representation result for strictly positive subharmonic functions of a one-dimensional regular diffusion is established. More precisely, any such function can be written as a linear combination of an increasing and a decreasing subharmonic function that solve an integral equation \[ g(x)=a + \int v(x,y)\mu_A(dy) + \kappa s(x), \] where $a>0$, $\kappa \in \mathbb{R}$, $s$ is a scale function of the diffusion, $\mu_A$ is a Radon measure, and $v$ is a kernel that is explicitly determined by the scale function. This integral equation in turn allows one construct a pair $(g,A)$ such that $g$ is a subharmonic function, $A$ is a continuous additive functional with Revuz measure $\mu_A$ and $g(X)\exp(-A)$ is a local martingale. The changes of measures associated with such pairs are studied and shown to modify the long term behaviour of the original diffusion process to exhibit transience. Theory is illustrated via examples that in particular contain a sequence of measure transformations that render the diffusion irregular in the limit by breaking the state space into distinct regions with soft and hard borders. Finally, the theory is applied to find an "explicit" solution to an optimal stopping problem with random discounting.
We examine noncommutative Chern-Simons theory on a bounded spatial domain. We argue that upon `turning on' the noncommutativity, the edge observables, which characterized the commutative theory, move into the bulk. We show this to lowest order in the noncommutativity parameter appearing in the Moyal star product.   If one includes all orders, the Hamiltonian formulation of the gauge theory ceases to exist, indicating that the Moyal star product must be modified in the presence of a boundary. Alternative descriptions are matrix models. We examine one such model, obtained by a simple truncation of Chern-Simons theory on the noncommutative plane, and express its observables in terms of Wilson lines.
We report bulk magnetization, and elastic and inelastic neutron scattering measurements under an external magnetic field, $H$, on the weakly coupled distorted kagome system, Cu_{2}(OD)_3Cl. Our results show that the ordered state below 6.7 K is a canted antiferromagnet and consists of large antiferromagnetic $ac$-components and smaller ferromagnetic $b$-components. By first-principle calculations and linear spin wave analysis, we present a simple spin hamiltonian with non-uniform nearest neighbor exchange interactions resulting in a system of coupled spin trimers with a single-ion anisotropy that can qualitatively reproduce the spin dynamics of Cu_{2}(OD)_3Cl.
Two-dimensional layered transition metal dichalcogenide (TMDC) materials often exhibit exotic quantum matter phases due to the delicate coupling and competitions between the charge, lattice, orbital, and spin degrees of freedom. Surprisingly, we here present, based on first-principles density-functional theory calculations, the incorporation of all such degrees of freedom in a charge density wave (CDW) of monolayer (ML) TMDC 1$T$-TaS$_2$. We reveal that the CDW formed via the electron-phonon coupling is significantly stabilized by the orbital hybridization. The resulting lattice distortion to the "David-star" superstructure constituted of one cental, six nearest-neighbor, and six next-nearest-neighbor Ta atoms is accompanied by the formation of quasimolecular orbitals due to a strong hybridization of the Ta $t_{\rm 2g}$ orbitals. Furthermore, the flat band of the quasimolecular orbital at the Fermi level has a spin splitting caused by an intramolecular exchange, yielding a full spin polarization with a band-gap opening. Our finding of the intricate charge-lattice-orbital-spin coupling in ML 1$T$-TaS$_2$ provides a framework for the exploration of various CDW phases observed in few-layer or bulk 1$T$-TaS$_2$.
Re-observations with the H.E.S.S. telescope array of the very-high-energy (VHE) source HESS J1018-589 A coincident with the Fermi-LAT $\gamma$-ray binary 1FGL J1018.6-5856 have resulted in a source detection significance of more than 9$\sigma$, and the detection of variability ($\chi^2$/$\nu$ of 238.3/155) in the emitted $\gamma$-ray flux. This variability confirms the association of HESS J1018-589 A with the high-energy $\gamma$-ray binary detected by Fermi-LAT, and also confirms the point-like source as a new very-high-energy binary system. The spectrum of HESS J1018-589 A is best fit with a power-law function with photon index $\Gamma = 2.20 \pm 0.14_{\rm stat} \pm 0.2_{\rm sys}$. Emission is detected up to ~20 TeV. The mean differential flux level is $(2.9 \pm 0.4)\times10^{-13}$ TeV$^{-1}$ cm$^{-2}$ s$^{-1}$ at 1 TeV, equivalent to ~1% of the flux from the Crab Nebula at the same energy. Variability is clearly detected in the night-by-night lightcurve. When folded on the orbital period of 16.58 days, the rebinned lightcurve peaks in phase with the observed X-ray and high-energy phaseograms. The fit of the H.E.S.S. phaseogram to a constant flux provides evidence of periodicity at the level of 3$\sigma$. The shape of the VHE phaseogram and measured spectrum suggest a low inclination, low eccentricity system with a modest impact from VHE $\gamma$-ray absorption due to pair production ($\tau$ < 1 at 300 GeV).
We have obtained nonperturbative one-loop expressions for the mean energy-momentum tensor and current density of Dirac's field on a constant electric-like background. One of the goals of this calculation is to give a consistent description of back-reaction in such a theory. Two cases of initial states are considered: the vacuum state and the thermal equilibrium state. First, we perform calculations for the vacuum initial state. In the obtained expressions, we separate the contributions due to particle creation and vacuum polarization. The latter contributions are related to the Heisenberg-Euler Lagrangian. Then, we study the case of the thermal initial state. Here, we separate the contributions due to particle creation, vacuum polarization, and the contributions due to the work of the external field on the particles at the initial state. All these contributions are studied in detail, in different regimes of weak and strong fields and low and high temperatures. The obtained results allow us to establish restrictions on the electric field and its duration under which QED with a strong constant electric field is consistent. Under such restrictions, one can neglect the back-reaction of particles created by the electric field. Some of the obtained results generalize the calculations of Heisenberg-Euler for energy density to the case of arbitrary strong electric fields.
There has been an increasing research interest in age-invariant face recognition. However, matching faces with big age gaps remains a challenging problem, primarily due to the significant discrepancy of face appearances caused by aging. To reduce such a discrepancy, in this paper we propose a novel algorithm to remove age-related components from features mixed with both identity and age information. Specifically, we factorize a mixed face feature into two uncorrelated components: identity-dependent component and age-dependent component, where the identity-dependent component includes information that is useful for face recognition. To implement this idea, we propose the Decorrelated Adversarial Learning (DAL) algorithm, where a Canonical Mapping Module (CMM) is introduced to find the maximum correlation between the paired features generated by a backbone network, while the backbone network and the factorization module are trained to generate features reducing the correlation. Thus, the proposed model learns the decomposed features of age and identity whose correlation is significantly reduced. Simultaneously, the identity-dependent feature and the age-dependent feature are respectively supervised by ID and age preserving signals to ensure that they both contain the correct information. Extensive experiments are conducted on popular public-domain face aging datasets (FG-NET, MORPH Album 2, and CACD-VS) to demonstrate the effectiveness of the proposed approach.
This article deals with classes of antagonistic games with two players. A game is specified in terms of two `hostile' stochastic processes representing mutual attacks upon random times exerting casualties of random magnitudes. The game ends when one of the players is defeated. We target the first passage time $\tau_\rho$ of the defeat and the number of casualties to either player upon $\tau_\rho$. Here we validate our claim of analytic tractability of the general formulas obtained in [1] under various transforms.
The Fermi Large Area Telescope has provided the measurement of the high energy (20 GeV to 1 TeV) cosmic ray electrons and positrons spectrum with unprecedented accuracy. This measurement represents a unique probe for studying the origin and diffusive propagation of cosmic rays as well as for looking for possible evidences of Dark Matter. In this contribution we focus mainly on astrophysical sources of cosmic ray electrons and positrons which include the standard primary and secondary diffuse galactic contribution, as well as nearby point-sources which are expected to contribute more significantly to higher energies. In this framework, we discuss possible interpretations of Fermi results in relation with other recent experimental data on energetic electrons and positrons (specifically the most recent ones reported by PAMELA, ATIC, PPB-BETS and H.E.S.S.).
We investigate the behavior of higher-form symmetries at various quantum phase transitions. We consider discrete 1-form symmetries, which can be either part of the generalized concept "categorical symmetry" (labelled as $\tilde{Z}_N^{(1)}$) introduced recently, or an explicit $Z_N^{(1)}$ 1-form symmetry. We demonstrate that for many quantum phase transitions involving a $Z_N^{(1)}$ or $\tilde{Z}_N^{(1)}$ symmetry, the following expectation value $ \langle \left( \log O_\mathcal{C} \right)^2 \rangle$ takes the form $\langle \left( \log O_\mathcal{C} \right)^2 \rangle \sim - \frac{A}{\epsilon} P+ b \log P $, where $O_\mathcal{C}$ is an operator defined associated with loop $\mathcal{C}$ (or its interior $\mathcal{A}$), which reduces to the Wilson loop operator for cases with an explicit $Z_N^{(1)}$ 1-form symmetry. $P$ is the perimeter of $\mathcal{C}$, and the $b \log P$ term arises from the sharp corners of the loop $\mathcal{C}$, which is consistent with recent numerics on a particular example. $b$ is a universal microscopic-independent number, which in (2+1)d is related to the universal conductivity at the quantum phase transition. $b$ can be computed exactly for certain transitions using the dualities between (2+1)d conformal field theories developed in recent years. We also compute the "strange correlator" of $O_\mathcal{C}$: $S_{\mathcal{C}} = \langle 0 | O_\mathcal{C} | 1 \rangle / \langle 0 | 1 \rangle$ where $|0\rangle$ and $|1\rangle$ are many-body states with different topological nature.
We investigate the structure of the dark matter halo formed in three different cold dark matter scenarios. We performed N-body simulations of formation of 13 cluster-sized halos. In all runs, density cusps proportional to $r^{-1.5}$ developed at the center. This result was independent of the cosmological models we simulated. We could not reproduce the cusp shallower than $r^{-1.5}$, which was obtained in some of previous studies. We also found that in all runs the density structure evolves in a self-similar way, even in $\Omega\ne 1$ universes. These results show that the formation of structural form is a process decoupled from a background cosmology.
We consider a gauge theory in which a nonassociative Moufang loop takes the place of a structure group. We construct Belavin-Polyakov-Schwartz-Tyupkin (BPST) and t'Hooft like instanton solutions of the gauge theory in seven and eight dimensions.
We present a method to compute the electrooptic tensor from first principles, explicitly taking into account the electronic, ionic and piezoelectric contributions. It allows us to study the non-linear optic behavior of three ferroelectric ABO_3 compounds : LiNbO_3, BaTiO_3 and PbTiO_3. Our calculations reveal the dominant contribution of the soft mode to the electrooptic coefficients in LiNbO_3 and BaTiO_3 and identify the coupling between the electric field and the polar atomic displacements along the B-O chains as the origin of the large electrooptic response in these compounds.
We investigate blow-up phenomena for positive solutions of nonlinear reaction-diffusion equations including a nonlinear convection term $\partial_t u = \Delta u - g(u) \cdot \nabla u + f(u)$ in a bounded domain of $\mathbb{R}^N$ under the dissipative dynamical boundary conditions $\sigma \partial_t u + \partial_\nu u =0$. Some conditions on $g$ and $f$ are discussed to state if the positive solutions blow up in finite time or not. Moreover, for certain classes of nonlinearities, an upper-bound for the blow-up time can be derived and the blow-up rate can be determinated.
Based on the first-principles evolutionary materials design, we report a stable boron Kagome lattice composed of triangles in triangles on a two-dimensional sheet. The Kagome lattice can be synthesized on a silver substrate, with selecting Mg atoms as guest atoms. While the isolated Kagome lattice is slightly twisted without strain, it turns into an ideal triangular Kagome lattice under tensile strain. In the triangular Kagome lattice, we find the exotic electronic properties, such as topologically non-trivial flat band near the Fermi energy and half-metallic ferromagnetism, and predict the quantum anomalous Hall effect in the presence of spin-orbit coupling.
In this elementary note we prove that a polynomial with rational coefficients divides the derivative of some polynomial which splits in $\Q$ if and only if all of its irrational roots are real and simple. This provides an answer to a question posed by Thomas Craven. Similar ideas also lead to a variation of the proof of Belyi's theorem that every algebraic curve defined over an algebraic number field admits a map to $P^1$ which is only ramified above three points. As it turned out, this variation was noticed previously by G. Belyi himself and Leonardo Zapponi.
The accurate determination of the elastic properties is non-trivial for metallic foils. The measured elastic modulus is often described in literature as significantly smaller than the respective modulus of the bulk counterparts. This paper describes a straight forward way to minimize the influence of the measurement on the calculated values using a standard tensile testing device combined with a laser speckle extensometer and advanced data evaluation. The elasticmodulus obtained with a monotonic tensile procedure is compared to values obtained frommultiple loading unloading cycles in the elastic regime. The latter were found to lead to more reproducible and reasonable values with significantly smaller standard deviations. To enable interpretation of the modulus values electron backscatter diffraction and X ray diffraction were used to emphasize the effects of texture and microstructure. Two different electrodeposited copper foilswere characterized since copper iswidely used in many industrial applications.
High real-space-resolution atomic pair distribution functions of La_(1-x)Ca_(x)MnO_3 (x=0.12, 0.25 and 0.33) have been measured using high-energy x-ray powder diffraction to study the size and shape of the MnO_6 octahedron as a function of temperature and doping. In the paramagnetic insulating phase we find evidence for three distinct bond-lengths (~ 1.88, 1.95 and 2.15A) which we ascribe to Mn^{4+}-O, Mn^{3+}-O short and Mn^{3+}-O long bonds respectively. In the ferromagnetic metallic (FM) phase, for x=0.33 and T=20K, we find a single Mn-O bond-length; however, as the metal-insulator transition is approached either by increasing T or decreasing x, intensity progressively appears around r=2.15 and in the region 1.8 - 1.9A suggesting the appearance of Mn^{3+}-O long bonds and short Mn^{4+}-O bonds. This is strong evidence that charge localized and delocalized phases coexist close to the metal-insulator transition in the FM phase.
We present new improved parton distributions for the photon. We fit {\bf all} available data on the photon structure function, $F^{\gamma}_{2}(x,Q^2)$, with $Q^2\ge 3$ GeV$^2$, in order to determine the quark distributions. We also pay particular attention to the gluon distribution in the photon, $g^{\gamma}(x,Q^2)$, which has been poorly constrained in earlier analyses which only include structure function data. We use large $p_T$ jet production in $\gamma \gamma$ collisions from TRISTAN to constrain $g^\gamma $. We also see what information can be gleaned from $\gamma p$ collisions at HERA on $g^{\gamma}$ and on the quark distributions at large $x$, where there are no structure function data. We review future prospects of elucidating the parton distributions of the photon.
We report spectroscopic observations of the $H\alpha$ emission line of the recurrent nova RS~Oph obtained between 12 and 23 August 2021 during the recent outburst. On the basis of the sharp P~Cyg profile superimposed onto the strong H-alpha emission, we estimate that the outflowing velocity of the material surrounding RS Oph is in the range 32 km/s < V_{out} < 68 km/s. The new GAIA distance indicates that the red giant should be probably classified in between II and III luminosity class.   The spectra are available upon request from the authors and on Zenodo.
Equivariant Ehrhart theory enumerates the lattice points in a polytope with respect to a group action. Answering a question of Stapledon, we describe the equivariant Ehrhart theory of the permutahedron, and we prove his Effectiveness Conjecture in this special case.
On the triangular and kagome lattices, short-ranged resonating valence bond (RVB) wave functions can be sampled without the sign problem using a recently-developed Pfaffian Monte Carlo scheme. In this paper, we study the Renyi entanglement entropy in these wave functions using a replica-trick method. Using various spatial bipartitions, including the Levin-Wen construction, our finite-size scaled Renyi entropy gives a topological contribution consistent with $\gamma = \text{ln}(2)$, as expected for a gapped $\mathbb{Z}_{2}$ quantum spin liquid. We prove that the mutual statistics are consistent with the toric code anyon model and rule out any other quasiparticle statistics such as the double semion model.
We report detailed and extensive first-principles molecular-dynamics (MD) simulations of the structure and electronic properties of amorphous InP produced by rapid quenching from the liquid. The structure of the material is found to be strongly ordered chemically, even though there is a significant number of coordination defects and despite the presence of odd-membered rings. We find, as a consequence, that there exists ``wrong bonds'' in the system, in an amount of about 8%; these result from the presence of coordination defects, not of local composition fluctuations, as has been conjectured. The system, in fact, is found to be over-coordinated, which might be the reason for the observed higher density of a-InP compared to c-InP. We have also investigated the possibility of pressure-amorphizing InP. Our calculations indicate that the cost of a transformation of the compressed zinc-blende crystal into an amorphous phase is so large that it is very unlikely that it would take place.
We present detailed temperature and field dependent data obtained from magnetization, resistivity, heat capacity, Hall resistivity and thermoelectric power measurements performed on single crystals of CeZn11. The compounds orders antiferromagnetically at $\sim$ 2 K. The zero-field resistivity and TEP data show features characteristic of a Ce-based intermetallic with crystal electric field splitting and possible correlated, Kondo lattice effects. We constructed the T-H phase diagram for the magnetic field applied along the easy, [110], direction which shows that the magnetic field required to suppress T_N below 0.4 K is in the range of 45-47.5 kOe. A linear behavior of the rho(T) data, H||[110], was observed only for H=45 kOe for 0.46 K<T<1.96 K followed by the Landau-Fermi-liquid regime for a limited range of fields, 47.5 kOe< H<60 kOe. From the analysis of our data, it appears that CeZn11 is a weakly to moderately correlated local moment compound with rather small Kondo temperature. The thermoelectric and transport properties of CeZn11 are mostly governed by the CEF effects. Given the very high quality of our single crystals, quantum oscillations are found for both CeZn11 and its non-magnetic analogue, LaZn11.