ShantanuT01/DACTYL-Pretraining huggingface dataset:
We implemented various DFT+U schemes, including the ACBN0 self-consistent density-functional version of the DFT+U method [Phys. Rev. X 5, 011006 (2015)] within the massively parallel real-space time-dependent density functional theory (TDDFT) code Octopus. We further extended the method to the case of the calculation of response functions with real-time TDDFT+U and to the description of non-collinear spin systems. The implementation is tested by investigating the ground-state and optical properties of various transition metal oxides, bulk topological insulators, and molecules. Our results are found to be in good agreement with previously published results for both the electronic band structure and structural properties. The self consistent calculated values of U and J are also in good agreement with the values commonly used in the literature. We found that the time-dependent extension of the self-consistent DFT+U method yields improved optical properties when compared to the empirical TDDFT+U scheme. This work thus opens a different theoretical framework to address the non equilibrium properties of correlated systems.
This paper is concerned with the positivity of solutions to the Cauchy problem for linear and nonlinear parabolic equations with the biharmonic operator as fourth order elliptic principal part. Generally, Cauchy problems for parabolic equations of fourth order have no positivity preserving property due to the change of sign of the fundamental solution. One has eventual local positivity for positive initial data, but on short time scales, one will in general have also regions of negativity. The first goal of this paper is to find sufficient conditions on initial data which ensure the existence of solutions to the Cauchy problem for the linear biharmonic heat equation which are positive for all times and in the whole space. The second goal is to apply these results to show existence of globally positive solutions to the Cauchy problem for a semilinear biharmonic parabolic equation.
We study the Evolutionary p-Laplace Equation in the singular case 1 < p < 2. We prove that a weak solution has a time derivative in Sobolev's sense and that the time derivative is locally summable to some power > 1.
Context: Swift observations suggest that the X-ray afterglow emission of some gamma-ray bursts (GRB) may have internal origins, and the conventional external shock (ES) cannot be the exclusive source of the afterglow emission. Aims: If the central compact objects of some GRBs are millisecond magentars, the magnetar winds could play an important role in the (internal) X-ray afterglow emission, which is our focus here. Methods: The dynamics and the synchrotron radiation of the termination shock (TS) of the magmnetar winds, as well as the simultaneous GRB ES, are investigated by considering the magnetization of the winds. Results: As a result of the competition between the emission of the wind TS and the GRB ES, two basic types of X-ray afterglows are predicted, i.e., the TS-dominated and the ES-dominated types. Moreover, our results also show that both of the two types of afterglows have a shallow-decay phase and a normal-decay one, as observed by the \textit{Swift} satellite. This indicates that some observed X-ray afterglows could be (internally) produced by the magnetar winds, but not necessarily GRB ESs.
This paper deals with a reduced reference (RR) image quality measure based on natural image statistics modeling. For this purpose, Tetrolet transform is used since it provides a convenient way to capture local geometric structures. This transform is applied to both reference and distorted images. Then, Gaussian Scale Mixture (GSM) is proposed to model subbands in order to take account statistical dependencies between tetrolet coefficients. In order to quantify the visual degradation, a measure based on Kullback Leibler Divergence (KLD) is provided. The proposed measure was tested on the Cornell VCL A-57 dataset and compared with other measures according to FR-TV1 VQEG framework.
We study the transport properties of Dirac electrons across a two-dimensional normal metal-barrier-normal metal (NBN) interfaces in monolayer borophane. We analyse the transmission probability with variation of the width of the barrier region, the incidence energy and transverse momentum. We demonstrate that a gap exists in the transmission probability spectrum and the position, width of transmission gap can be tuned by the barrier strength and transverse momentum respectively. We point out the variation of the ballistic tunneling conductance as a function of the width of the barrier region and incident energy. We find that the oscillatory or decaying nature of the conductance with variation in barrier width depends upon the number of propagating and evanescent modes which are controlled by the incident energy and barrier strength. We show that the conductance as a function of incident energy drops to a minimum value when the incident energy becomes identical to the barrier height and identify that this effect is caused by the presence of evanescent modes inside the barrier. Based on these findings we propose a perfectly tunable wavevector filter for Borophane. We expect our findings posses useful applications in borophane based nano-electronic devices.
We suggest how to construct non-perturbatively a renormalized action in quantum mechanics. We discuss similarties and differences with the standard effective action. We propose that the new quantum action is suitable to define and compute quantum instantons and quantum chaos.
A practical method to compute the Riemann zeta function is presented. The method can compute $\zeta(1/2+it)$ at any $\lfloor T^{1/4} \rfloor$ points in $[T,T+T^{1/4}]$ using an average time of $T^{1/4+o(1)}$ per point. This is the same complexity as the Odlyzko-Sch\"onhage algorithm over that interval. Although the method far from competes with the Odlyzko-Sch\"onhage algorithm over intervals much longer than $T^{1/4}$, it still has the advantages of being elementary, simple to implement, it does not use the fast Fourier transform or require large amounts of storage space, and its error terms are easy to control. The method has been implemented, and results of timing experiments agree with its theoretical amortized complexity of $T^{1/4+o(1)}$.
Currently, there is much interest in discovering analytically tractable (3+1)-dimensional models that describe interacting fermions with emerging topological properties. Towards that end we present a three-dimensional tight-binding model of spinless interacting fermions that reproduces, in the low energy limit, a (3+1)-dimensional Abelian topological quantum field theory called BF model. By employing a mechanism equivalent to the Haldane's Chern insulator, we can turn the non-interacting model into a three-dimensional chiral topological insulator. We then isolate energetically one of the two Fermi points of the lattice model. In the presence of suitable fermionic interactions, the system, in the continuum limit, is equivalent to a generalised (3+1)-dimensional Thirring model. The low energy limit of this model is faithfully described by the BF theory. Our approach directly establishes the presence of (2+1)-dimensional BF theory at the boundary of the lattice and it provides a way to detect the topological order of the model through fermionic density measurements.
We propose two methods of estimating a systematic error in extrapolation to the infinite-size limit in the study of measuring the Haldane gaps of the one-dimensional Heisenberg antiferromagnet with the integer spin up to S=5. The finite-size gaps obtained by numerical diagonalizations based on Lanczos algorithm are presented for sizes that have not previously been reported. The changes of boundary conditions are also examined. We successfully demonstrate that our methods of extrapolation work well. The Haldane gap for S=1 is stimated to be $0.4104789 \pm 0.0000013$. We successfully obtain the gaps up to S=5, which make us confirm the asymptotic formula of the Haldane gap in $S\to\infty$.
We investigate the occurrence and nature of naked singularities in the gravitational collapse of an adiabatic perfect fluid in self-similar higher dimensional space-times. It is shown that strong curvature naked singularities could occur if the weak energy condition holds. Its implication for cosmic censorship conjecture is discussed. Known results of analogous studies in four dimensions can be recovered.
A relativistic model for quasielastic (QE) lepton-nucleus scattering is presented. The effects of final-state interactions (FSI) between the ejected nucleon and the residual nucleus are described in the relativistic Green's function (RGF) model where FSI are consistently described with exclusive scattering using a complex optical potential. The results of the model are compared with experimental results of electron and neutrino scattering.
We analyse the two-point and marked correlation functions of haloes and galaxies in three variants of the chameleon $f(R)$ gravity model using N-body simulations, and compare to a fiducial $\Lambda$CDM model based on general relativity (GR). Using a halo occupation distribution prescription (HOD) we populate dark matter haloes with galaxies, where the HOD parameters have been tuned such that the galaxy number densities and the real-space galaxy two-point correlation functions in the modified gravity models match those in GR to within $1\sim3\%$. We test the idea that since the behaviour of gravity is dependent on environment, marked correlation functions may display a measurable difference between the models. For this we test marks based on the density field and the Newtonian gravitational potential. We find that the galaxy marked correlation function shows significant differences measured in different models on scales smaller than $r\lesssim 20~h^{-1}$ Mpc. Guided by simulations to identify a suitable mark, this approach could be used as a new probe of the accelerated expansion of the Universe.
We consider Serrin's overdetermined problem for the torsional rigidity and Alexandrov's Soap Bubble Theorem. We present new integral identities, that show a strong analogy between the two problems and help to obtain better (in some cases optimal) quantitative estimates for the radially symmetric configuration. The estimates for the Soap Bubble Theorem benefit from those of Serrin's problem.
In this article, we consider two models of directed polymers in random environment: a discrete model and a continuous model. We consider these models in dimension greater or equal to 3 and we suppose that the normalized partition function is bounded in L^2. Under these assumptions, Sinai proved a local limit theorem for the discrete model, using a perturbation expansion. In this article, we give a new method for proving Sinai's local limit theorem. This new method can be transposed to the continuous setting in which we prove a similar local limit theorem.
We present an encoded hybrid quantum repeater scheme using qubit-repetition and Calderbank-Shor-Steane codes. For the case of repetition codes, we propose an explicit implementation of the quantum error-correction protocol. Moreover, we analyze the entangled-pair distribution rate for the hybrid quantum repeater with encoding and we clearly identify a triple trade-off between the efficiency of the codes, the memory decoherence time, and the local gate errors. Finally, we show that in the presence of reasonable imperfections our system can achieve rates of roughly 24 Hz per memory for 20 km repeater spacing, a final distance of 1280 km, and a final fidelity of about 0.95.
We give a generic spectral decomposition of the derived category of twisted D-modules on a moduli stack of mirabolic vector bundles on a curve X in characteristic p: that is, we construct an equivalence with the derived category of quasi-coherent sheaves on a moduli stack of mirabolic local systems on X. This equivalence may be understood as a tamely ramified form of the geometric Langlands equivalence. When X has genus 1, this equivalence generically solves (in the sense of noncommutative geometry) the quantum Calogero-Moser system.
The highly flattened distribution of satellite galaxies in the Milky Way presents a number of puzzles. Firstly, its polar alignment stands out from the planar alignments commonly found in other galaxies. Secondly, recent proper motion measurements reveal that the orbital angular momentum of at least 3, and possibly as many as 8, of the Milky Ways satellites point (within 30 degrees) along the axis of their flattened configuration, suggesting some form of coherent motion. In this paper we use a high resolution cosmological simulation to investigate whether this pattern conflicts with the expectations of the cold dark matter model of structure formation. We find that this seemingly unlikely set up occurs often: approximately 35% of the time we find systems in which the angular momentum of 3 individual satellites point along, or close to, the short axis of the satellite distribution. In addition, in 30% of the systems we find that the net angular momentum of the 6 best aligned satellites lies within 35 degrees of the short axis of the satellite distribution, as observed for the Milky Way.
We consider a dilute gas of granular material inside a box, kept in a stationary state by shaking. A wall separates the box into two identical compartments, save for a small hole at some finite height $h$. As the gas is cooled, a second order phase transition occurs, in which the particles preferentially occupy one side of the box. We develop a quantitative theory of this clustering phenomenon and find good agreement with numerical simulations.
An example of entropy enigma with a controlled CFT dual was recently studied in arXiv:1108.0411. The enigmatic bulk configurations, considered within the STU model, can be mapped under spectral flow into black rings with three monopole and dipole charges. Even though the bulk and CFT configurations existed in the same region of parameter space, the Bekenstein-Hawking entropy of the bulk configurations was found to be lower than the microscopic entropy from the CFT. While it is possible that the difference in entropy is due to the bulk and boundary configurations being at different points in the moduli space, it is also possible that the bulk configurations embeddable within the STU model are not the most entropic. New families of BPS black ring solutions with four electric and four dipole magnetic charges have recently been explicitly constructed in arXiv:1201.2585. These black rings are not embeddable within the STU model. In this paper we investigate if these black rings can be entropically dominant over the STU model black rings. We find that the new black rings are always entropically subdominant to the STU-model black rings. However, for small fourth dipole charge these black rings continue to be dominant over the BMPV in a small region of parameters and are thus enigmatic.
Non-Rigid Structure from Motion (NRSfM) refers to the problem of reconstructing cameras and the 3D point cloud of a non-rigid object from an ensemble of images with 2D correspondences. Current NRSfM algorithms are limited from two perspectives: (i) the number of images, and (ii) the type of shape variability they can handle. These difficulties stem from the inherent conflict between the condition of the system and the degrees of freedom needing to be modeled -- which has hampered its practical utility for many applications within vision. In this paper we propose a novel hierarchical sparse coding model for NRSFM which can overcome (i) and (ii) to such an extent, that NRSFM can be applied to problems in vision previously thought too ill posed. Our approach is realized in practice as the training of an unsupervised deep neural network (DNN) auto-encoder with a unique architecture that is able to disentangle pose from 3D structure. Using modern deep learning computational platforms allows us to solve NRSfM problems at an unprecedented scale and shape complexity. Our approach has no 3D supervision, relying solely on 2D point correspondences. Further, our approach is also able to handle missing/occluded 2D points without the need for matrix completion. Extensive experiments demonstrate the impressive performance of our approach where we exhibit superior precision and robustness against all available state-of-the-art works in some instances by an order of magnitude. We further propose a new quality measure (based on the network weights) which circumvents the need for 3D ground-truth to ascertain the confidence we have in the reconstructability. We believe our work to be a significant advance over state-of-the-art in NRSFM.
We study in the physical frame the phenomenon of spontaneous scalarization that occurs in scalar-tensor theories of gravity for compact objects. We discuss the fact that the phenomenon occurs exactly in the regime where the Newtonian analysis indicates it should not. Finally we discuss the way the phenomenon depends on the equation of state used to describe the nuclear matter.
Baryon density and magnetic field effect on chaos for the holographic dual of a $Q \bar Q$ system at finite temperature is studied. A string in an AdS Reissner Nordstrom background, and in a metric with magnetic field near the black hole horizon is considered and small time-dependent perturbations of the static configurations are investigated. The proximity to the horizon induces chaos, which is softened increasing the chemical potential or the magnetic field. A background geometry including the effect of a dilaton is also examined. The Maldacena, Shenker, and Stanford bound on the Lyapunov exponents characterizing the perturbations is satisfied for finite baryon chemical potential and magnetic field and when the dilaton is included in the metric.
We investigate turbulent properties of the non-star-forming, translucent molecular cloud, MBM16 by applying the statistical technique of a two-dimensional spatial power spectrum (SPS) on the neutral hydrogen (HI) observations obtained by the Galactic Arecibo L-Band Feed Array HI (GALFA-HI) survey. The SPS, calculated over the range of spatial scales from 0.1 to 17 pc, is well represented with a single power-law function, with a slope ranging from -3.3 to -3.7 and being consistent over the velocity range of MBM16 for a fixed velocity channel thickness. However, the slope varies significantly with the velocity slice thickness, suggesting that both velocity and density contribute to HI intensity fluctuations. By using this variation we estimate the slope of 3D density fluctuations in MBM16 to be -3.7\pm0.2. This is significantly steeper than what has been found for HI in the Milky Way plane, the Small Magellanic Cloud, or the Magellanic Bridge, suggesting that interstellar turbulence in MBM16 is driven on scales >17 pc and that the lack of stellar feedback could be responsible for the steep power spectrum.
In framework of classical consideration of electron trajectories in crossed electric and magnetic fields and conductivity of electron system on cyclotron resonance in single layer graphene possibility to achieve cyclotron lasing in hexagonal boron nitride single layer graphene sandwiches is discussed. By simplified consideration with known data on scattering rate in the sandwiches it is demonstrated that the continuing wave laser action can be achieved in high quality sandwiches at room temperature at frequencies above one tera hertz in magnetic field above one Tesla.
This paper introduces the Attracting Random Walks model, which describes the dynamics of a system of particles on a graph with $n$ vertices. At each step, a single particle moves to an adjacent vertex (or stays at the current one) with probability proportional to the exponent of the number of other particles at a vertex. From an applied standpoint, the model captures the rich get richer phenomenon. We show that the Markov chain exhibits a phase transition in mixing time, as the parameter governing the attraction is varied. Namely, mixing time is $O(n\log n)$ when the temperature is sufficiently high and $\exp(\Omega(n))$ when temperature is sufficiently low. When $\mathcal{G}$ is the complete graph, the model is a projection of the Potts model, whose mixing properties and the critical temperature have been known previously. However, for any other graph our model is non-reversible and does not seem to admit a simple Gibbsian description of a stationary distribution. Notably, we demonstrate existence of the dynamic phase transition without decomposing the stationary distribution into phases.
For fixed weights w_1,...,w_n, and for d>0, we let B denote a collection of d*n balls, with d balls of weight w_i for each i=1,...,n. We consider the problem of assigning the balls to n bins with capacities C_1,...,C_n, in such a way that each bin is assigned d balls, without exceeding its capacity. When d>>0, we give sufficient criteria for the feasibility of this problem, which coincide up to explicit constants with the natural set of necessary conditions. Furthermore, we show that our constants are optimal when the weights w_i are distinct. The feasibility criteria that we present here are used elsewhere (in commutative algebra) to study the asymptotic behavior of the Castelnuovo-Mumford regularity of symmetric monomial ideals.
We analyze the branching ratio for the FCNC mode $K^+\to\pi^+\nu\bar\nu$\ in the standard model with QCD effects taken into account consistently to next-to-leading order. This involves a two-loop renormalization group analysis for the charm contribution, presented in this paper, and the calculation of $O(\alpha_s)$ corrections to all orders in $m_t/M_W$ for the top-quark case that we have described elsewhere. The inclusion of next-to-leading corrections reduces considerably the theoretical uncertainty due to the choice of the renormalization scales, inherent in any calculation to finite order in perturbation theory. For $K^+\to\pi^+\nu\bar\nu$\ this point has not been discussed previously. In particular, the related uncertainty in the determination of $|V_{td}|$ from $B(K^+\to\pi^+\nu\bar\nu)$ is reduced from $\sim 30\%$ to $\sim 7\%$ for typical values of the parameters. Simultaneously also the dependence of $B(K^+\to\pi^+\nu\bar\nu)$ on the choice of $m_c$ is considerably reduced. We also give the next-to-leading order expression for the short-distance part of $K_L\to\mu^+\mu^-$. Impacts of our calculations on the determination of the unitarity triangle are presented.
We investigate the extent to which the nuclear transverse response to electron scattering in the quasielastic region, evaluated in the random-phase approximation can be described by ring approximation calculations. Different effective interactions based on a standard model of the type g'+V_pi+V_rho are employed. For each momentum transfer, we have obtained the value of g'_0 permitting the ring response to match the position of the peak and/or the non-energy weighted sum rule provided by the random-phase approach has been obtained. It is found that, in general, it is not possible to reproduce both magnitudes simultaneously for a given g'_0 value.