ShantanuT01/DACTYL-Pretraining huggingface dataset:
A class of Fleming-Viot processes with decaying sampling rates and $\alpha$-stable motions that correspond to distributions with growing populations are introduced and analyzed. Almost sure long-time scaling limits for these processes are developed, addressing the question of long-time population distribution for growing populations. Asymptotics in higher orders are investigated. Convergence of particle location occupation and inhabitation time processes are also addressed and related by way of the historical process. The basic results and techniques allow general Feller motion/mutation and may apply to other measure-valued Markov processes.
The equatorial motion of extended bodies in a Kerr spacetime is investigated in the framework of the Mathisson-Papapetrou-Dixon model, including the full set of effective components of the quadrupole tensor. The numerical integration of the associated equations shows the specific role of the mass and current quadrupole moment components. While most of the literature on this topic is limited to spin-induced (purely electric) quadrupole tensor, the present analysis highlights the effect of a completely general quadrupole tensor on the dynamics. The contribution of the magnetic-type components is indeed related to a number of interesting features, e.g., enhanced inward/outward spiraling behavior of the orbit and spin-flip-like effects, which may have observational counterparts. Finally, the validity limit of the Mathisson-Papapetrou-Dixon model is also discussed through explicit examples.
We demonstrate that the proper calculation of the linear response for finite-size systems can only be performed if the coupling to the leads/baths is explicitly taken into consideration. We exemplify this by obtaining a Kubo-type formula for heat transport in a finite-size system coupled to two thermal baths, kept at different temperatures. We show that the proper calculation results in a well-behaved response, without the singular contributions from degenerate states encountered when Kubo formulae for infinite-size systems are inappropriately used for finite-size systems.
In a recent paper L.G. Moretto et al [nucl-th/0208024] claim that the negative heat capacities presented in our previously published paper \cite{PRL2000} are "artifacts" coming from the use of periodic boundary conditions in the Lattice-Gas calculations. We stress in this comment that this claim is wrong: in ref. \cite{PRL2000} we did not use periodic boundary conditions and anyhow the boundary conditions are irrelevant for the statistical ensemble used in \cite{PRL2000}. The second claim of [nucl-th/0208024] is that, because of the Coulomb repulsion, systems "with A>60 should present no anomalous negative heat capacities". We show that this conclusion is contradicted by exact Lattice-gas simulations including Coulomb forces which present negative heat capacities even for A>200.
We have obtained deep near infrared J- and K-band observations of 14 BL Herculis and 5 W Virginis SMC stars from the OGLE III survey with the ESO New Technology Telescope equipped with the SOFI infrared camera. From these observations, period-luminosity (P-L) relations in the J and Ks 2MASS bands were derived. The slopes of the K and J band relations of -2.15 +- 0.19 and -1.95 +- 0.24, respectively, agree very well with the corresponding slopes derived previously for population II Cepheids in globular clusters, Galactic bulge and in the Large Magellanic Cloud. The distance modulus to the SMC obtained from our data using P-L relation derived for globular cluster Cepheids equals 18.85 +- 0.07 (statistical) +- 0.07 (systematic without including potential metallicity effect), which within the uncertainties agrees well with the results obtained with other methods.
The Wiener index of a connected graph is the sum of topological distances between all pairs of vertices. Since Wang gave a mistake result on the maximum Wiener index for given tree degree sequence, in this paper, we investigate the maximum Wiener index of trees with given degree sequences and extremal trees which attain the maximum value.
This contribution to the proceedings of the 1999 NATO ASI on Quantum Geometry at Akureyri, Iceland, is based on notes of lectures given by A. Strominger. Topics include N-particle conformal quantum mechanics, extended superconformal quantum mechanics and multi-black hole moduli spaces.
We propose a new method for probing the time variation of the effective Newton's constant $G_{\rm eff}$, based on the optimal redshift weighting scheme, and demonstrate the efficacy using the DESI galaxy spectroscopic survey. We find that with the optimal redshift weights, the evolution of $G_{\rm eff}(z)$ can be significantly better measured: the uncertainty of $G_{\rm eff}(z)$ can be reduced by a factor of $2.2\sim12.8$ using the DESI BGS sample at $z \lesssim0.45$, and by a factor of $1.3\sim4.4$ using the DESI ELG sample covering $0.65\lesssim z\lesssim1.65$.
We study the effect of a single driven tracer particle in a bath of other particles performing the random average process on an infinite line using a stochastic hydrodynamics approach. We consider arbitrary fixed as well as random initial conditions and compute the two-point correlations. For quenched uniform and annealed steady state initial conditions we show that in the large time $T$ limit the fluctuations and the correlations of the positions of the particles grow subdiffusively as $\sqrt{T}$ and have well defined scaling forms under proper rescaling of the labels. We compute the corresponding scaling functions exactly for these specific initial configurations and verify them numerically. We also consider a non translationally invariant initial condition with linearly increasing gaps where we show that the fluctuations and correlations grow superdiffusively as $T^{3/2}$ at large times.
An important theorem by Timofte states that nonnegativity of real $n$-variate symmetric polynomials of degree $d$ can be decided at test sets given by all points with at most $\lfloor\frac{d}{2}\rfloor$ distinct components. However, if the degree is sufficiently larger than the number of variables, then the theorem obviously does not provide nontrivial information. Our approach is to look at $(m + 1)$-dimensional subspaces of even symmetric forms of degree 4d, at which nonnegativity can be checked at $(m - 1)$-points, i.e., points with at most $m - 1 \in \N$ distinct components, where $m$ is independent of the degree of the forms and better than Timofte's bound. Furthermore, for fixed $k \in \N$, we tackle problems concerning the maximum dimension of such subspaces, at which nonnegativity can be checked at all $k$-points, as well as the geometrical and topological structure of the set of all forms whose nonnegativity can be decided at all $k$-points.
The quantum transport properties of graphene and monolayer $MoS_2$ superconductor heterostructures has been of considerable importance in the recent few years. Layered nature of molybdenum disulfide permits the superconducting correlation induction. Moreover, peculiar dynamical features of monolayer $MoS_2$, such as valence band spin-splitting in the nondegenerate $K$ and $K'$ valleys originated from strong spin-orbit coupling, and considerable direct band gap can make it potentially a useful material for electronics applications. Using the Dirac-like Hamiltonian of $MoS_2$ with taking into account the related mass asymmetry and topological contributions, we investigate the effect of spin-triplet $p$-wave pairing symmetry on the superconducting excitations, resulting in Andreev reflection process and Andreev bound state in the corresponding normal-superconductor (NS) and superconductor-normal-superconductor (SNS) structures, respectively. We study how the resulting subgap conductance and Josephson current are affected by the particular symmetry of order parameter. The signature of $p_x$-wave symmetry is found to decline the subgap superconducting energy excitations and, consequently, slightly suppress the Andreev reflection in the case of $p$-doped S region. The essential dynamical parameters $\lambda$ and $\beta$ of $MoS_2$ have significant effect on the both tunneling conductance and Josephson current. Particularly, the considered $p$-wave symmetry in the superconducting bound energies may feature the zero energy states at the interfaces. The critical current oscillations as a function of length of junction are obtained in the $p$-doped S region.
The field-induced multiferroic transition in TbMnO3 has been studied by neutron scattering. Apart strong hysteresis, the magnetic transition associated with the flop of electronic polarization exhibits a memory effect: after a field sweep, TbMnO3 does not exhibit the same phase as that obtained by zero-field cooling. The strong changes in the magnetic excitations across the transition perfectly agree with a rotation of the cycloidal spiral plane indicating that the inverse Dzyaloshinski-Moriya coupling causes the giant magnetoelectric effect at the field-induced transition. The analysis of the zone-center magnetic excitations identifies the electromagnon of the multiferroic high-field phase.
We study the fission yield of recently predicted thermally fissile neutron-rich uranium and thorium nuclei using statistical model. The level density parameters needed for the study are evaluated from the excitation energies of temperature dependent relativistic mean field formalism. The excitation energy and the level density parameter for a given temperature are employed in the convolution integral method to obtain the probability of the particular fragmentation. As representative case, we present the results for the binary fission yield of 250 U and 254 Th. The relative yields are presented for three different temperatures T = 1, 2 and 3 MeV.
In 1980, Gizatullin classified rational surfaces endowed with an automorphism whose action on the Neron-Severi group is parabolic: these surfaces are endowed with an elliptic fibration invariant by the automorphism. The aim of this expository paper is to present for non-experts the details of Gizatullin's original proof, and to provide an introduction to a recent paper by Cantat and Dolgachev.
Topological insulators doped with transition metals have recently been found to host a strong ferromagnetic state with perpendicular to plane anisotropy as well as support a quantum Hall state with edge channel transport, even in the absence of an external magnetic field. It remains unclear however why a robust magnetic state should emerge in materials of relatively low crystalline quality and dilute magnetic doping. Indeed, recent experiments suggest that the ferromagnetism exhibits at least some superparamagnetic character. We report on transport measurements in a sample that shows perfect quantum anomalous Hall quantization, while at the same time exhibits traits in its transport data which suggest inhomogeneities. We speculate that this may be evidence that the percolation path interpretation used to explain the transport during the magnetic reversal may actually have relevance over the entire field range.
We consider field-theoretic models, one consisting purely of scalars, the other also involving fermions, that couple to a set of constant background coupling coefficients transforming as a symmetric observer Lorentz two-tensor. We show that the exact propagators can be cast in the form of a K\"all\'en-Lehmann representation. We work out the resulting form of the Feynman propagators and the equal-time field commutators, and derive sum rules for the spectral density functions.
In the present work, we perform a systematic investigation on p-type codoping in (Ga,Mn)As. Through gradually increasing Zn doping concentration, the hole concentration increases, which should theoretically lead to an increase of the Curie temperature (TC) according to the p-d Zener model. Unexpectedly, although the film keeps its epitaxial structure, both TC and the magnetization decrease. The samples present a phase transition from ferromagnetism to paramagnetism upon increasing hole concentration. In the intermediate regime, we observe a signature of antiferromagnetism. By using channeling Rutherford backscattering spectrometry and particle-induced x-ray emission, the substitutional Mn atoms are observed to shift to interstitial sites, while more Zn atoms occupy Ga sites, which explains the observed behavior. This is also consistent with first-principles calculations, showing that the complex of substitutional Zn and interstitial Mn has the lowest formation energy.
Using the effective mass model for an electron and the dielectric continuum model, analytical solutions of the self-consistent Schr\"odinger-Poisson system of equations are obtained. Quantum mechanical theory of electronic stationary states, the oscillator strengths of quantum transitions and a method of potential profile calculation is developed for the experimentally constructed three-well resonance-tunneling structure --- a separate cascade of quantum cascade detector. For the proposed method, a comparison with the results of other methods and with the results of the experiment was carried out. A good agreement between the calculated value of the detected energy and its experimental value has been obtained, the difference being no more than $2.5\%$.
We present results on the clustering of 282,068 galaxies in the Baryon Oscillation Spectroscopic Survey (BOSS) sample of massive galaxies with redshifts 0.4<z<0.7 which is part of the Sloan Digital Sky Survey III project. Our results cover a large range of scales from ~0.5 to ~90 Mpc/h. We compare these estimates with the expectations of the flat LCDM cosmological model with parameters compatible with WMAP7 data. We use the MultiDark cosmological simulation together with a simple halo abundance matching technique, to estimate galaxy correlation functions, power spectra, abundance of subhaloes and galaxy biases. We find that the LCDM model gives a reasonable description to the observed correlation functions at z~0.5, which is a remarkably good agreement considering that the model, once matched to the observed abundance of BOSS galaxies, does not have any free parameters. However, we find a deviation (>~10%) in the correlation functions for scales less than ~1 Mpc/h and ~10-40 Mpc/h. A more realistic abundance matching model and better statistics from upcoming observations are needed to clarify the situation. We also estimate that about 12% of the "galaxies" in the abundance-matched sample are satellites inhabiting central haloes with mass M>~1e14 M_sun/h. Using the MultiDark simulation we also study the real space halo bias b(r) of the matched catalogue finding that b=2.00+/-0.07 at large scales, consistent with the one obtained using the measured BOSS projected correlation function. Furthermore, the linear large-scale bias depends on the number density n of the abundance-matched sample as b=-0.048-(0.594+/-0.02)*log(n/(h/Mpc)^3). Extrapolating these results to BAO scales we measure a scale-dependent damping of the acoustic signal produced by non-linear evolution that leads to ~2-4% dips at ~3 sigma level for wavenumbers k>~0.1 h/Mpc in the linear large-scale bias.
We present Lya luminosity function (LF), clustering measurements, and Lya line profiles based on the largest sample, to date, of 207 Lya emitters (LAEs) at z=6.6 on the 1-deg^2 sky of Subaru/XMM-Newton Deep Survey (SXDS) field. Our z=6.6 Lya LF including cosmic variance estimates yields the best-fit Schechter parameters of phi*=8.5 +3.0/-2.2 x10^(-4) Mpc^(-3) and L*(Lya)=4.4 +/-0.6 x10^42 erg s^(-1) with a fixed alpha=-1.5, and indicates a decrease from z=5.7 at the >~90% confidence level. However, this decrease is not large, only =~30% in Lya luminosity, which is too small to be identified in the previous studies. A clustering signal of z=6.6 LAEs is detected for the first time. We obtain the correlation length of r_0=2-5 h^(-1) Mpc and bias of b=3-6, and find no significant boost of clustering amplitude by reionization at z=6.6. The average hosting dark halo mass inferred from clustering is 10^10-10^11 Mo, and duty cycle of LAE population is roughly ~1% albeit with large uncertainties. The average of our high-quality Keck/DEIMOS spectra shows an FWHM velocity width of 251 +/-16 km s^(-1). We find no large evolution of Lya line profile from z=5.7 to 6.6, and no anti-correlation between Lya luminosity and line width at z=6.6. The combination of various reionization models and our observational results about the LF, clustering, and line profile indicates that there would exist a small decrease of IGM's Lya transmission owing to reionization, but that the hydrogen IGM is not highly neutral at z=6.6. Our neutral-hydrogen fraction constraint implies that the major reionization process took place at z>~7.
The analysis of the properties of rare-earth based materials relies on the Crystalline Electric Field theory. This theory has to be reconsidered in case of cage-type compounds, where the rare-earth ion can substantially depart from its, high symmetry, average position. It is shown that, in case of an orbital degeneracy at the cage center, a specific Jahn-Teller effect develops in the paramagnetic range: at low temperature, the distribution of the magnetic ion spreads inside the cage, the magnetic entropy is reduced, whereas the cage multipolar susceptibilities are increased. These consequences are put in relation with the properties of some metallic rare-earth cage compounds.
Normal mode decomposition of atomic vibrations has been used to provide microscopic under-standing of thermal transport in amorphous solids for decades. In normal mode methods, it is naturally assumed that atoms vibrate around their equilibrium positions and that individual normal modes are the fundamental vibrational excitations transporting heat. With the abundance of predictions from normal mode methods and experimental measurements now available, we care-fully analyze these calculations in amorphous silicon, a model amorphous solid. We find a number of discrepancies, suggesting that treating individual normal modes as fundamental heat carriers may not be accurate in amorphous solids. Further, our classical and ab-initio molecular dynamics simulations of amorphous silicon demonstrate a large degree of atomic diffusion, especially at high temperatures, leading to the conclusion that thermal transport in amorphous solids could be better described starting from the perspective of liquid dynamics rather than from crystalline solids
We address the problems of an energy spectrum and backscattering of massive Dirac fermions confined in a cylindrical quantum wire. The Dirac fermions are described by the 3D Dirac equation supplemented by time-reversal-invariant boundary conditions at a surface of the wire. Even in zero magnetic field, spectra quantum-confined and surface states substantially depend on a boundary parameter a0. At the wire surface with a0 > 0 (a0 < 0) the surface states form 1D massive subbands inside (outside) the bulk gap. The longitudinal magnetic field transforms the energy spectra. In the limit of the thick wires and the weak magnetic fields, the 1D massless surface subbands arise at half- integer number of magnetic flux quanta passing through the wire cross section. We reveal conditions when backscattering of the surface Dirac fermions by a non-magnetic impurity is suppressed. In addition, we calculate a conductance formed by the massless surface Dirac fermions in the magnetic field in collisional and ballistic regimes.
The homogeneous, isotropic, and flat $\Lambda$CDM universe favored by observations of the cosmic microwave background can be described using only Euclidean geometry, locally correct Newtonian mechanics, and the basic postulates of special and general relativity. We present simple derivations of the most useful equations connecting astronomical observables (redshift, flux density, angular diameter, brightness, local space density,...) with the corresponding intrinsic properties of distant sources (lookback time, distance, spectral luminosity, linear size, specific intensity, source counts,...). We also present an analytic equation for lookback time that is accurate within 0.1% for all redshifts $z$. The exact equation for comoving distance is an elliptic integral that must be evaluated numerically, but we found a simple approximation with errors $< 0.2$% for all redshifts up to $z \approx 50$.
The data indicating existence of different forms of dark matter in the universe as well as the role of this matter in structure formation are briefly reviewed. It is argued that vacuum energy gives a dominant contribution into the total energy density of the universe. The model of structure formation with unstable tau-neutrino with MeV-mass and KeV-majoron is described.
In this paper, we prove the existence of a unique maximal local strong solutions to a stochastic system for both 2D and 3D penalised nematic liquid crystals driven by multiplicative Gaussian noise. In the 2D case, we show that this solution is global.As a by-product of our investigation, but of independent interest, we present a general method based on fixed point arguments to establish the existence and uniqueness of a maximal local solution of an abstract stochastic evolution equations with coefficients satisfying local Lipschitz condition involving the norms of two different Banach spaces.
Jacobi-Forms can be decomposed as a linear combination of Thetafunctions with modular forms as coefficients. It is shown that the space of these coefficient modular forms of Fourier-Jacobi-Forms, which come from Siegel cusp forms, has full rank in every point of the Satake boundary, if the index is 1, the weight is sufficiently large and the Satake boundary point has trivial stabilizer in $\Gamma_{n-1}$. This yields a local automorphic embedding of the Siegel modular variety. Klingen-Poincare series are the main tool. Despite of this richness it is proved that there are more Jacobi index 1 cusp forms than Fourier-Jacobi index 1 cusp forms for all sufficiently large weights extending a result of Dulinski.
Recently neural scene representations have provided very impressive results for representing 3D scenes visually, however, their study and progress have mainly been limited to visualization of virtual models in computer graphics or scene reconstruction in computer vision without explicitly accounting for sensor and pose uncertainty. Using this novel scene representation in robotics applications, however, would require accounting for this uncertainty in the neural map. The aim of this paper is therefore to propose a novel method for training {\em probabilistic neural scene representations} with uncertain training data that could enable the inclusion of these representations in robotics applications. Acquiring images using cameras or depth sensors contains inherent uncertainty, and furthermore, the camera poses used for learning a 3D model are also imperfect. If these measurements are used for training without accounting for their uncertainty, then the resulting models are non-optimal, and the resulting scene representations are likely to contain artifacts such as blur and un-even geometry. In this work, the problem of uncertainty integration to the learning process is investigated by focusing on training with uncertain information in a probabilistic manner. The proposed method involves explicitly augmenting the training likelihood with an uncertainty term such that the learnt probability distribution of the network is minimized with respect to the training uncertainty. It will be shown that this leads to more accurate image rendering quality, in addition to more precise and consistent geometry. Validation has been carried out on both synthetic and real datasets showing that the proposed approach outperforms state-of-the-art methods. The results show notably that the proposed method is capable of rendering novel high-quality views even when the training data is limited.