ShantanuT01/DACTYL-Pretraining huggingface dataset:
For smooth solutions to Maxwell's equations sourced by a smooth charge-current distribution $j_a$ in stationary, asymptotically flat spacetimes, one can prove an energy conservation theorem which asserts the vanishing of the sum of (i) the difference between the final and initial electromagnetic self-energy of the charge distribution, (ii) the net electromagnetic energy radiated to infinity (and/or into a black hole/white hole), and (iii) the total work done by the electromagnetic field on the charge distribution via the Lorentz force. A similar conservation theorem can be proven for linearized gravitational fields off of a stationary, asymptotically flat background, with the second order Einstein tensor playing the role of an effective stress-energy tensor of the linearized field. In this paper, we prove the above theorems for smooth sources and then investigate the extent to which they continue to hold for point particle sources. The ``self-energy'' of point particles is ill defined, but in the electromagnetic case, we can consider situations where, initially and finally, the point charges are stationary and in the same spatial position, so that the self-energy terms should cancel. Under certain assumptions concerning the decay behavior of source-free solutions to Maxwell's equations, we prove the vanishing of the sum of the net energy radiated to infinity and the net work done on the particle by the DeWitt-Brehme radiation reaction force. We also obtain a similar conservation theorem for angular momentum in an axisymmetric spacetime. In the gravitational case, we argue that similar conservation results should hold for freely falling point masses whose orbits begin and end at infinity.
The hopping dynamics of two fermionic species with different effective masses in the one-dimensional Hubbard model driven by an external field is theoretically investigated. A multiple-time-scale asymptotic analysis of the driven asymmetric Hubbard model shows that a high-frequency bichromatic external field can sustain a new kind of low-energy particle bound state (doublon), in which two fermions of different species occupy nearest neighbor sites and co-tunnel along the lattice. The predictions of the asymptotic analysis are confirmed by direct numerical simulations of the two-particle Hubbard Hamiltonian.
In this paper we start to investigate a new body of questions in additive combinatorics. The fundamental Cauchy--Davenport theorem gives a lower bound on the size of a sumset A+B for subsets of the cyclic group Zp of order p (p prime), and this is just one example of a large family of results. Our aim in this paper is to investigate what happens if we restrict the number of elements of one set that we may use to form the sums. Here is the question we set out to answer: given two subsets, A and B, does B have a subset C of bounded size such that A+C is large, perhaps even comparable to the size of A+B? In particular, can we get close to the lower bound of the Cauchy--Davenport theorem? Our main results show that, rather surprisingly, in many circumstances it is possible to obtain not merely an asymptotic version of the usual sumset bound, but even the exact bound itself.
[Abridged]We present the morphological analysis based on HST-NICMOS observations in the F160W filter of a sample of 32 early-type galaxies (ETGs) at 1<z<2 with spectroscopic confirmation of their redshift and spectral type. We find that ETGs at are composed of two distinct populations, an older population (oETGs) and a younger population (yETGs) whose mean ages differ by about 1.5-2 Gyr. Young ETGs are not denser than local ones since they follow the size-mass relation of local ETGs and luminosity evolution brings them onto the local Kormendy and size-luminosity relations. On the constrary, old ETGs do not follow the size-mass relation of local ETGs and luminosity evolution does not account for the discrepancy they show with respect to the local size-luminosity and Kormendy relations. An increase of their effective radius R_e by a factor 2.5-3 (a density decrease by a factor 15-30) from z~1.5-2 to z~0 is required to bring these galaxies onto the local scaling relations. The different behaviour shown by the two populations implies different formation and evolution scenarios. The older population must have formed at higher-z in a sort of dissipative gas-rich collapse ables to produce remnants which at z~2 are old and compact. The size evolution they must experience from z~2 to z~0 has to leave unchanged their mass to not exceed the local number of high-mass ETGs. Thus, major merging cannot fit this requirement. The younger population of ETGs can be formed later through subsequent episodes of merging which increased progressively their size and assembled their mass down to z~2. At z<2 they evolve purely in luminosity since episodes of major merging would bring them far from the local scaling relations.
We consider motion of an underdamped Brownian particle in a washboard potential that is subjected to an unbiased time-periodic external field. While in the limiting deterministic system in dependence of the strength and phase of the external field directed net motion can exist, for a finite temperature the net motion averages to zero. Strikingly, with the application of an additional time-delayed feedback term directed particle motion can be accomplished persisting up to fairly high levels of the thermal noise. In detail, there exist values of the feedback strength and delay time for which the feedback term performs oscillations that are phase locked to the time-periodic external field. This yields an effective biasing rocking force promoting periods of forward and backward motion of distinct duration, and thus directed motion. In terms of phase space dynamics we demonstrate that with applied feedback desymmetrization of coexisting attractors takes place leaving the ones supporting either positive or negative velocities as the only surviving ones. Moreover, we found parameter ranges for which in the presence of thermal noise the directed transport is enhanced compared to the noise-less case.
We measure the evolution of the galaxy stellar mass function from z=1.3 to z=0.5 using the first 53,608 redshifts of the ongoing VIMOS Public Extragalactic Survey (VIPERS). We estimate the galaxy stellar mass function at several epochs discussing in detail the amount of cosmic variance affecting our estimate. We find that Poisson noise and cosmic variance of the galaxy mass function in the VIPERS survey are comparable with the statistical uncertainties of large surveys in the local universe. VIPERS data allow us to determine with unprecedented accuracy the high-mass tail of the galaxy stellar mass function, which includes a significant number of galaxies that are usually too rare to detect with any of the past spectroscopic surveys. At the epochs sampled by VIPERS, massive galaxies had already assembled most of their stellar mass. We apply a photometric classification in the (U-V) rest-frame colour to compute the mass function of blue and red galaxies, finding evidence for the evolution of their contribution to the total number density budget: the transition mass above which red galaxies dominate is found to be about 10^10.4 M_sun at z=0.55 and evolves proportionally to (1+z)^3. We are able to trace separately the evolution of the number density of blue and red galaxies with masses above 10^11.4 M_sun, in a mass range barely studied in previous work. We find that for such large masses, red galaxies show a milder evolution with redshift, when compared to objects at lower masses. At the same time, we detect a population of similarly massive blue galaxies, which are no longer detectable below z=0.7. These results show the improved statistical power of VIPERS data, and give initial promising indications of mass-dependent quenching of galaxies at z~1. [Abridged]
In this work, we use different methods to extract the surface rotation rate of Kepler targets showing solar-like oscillations.
Pion-photoproduction data is examined to check for the nucleon-helicity conservation predicted by asymptotic QCD. The differential cross section shows agreement with constituent-counting rules, and polarization data is not in disagreement with conservation of nucleon helicity. However large uncertainties in the polarization measurements do not allow a conclusive statement. The helicity amplitudes from a partial-wave analysis are also examined for helicity conservation. While the amplitudes become small as $s$ increases, the $s$ dependence of the helicity-conserving amplitudes is similar to the dependence of the non-conserving amplitudes.
In action understanding in indoor, we have to recognize human pose and action considering privacy. Although camera images can be used for highly accurate human action recognition, camera images do not preserve privacy. Therefore, we propose a new task for human instance segmentation from invisible information, especially airborne ultrasound, for action recognition. To perform instance segmentation from invisible information, we first convert sound waves to reflected sound directional images (sound images). Although the sound images can roughly identify the location of a person, the detailed shape is ambiguous. To address this problem, we propose a collaborative learning variational autoencoder (CL-VAE) that simultaneously uses sound and RGB images during training. In inference, it is possible to obtain instance segmentation results only from sound images. As a result of performance verification, CL-VAE could estimate human instance segmentations more accurately than conventional variational autoencoder and some other models. Since this method can obtain human segmentations individually, it could be applied to human action recognition tasks with privacy protection.
The existence of a minimum time uncertainty is usually argued to be a consequence of the combination of quantum mechanics and general relativity. Most of the studies that point to this result are nonetheless based on perturbative quantization approaches, in which the effect of matter on the geometry is regarded as a correction to a classical background. In this paper, we consider rainbow spacetimes constructed from doubly special relativity by using a modification of the proposals of Magueijo and Smolin. In these models, gravitational effects are incorporated (at least to a certain extent) in the definition of the energy-momentum of particles without adhering to a perturbative treatment of the back reaction. In this context, we derive and compare the expressions of the time uncertainty in quantizations that use as evolution parameter either the background or the rainbow time coordinates. These two possibilities can be regarded as corresponding to perturbative and non-perturbative quantization schemes, respectively. We show that, while a non-vanishing time uncertainty is generically unavoidable in a perturbative framework, an infinite time resolution can in fact be achieved in a non-perturbative quantization for the whole family of doubly special relativity theories with unbounded physical energy.
Several studies have tried to ascertain whether or not the increase in abundance of the early-type galaxies (E-S0a's) with time is mainly due to major mergers, reaching opposite conclusions. We have tested it directly through semi-analytical modelling, by studying how the massive early-type galaxies with log(M_*/Msun)>11 at z~0 (mETGs) would have evolved backwards-in-time, under the hypothesis that each major merger gives place to an early-type galaxy. The study was carried out just considering the major mergers strictly reported by observations at each redshift, and assuming that gas-rich major mergers experience transitory phases of dust-reddened, star-forming galaxies (DSFs). The model is able to reproduce the observed evolution of the galaxy LFs at z<~1, simultaneously for different rest-frame bands (B, I, and K) and for different selection criteria on color and morphology. It also provides a framework in which apparently-contradictory results on the recent evolution of the luminosity function (LF) of massive, red galaxies can be reconciled, just considering that observational samples of red galaxies can be significantly contaminated by DSFs. The model proves that it is feasible to build up ~50-60% of the present-day mETG population at z<~1 and to reproduce the observational excess by a factor of ~4-5 of late-type galaxies at 0.8<z<1 through the coordinated action of wet, mixed, and dry major mergers, fulfilling global trends that are in general agreement with mass-downsizing. The bulk of this assembly takes place during ~1 Gyr elapsed at 0.8<z<1. The model suggests that major mergers have been the main driver for the observational migration of mass from the massive-end of the blue galaxy cloud to that of the red sequence in the last ~8 Gyr.(Abridged)
The conversion of the IR emission into star formation rate can be strongly dependent on the physical properties of the dust, which are affected by the environmental conditions where the dust is embedded. We study here the dust properties of a set of HII regions in the Local Group Galaxy M33 presenting different spatial configurations between the stars, gas and dust to understand the dust evolution under different environments. We model the SED of each region using the DustEM tool and obtain the mass relative to hydrogen for Very Small Grains (YVSG), Polycyclic Aromatic Hydrocarbons (YPAH) and Big Grains (YBG). The relative mass of the VSGs (YVSG/YTOT) is a factor of 1.7 higher for HII regions classified as filled and mixed than for regions presenting a shell structure. The enhancement of VSGs within NGC 604 and NGC 595 is correlated to expansive gas structures with velocities greater than 50 km/s. The gas-to-dust ratio derived for the HII regions in our sample exhibits two regimes related to the HI-H2 transition of the ISM. Regions corresponding to the HI diffuse regime present a gas-to-dust ratio compatible with the expected value if we assume that the gas-to-dust ratio scales linearly with metallicity, while regions corresponding to a H2 molecular phase present a flatter dust-gas surface density distribution. The fraction of VSGs can be affected by the conditions of the interstellar environment: strong shocks of 50-90 km/s existing in the interior of the most luminous HII regions can lead to fragmentation of BGs into smaller ones, while the more evolved shell and clear shell objects provide a more quiescent environment where reformation of dust BG grains might occur. The gas-to-dust variations found in this analysis might imply that grain coagulation and/or gas-phase metals incorporation to the dust mass is occurring in the interior of the HII regions in M33.
Constants of motion are calculated for 2+1 dimensional gravity with topology R \times T^2 and negative cosmological constant. Certain linear combinations of them satisfy the anti - de Sitter algebra so(2,2) in either ADM or holonomy variables. Quantisation is straightforward in terms of the holonomy parameters, and the modular group is generated by these conserved quantities. On inclusion of the Hamiltonian three new global constants are derived and the quantum algebra extends to the conformal algebra so(2,3).
The optical beam splitter is a widely-used device in photonics-based quantum information processing. Specifically, linear optical networks demand large numbers of beam splitters for unitary matrix realization. This requirement comes from the beam splitter property that a photon cannot go back out of the input ports, which we call "directionally-biased". Because of this property, higher dimensional information processing tasks suffer from rapid device resource growth when beam splitters are used in a feed-forward manner. Directionally-unbiased linear-optical devices have been introduced recently to eliminate the directional bias, greatly reducing the numbers of required beam splitters when implementing complicated tasks. Analysis of some originally directional optical devices and basic principles of their conversion into directionally-unbiased systems form the base of this paper. Photonic quantum walk implementations are investigated as a main application of the use of directionally-unbiased systems. Several quantum walk procedures executed on graph networks constructed using directionally-unbiased nodes are discussed. A significant savings in hardware and other required resources when compared with traditional directionally-biased beam-splitter-based optical networks is demonstrated.
Electron spins in a semiconductor quantum well couple to an electric field {\it via} spin-orbit interaction. We show that the standard spin-orbit coupling mechanisms can provide extraordinary efficient electron spin manipulation by an in-plane ac electric field.
Consecutive stochastic 90{\deg} polarization switching events, clearly resolved in recent experiments, are described by a new nucleation and growth multi-step model. It extends the classical Kolmogorov-Avrami-Ishibashi approach and includes possible consecutive 90{\deg}- and parallel 180{\deg}-switching events. The model predicts the results of simultaneous time-resolved macroscopic measurements of polarization and strain, performed on a tetragonal Pb(Zr,Ti)O3 ceramic in a wide range of electric fields over a time domain of five orders of the magnitude. It allows the determination of the fractions of individual switching processes, their characteristic switching times, activation fields, and respective Avrami indices.
The velocity dispersion of the ultra diffuse galaxy NGC1052-DF2 was found to be $\sigma_{\rm gc}=7.8^{+5.2}_{-2.2} \ \mathrm{kms^{-1}}$, much lower than expected from the stellar mass -- halo mass relation and nearly identical to the expected value from the stellar mass alone. This result was based on the radial velocities of ten luminous globular clusters that were assumed to be associated with the galaxy. A more precise measurement is possible from high resolution spectroscopy of the diffuse stellar light. Here we present an integrated spectrum of the diffuse light of NGC1052-DF2 obtained with the Keck Cosmic Web Imager, with an instrumental resolution of $\sigma_{\rm instr}\approx 12 \ \mathrm{kms^{-1}}$. The systemic velocity of the galaxy is $v_{\rm sys}=1805\pm 1.1 \ \mathrm{kms^{-1}}$, in very good agreement with the average velocity of the globular clusters ($\langle v_{\rm gc}\rangle = 1803\pm 2 \ \mathrm{kms^{-1}}$). There is no evidence for rotation within the KCWI field of view. We find a stellar velocity dispersion of $\sigma_{\rm stars}=8.4 \pm 2.1 \ \mathrm{kms^{-1}}$, consistent with the dispersion that was derived from the globular clusters. The implied dynamical mass within the half-light radius $r_{1/2}=2.7 \ \mathrm{kpc}$ is $M_{\rm dyn}= (1.3 \pm 0.8) \times 10^8 $ M$_{\odot}$, similar to the stellar mass within that radius ($M_{\rm stars}=(1.0 \pm 0.2) \times 10^8 \ \mathrm{M}_{\odot}$). With this confirmation of the low velocity dispersion of NGC1052-DF2, the most urgent question is whether this "missing dark matter problem" is unique to this galaxy or applies more widely.
We model the large kinematic data sets for the four Milky Way dwarf spheroidal (dSph) satellites: Carina, Fornax, Sculptor and Sextans, recently published by Walker et al. The member stars are selected using a reliable dynamical interloper removal scheme tested on simulated data. Our member selection is more restrictive than the one based on metallicity indicators as it removes not only contamination due to Milky Way stars but also the unbound stars from the tidal tails. We model the cleaned data sets by adjusting the solutions of the Jeans equations to the profiles of the projected velocity dispersion and kurtosis. The data are well reproduced by models where mass follows light and the best-fitting stellar orbits are isotropic to weakly tangential, as expected from the tidal stirring scenario. The Fornax dwarf, with more than 2400 member stars, is a dSph galaxy with the most accurately determined mass to date: its 1 sigma error following from the sampling errors of the velocity moments is below 5 percent. With mass-to-light ratio of 97 solar units, Sextans seems to be the most dark matter dominated of the four dSph galaxies.
We have derived a fractional Fokker-Planck equation for subdiffusion in a general space-and- time-dependent force field from power law waiting time continuous time random walks biased by Boltzmann weights. The governing equation is derived from a generalized master equation and is shown to be equivalent to a subordinated stochastic Langevin equation.
The linear positive magnetoresistance (LPMR) is a widely observed phenomenon in topological materials, which is promising for potential applications on topological spintronics. However, its mechanism remains ambiguous yet and the effect is thus uncontrollable. Here, we report a quantitative scaling model that correlates the LPMR with the Berry curvature, based on a ferromagnetic Weyl semimetal CoS2 that bears the largest LPMR of over 500% at 2 Kelvin and 9 Tesla, among known magnetic topological semimetals. In this system, masses of Weyl nodes existing near the Fermi level, revealed by theoretical calculations, serve as Berry-curvature monopoles and low-effective-mass carriers. Based on the Weyl picture, we propose a relation \[\text{MR}=\frac{e}{\hbar }B{{\Omega }_{\text{F}}}\], with B being the applied magnetic field and \[{{\Omega }_{\text{F}}}\] the average Berry curvature near the Fermi surface, and further introduce temperature factor to both MR/B slope (MR per unit field) and anomalous Hall conductivity, which establishes the connection between the model and experimental measurements. A clear picture of the linearly slowing down of carriers, i.e., the LPMR effect, is demonstrated under the cooperation of the k-space Berry curvature and real-space magnetic field. Our study not only provides an experimental evidence of Berry curvature induced LPMR for the first time, but also promotes the common understanding and functional designing of the large Berry-curvature MR in topological Dirac/Weyl systems for magnetic sensing or information storage.
To date, almost all of the discussions on topological insulators (TIs) have focused on two- and three-dimensional systems. One-dimensional (1D) TIs manifested in real materials, in which localized spin states may exist at the end or near the junctions, have largely been unexplored. Previous studies have considered the system of gapped graphene nanoribbons (GNRs) possessing spatial symmetries (e.g. inversion) with only termination patterns commensurate with inversion- or mirror-symmetric unit cells. In this work, we prove that a symmetry-protected $\mathbb{Z}_{2}$ topological classification exists for any type of termination. In these cases the Berry phase summed up over all occupied bands turns out to be $\pi$-quantized in the presence of the chiral symmetry. However, it does not always provide the correct corresponding $\mathbb{Z}_{2}$ as one would have expected. We show that only the origin-independent part of the Berry phase gives the correct bulk-boundary correspondence by its $\pi$-quantized values. The resulting $\mathbb{Z}_{2}$ invariant depends on the choice of the 1D unit cell (defined by the nanoribbon termination) and is shown to be connected to the symmetry eigenvalues of the wave functions at the center and boundary of the Brillouin zone. Using the cove-edged GNRs as examples, we demonstrate the existence of localized states at the end of some GNR segments and at the junction between two GNRs based on a topological analysis. The current results are expected to shed light on the design of electronic devices based on GNRs as well as the understanding of the topological features in 1D systems.