ShantanuT01/DACTYL-Pretraining huggingface dataset:
We investigate the Hall effect in two different theoretical models of strongly correlated systems: a system made of weakly coupled Luttinger liquids, in the presence of umklapp scattering, and the 2D triangular lattice, with nearest-neighbor hopping and a local Hubbard interaction. In the first model we use a memory function approach to compute the Hall coefficient as a function of temperature and frequency in the presence of umklapp scattering. We find a power-law correction to the free-fermion value (band value), with an exponent depending on the Luttinger parameter $K_{\rho}$. At sufficiently high temperature or frequency the Hall coefficient approaches the band value. We discuss the applications to Hall experiments made in quasi 1D organic compounds. In the second model, the complete temperature and doping dependencies of the high-frequency Hall coefficient $\RH$ are evaluated analytically and numerically for small, intermediate, and strong interactions using various approximation schemes. We find that $\RH$ follows the semiclassical $1/qn^*$ law near T=0, but exhibits a striking $T$-linear behavior with an interaction- and doping-dependent slope at high temperature. We compare our results with Hall measurements performed in cobaltates.
The growing number of stellar-mass binary black hole mergers discovered by Advanced LIGO and Advanced Virgo are starting to constrain the binaries' origin and environment. However, we still lack sufficiently accurate modeling of binary formation channels to obtain strong constraints, or to identify sub-populations. One promising formation mechanism that could result in different black hole properties is binaries merging within the accretion disks of Active Galactic Nuclei (AGN). Here we show that the black holes' orbital alignment with the AGN disks preferentially selects heavier black holes. We carry out Monte Carlo simulations of orbital alignment with AGN disks, and find that AGNs harden the initial black hole mass function. Assuming an initial power law mass distribution $M_{\rm bh}^{-\beta}$, we find that the power law index changes by $\Delta \beta\sim1.3$, resulting in a more top-heavy population of merging black holes. This change is independent of the mass of, and accretion rate onto, the supermassive black hole in the center of the AGN. Our simulations predict an AGN-assisted merger rate of $\sim4$Gpc$^{-3}$yr$^{-1}$. With its hardened mass spectra, the AGN channel could be responsible for $10-50$% of gravitational-wave detections.
The magnetic states of the non-centrosymmetric, pressure induced superconductor CeCoGe3 have been studied with magnetic susceptibility, muon spin relaxation(muSR), single crystal neutron diffraction and inelastic neutron scattering (INS). CeCoGe3 exhibits three magnetic phase transitions at T_N1 = 21 K, T_N2 = 12 K and T_N3 = 8 K. The presence of long range magnetic order below T_N1 is revealed by the observation of oscillations of the asymmetry in the muSR spectra between 13 K and 20 K and a sharp increase in the muon depolarization rate. Single crystal neutron diffraction measurements reveal magnetic Bragg peaks consistent with propagation vectors of k = 2/3 between T_N1 and T_N2, k = 5/8between T_N2 and T_N3 and k = 1/2 below T_N3. An increase in intensity of the (1 1 0) reflection between T_N1 and T_N3 also indicates a ferromagnetic component in these phases. These measurements are consistent with an equal moment, two-up, two-down magnetic structure below T_N3, with a magnetic moment of 0.405(5) mu_B/Ce. Above T_N2, the results are consistent with an equal moment, two-up, one-down structure with a moment of 0.360(6) mu_B/Ce. INS studies reveal two crystal-field (CEF) excitations at 19 and 27 meV. From an analysis with a CEF model, the wave-functions of the J = 5/2 multiplet are evaluated along with a prediction for the magnitude and direction of the ground state magnetic moment. Our model correctly predicts that the moments order along the c axis but the observed magnetic moment of 0.405(5) mu_B is reduced compared to the predicted moment of 1.01 mu_B. This is ascribed to hybridization between the localized Ce^3+ f-electrons and the conduction band. This suggests that CeCoGe3 has a degree of hybridization between that of CeRhGe3 and the non-centrosymmetric superconductor CeRhSi3.
It is well known that photospheric flux emergence is an important process for stressing coronal fields and storing magnetic free energy, which may then be released during a flare. The \emph{Helioseismic and Magnetic Imager} (HMI) onboard the \emph{Solar Dynamics Observatory} (SDO) captured the entire emergence of NOAA AR 11158. This region emerged as two distinct bipoles, possibly connected underneath the photosphere, yet characterized by different photospheric field evolutions and fluxes. The combined active region complex produced 15 GOES C--class, 2 M--class, and the X2.2 Valentine's Day Flare during the four days after initial emergence on February 12th, 2011. The M and X class flares are of particular interest because they are nonhomologous, involving different subregions of the active region. We use a Magnetic Charge Topology together with the Minimum Current Corona model of the coronal field to model field evolution of the complex. Combining this with observations of flare ribbons in the 1600\AA\ channel of the \emph{Atmospheric Imaging Assembly} (AIA) onboard SDO, we propose a minimization algorithm for estimating the amount of reconnected flux and resulting drop in magnetic free energy during a flare. For the M6.6, M2.2, and X2.2 flares, we find a flux exchange of $4.2\times 10^{20}\unit{Mx},\ 2.0 \times 10^{20}\unit{Mx}, \hbox{and} 21.0 \times 10^{20}\unit{Mx}$, respectively, resulting in free energy drops of $3.89\times 10^{30}\unit{ergs}, 2.62\times 10^{30}\unit{ergs}, \hbox{and} 1.68\times 10^{32}\unit{ergs}$.
We present two results concerning the relation between poles and cuts by using the example of N=1 U(N_c) gauge theories with matter fields in the adjoint, fundamental and anti-fundamental representations. The first result is the on-shell possibility of poles, which are associated with flavors and on the second sheet of the Riemann surface, passing through the branch cut and getting to the first sheet. The second result is the generalization of hep-th/0311181 (Intriligator, Kraus, Ryzhov, Shigemori, and Vafa) to include flavors. We clarify when there are closed cuts and how to reproduce the results of the strong coupling analysis by matrix model, by setting the glueball field to zero from the beginning. We also make remarks on the possible stringy explanations of the results and on generalization to SO(N_c) and USp(2N_c) gauge groups.
We reconsider the GUT-baryogenesis mechanism for generating the baryon asymmetry of the Universe. The baryon asymmetry is produced by the out of equilibrium decay of coloured Higgs bosons at the GUT scale, conserving B-L. If neutrinos are Majorana particles, lepton number violating interactions erase the lepton number excess, but part of the baryon asymmetry may be preserved, provided those interactions are not in thermal equilibrium when the sphaleron processes become effective, at $T \sim 10^{12}~ GeV$. We analyse whether this mechanism for baryogenesis is feasible in a variety of GUT models of fermion masses proposed in the literature, based on horizontal symmetries.
We consider disorder-order phase transitions in the three-dimensional version of the scalar noise model (SNM) of flocking. Our results are analogous to those found for the two-dimensional case. For small velocity (v <= 0.1) a continuous, second-order phase transition is observable, with the diffusion of nearby particles being isotropic. By increasing the particle velocities the phase transition changes to first order, and the diffusion becomes anisotropic. The first-order transition in the latter case is probably caused by the interplay between anisotropic diffusion and periodic boundary conditions, leading to a boundary condition dependent symmetry breaking of the solutions.
The many worlds interpretation of quantum mechanics (MWI) states that the world we live in is just one among many parallel worlds. It is widely believed that because of this commitment to parallel worlds, the MWI violates common sense. Some go so far as to reject the MWI on this basis. This is despite its myriad of advantages to physics (e.g. consistency with relativity theory, mathematical simplicity, realism, determinism, etc.). Here, we make the case that common sense in fact favors the MWI. We argue that causal explanations are commonsensical only when they are local causal explanations. We present several quantum mechanical experiments that seem to exhibit nonlocal "action at a distance". Under the assumption that only one world exists, these experiments seem immune to local causal explanation. However, we show that the MWI, by taking all worlds together, can provide local causal explanations of the experiments. The MWI therefore restores common sense to physical explanation.
Phase perturbations due to inclined surface magnetic field of active region strength are calculated numerically in quiet Sun and simple sunspot models in order to estimate and compare the direct and indirect (thermal) effects of the fields on helioseismic waves. It is found that the largest direct effects occur in highly inclined field characteristic of penumbrae, and scale roughly linearly with magnetic field strength. The combined effects of sunspot magnetic and thermal anomalies typically yield negative travel-time perturbations in penumbrae. Travel-time shifts in umbrae depend on details of how the thermal and density structure differs from the quiet Sun. The combined shifts are generally not well approximated by the sum of the thermal and magnetic effects applied separately, except at low field strengths of around 1 kG or less, or if the thermal shift is small. A useful rule-of-thumb appears to be that travel-time perturbations in umbrae are predominantly thermal, whereas in penumbrae they are mostly magnetic.
Since the solution of the so-called folk problems of smoothability, there has been a special interest in the properties of classical time and volume functions of spacetimes. Here we supply some information that complements the one provided in arXiv:1108.5120v3 and arXiv:1301.2909v1, and discuss some results. As an illustration, we show that any Cauchy temporal function for a globally hyperbolic spacetime remains Cauchy temporal for close metrics ---which, in particular, implies stability for global hyperbolicity.
To clarify the electronic density of states (DOS) around the conduction band bottom for state of the art transparent amorphous oxide semiconductors (TAOSs), InGaZnO4 and In2MgO4, we fabricated TAOS-based transparent thin film transistors (TTFTs) and measured their gate voltage dependence of thermopower (S). TAOS-based TTFTs exhibit an unusual S behavior. The |S|-value abruptly increases, but then gradually decreases as Vg increases, clearly suggesting the anti-parabolic shaped DOS is hybridized with the original parabolic shaped DOS around the conduction band bottom.
This paper analytically investigates the Darcy-Poisson-Nernst-Planck system. This system is a mathematical model for electrolyte solutions. In this paper, we consider electrolyte solutions, which consist of a neutral fluid and multiple suspended charged chemical species with arbitrary valencies. We prove global existence and uniqueness of weak solutions in two space dimensions.
We present a cosmological zoom-in simulation of a Milky Way-like galaxy used to explore the formation and evolution of star clusters. We investigate in particular the origin of the bimodality observed in the colour and metallicity of globular clusters, and the environmental evolution through cosmic times in the form of tidal tensors. Our results self-consistently confirm previous findings that the blue, metal-poor clusters form in satellite galaxies which are accreted onto the Milky Way, while the red, metal-rich clusters form mostly in situ or, to a lower extent in massive, self-enriched galaxies merging with the Milky Way. By monitoring the tidal fields these populations experience, we find that clusters formed in situ (generally centrally concentrated) feel significantly stronger tides than the accreted ones, both in the present-day, and when averaged over their entire life. Furthermore, we note that the tidal field experienced by Milky Way clusters is significantly weaker in the past than at present-day, confirming that it is unlikely that a power-law cluster initial mass function like that of young massive clusters, is transformed into the observed peaked distribution in the Milky Way with relaxation-driven evaporation in a tidal field.
We report quantum Monte Carlo calculations of ground and low-lying excited states for nuclei with A \leq 7 using a realistic Hamiltonian containing the Argonne v18 two-nucleon and Urbana IX three-nucleon potentials. A detailed description of the Green's function Monte Carlo algorithm for systems with state-dependent potentials is given and a number of tests of its convergence and accuracy are performed. We find that the Hamiltonian being used results in ground states of both 6Li and 7Li that are stable against breakup into subclusters, but somewhat underbound compared to experiment. We also have results for 6He, 7He, and their isobaric analogs. The known excitation spectra of all these nuclei are reproduced reasonably well and we predict a number of excited states in 6He and 7He. We also present spin-polarized one-body and several different two-body density distributions. These are the first microscopic calculations that directly produce nuclear shell structure from realistic interactions that fit NN scattering data.
In this brief note we bring out the analogy between the arithmetic of elliptic curves and the Riemann zeta-function.
In this paper we study a subordinate Brownian motion with a Gaussian component and a rather general discontinuous part. The assumption on the subordinator is that its Laplace exponent is a complete Bernstein function with a L\'evy density satisfying a certain growth condition near zero. The main result is a boundary Harnack principle with explicit boundary decay rate for non-negative harmonic functions of the process in $C^{1,1}$ open sets. As a consequence of the boundary Harnack principle, we establish sharp two-sided estimates on the Green function of the subordinate Brownian motion in any bounded $C^{1,1}$ open set $D$ and identify the Martin boundary of $D$ with respect to the subordinate Brownian motion with the Euclidean boundary.
We present inelastic neutron scattering and magnetization measurements of the antiferromagnetic insulator LaMnPO that are well described by a Heisenberg spin model. These measurements are consistent with the presence of two-dimensional magnetic correlations up to a temperature T$_{max}$ $\approx$ 700 K >> T$_{N}$ = 375 K, the N\'eel temperature. Optical transmission measurements show the T = 300 K direct charge gap $\Delta$ = 1 eV has decreased only marginally by 500 K and suggest it decreases by only 10% at T$_{max}$. Density functional theory and dynamical mean field theory calculations reproduce a direct charge gap in paramagnetic LaMnPO only when a strong Hund's coupling J$_{H}$ = 0.9 eV is included, as well as onsite Hubbard U = 8 eV. These results show the direct charge gap in LaMnPO is rather insensitive to antiferromagnetic exchange coupling and instead is a result of the local physics governed by U and J$_{H}$.
We study the topological phase diagram of a setup composed of two nanowires with strong Rashba spin-orbit interaction subjected to an external magnetic field and brought into the proximity to a bulk $s$-wave superconductor in the presence of a supercurrent flowing through it. The supercurrent reduces the critical values of the Zeeman energy and crossed Andreev superconducting pairing required to reach the topological phase characterized by the presence of one Majorana bound state localized at each system end. We demonstrate that, even in the regime of the crossed Andreev pairing being smaller than the direct proximity pairing, a relatively weak magnetic field drives the system into the topological phase due to the presence of the supercurrent.
Considering an arbitrary, varying equation of the state parameter, the thermodynamic properties of the dark energy fluid in a semiclassical loop quantum cosmology scenario, which we consider the inverse volume modification, is studied. The equation of the state parameters are corrected as a semiclassical one during considering the effective behavior. Assuming that the apparent horizon has Hawking temperature, the modified entropy-area relation is obtained, we find that this relation is different from the one which is obtained by considering the holonomy correction. Considering the dark energy is a thermal equilibrium fluid, we get the expressions for modified temperature, chemical potential and entropy. The temperature, chemical potential and entropy are well-defined in the semiclassical regions.
For compact, even-dimensional, locally symmetric spaces, we obtain precise estimates on the number of singularities of Selberg's and Ruelle's zeta functions considered by U. Bunke and M. Olbrich.
The infrared-radio correlation (IRRC) underpins many commonly used radio luminosity-star formation rate (SFR) calibrations. In preparation for the new generation of radio surveys we revisit the IRRC of low-$z$ galaxies by (a) drawing on the best currently available IR and 1.4 GHz radio photometry, plus ancillary data over the widest possible area, and (b) carefully assessing potential systematics. We compile a catalogue of $\sim$9,500 z $<$ 0.2 galaxies and derive their 1.4 GHz radio ($L_{\mathrm{1.4}}$), total IR, and monochromatic IR luminosities in up to seven bands, allowing us to parameterize the wavelength-dependence of monochromatic IRRCs from 22-500 $\mu$m. For the first time for low-$z$ samples, we quantify how poorly matched IR and radio survey depths bias measured median IR/radio ratios, $\overline{q}_{\mathrm{TIR}}$, and discuss the level of biasing expected for low-z IRRC studies in ASKAP/MeerKAT fields. For our subset of $\sim$2,000 high-confidence star-forming galaxies we find a median $\overline{q}_{\mathrm{TIR}}$ of 2.54 (scatter: 0.17 dex). We show that $\overline{q}_{\mathrm{TIR}}$ correlates with $L_{\mathrm{1.4}}$, implying a non-linear IRRC with slope 1.11$\pm$0.01. Our new $L_{\mathrm{1.4}}$-SFR calibration, which incorporates this non-linearity, reproduces SFRs from panchromatic SED fits substantially better than previous IRRC-based recipes. Finally, we match the evolutionary slope of recently measured $\overline{q}_{\mathrm{TIR}}$-redshift trends without having to invoke redshift evolution of the IRRC. In this framework, the redshift evolution of $\overline{q}_{\mathrm{TIR}}$ reported at GHz frequencies in the literature is the consequence of a partial, redshift-dependent sampling of a non-linear IRRC obeyed by low-$z$ {\it and} distant galaxies.
We propose a simple and systematic method to quantize the cranking model and to calculate the matrix elements of intrinsic operators entering the generalized intensity relations. An example of the application is given to show the Coriolis coupling effects for B(E3) values of the 3- octupole states in Gd isotopes.
In analogy with the classical theory of Eichler integrals for integral weight modular forms, Lawrence and Zagier considered examples of Eichler integrals of certain half-integral weight modular forms. These served as early prototypes of a new type of object, which Zagier later called a quantum modular form. Since then, a number of others have studied similar examples. Here we develop the theory in a general context, giving rise to a well-defined class of quantum modular forms. Since elements of this class show up frequently in examples of combinatorial and number theoretical interest, we propose the study of the general properties of this space of quantum modular forms. We conclude by giving a set of fundamental questions concerning this space of objects which merit further study.
Most popular deep models for action recognition in videos generate independent predictions for short clips, which are then pooled heuristically to assign an action label to the full video segment. As not all frames may characterize the underlying action---many are common across multiple actions---pooling schemes that impose equal importance on all frames might be unfavorable. In an attempt to tackle this problem, we propose discriminative pooling, based on the notion that among the deep features generated on all short clips, there is at least one that characterizes the action. To identify these useful features, we resort to a negative bag consisting of features that are known to be irrelevant, for example, they are sampled either from datasets that are unrelated to our actions of interest or are CNN features produced via random noise as input. With the features from the video as a positive bag and the irrelevant features as the negative bag, we cast an objective to learn a (nonlinear) hyperplane that separates the unknown useful features from the rest in a multiple instance learning formulation within a support vector machine setup. We use the parameters of this separating hyperplane as a descriptor for the full video segment. Since these parameters are directly related to the support vectors in a max-margin framework, they can be treated as a weighted average pooling of the features from the bags, with zero weights given to non-support vectors. Our pooling scheme is end-to-end trainable within a deep learning framework. We report results from experiments on eight computer vision benchmark datasets spanning a variety of video-related tasks and demonstrate state-of-the-art performance across these tasks.
For d-dimensional irrational ellipsoids E with d >= 9 we show that the number of lattice points in rE is approximated by the volume of rE, as r tends to infinity, up to an error of order o(r^{d-2}). The estimate refines an earlier authors' bound of order O(r^{d-2}) which holds for arbitrary ellipsoids, and is optimal for rational ellipsoids. As an application we prove a conjecture of Davenport and Lewis that the gaps between successive values, say s<n(s), s,n(s) in Q[Z^d], of a positive definite irrational quadratic form Q[x], x in R^d, are shrinking, i.e., that n(s) - s -> 0 as s -> \infty, for d >= 9. For comparison note that sup_s (n(s)-s) < \infty and \inf_s (n(s)-s) >0, for rational Q[x] and d>= 5. As a corollary we derive Oppenheim's conjecture for indefinite irrational quadratic forms, i.e., the set Q[Z^d] is dense in R, for d >= 9, which was proved for d >= 3 by G. Margulis in 1986 using other methods. Finally, we provide explicit bounds for errors in terms of certain characteristics of trigonometric sums.
This work is devoted to improving empirical mass-luminosity relations and mass-metallicity-luminosity relation for low mass stars. For these stars, observational data in the mass-luminosity plane or the mass-metallicity-luminosity space subject to non-negligible errors in all coordinates with different dimensions. Thus a reasonable weight assigning scheme is needed for obtaining more reliable results. Such a scheme is developed, with which each data point can have its own due contribution. Previous studies have shown that there exists a plateau feature in the mass-luminosity relation. Taking into account the constraints from the observational luminosity function, we find by fitting the observational data using our weight assigning scheme that the plateau spans from 0.28 to 0.50 solar mass. Three-piecewise continuous improved mass-luminosity relations in K, J, H and V bands, respectively, are obtained. The visual mass-metallicity-luminosity relation is also improved based on our K band mass-luminosity relation and the available observational metallicity data.
This article gives a self-contained exposition on Ribet's construction of a Hecke eigenform of weight 2 with certain congruence properties.