ShantanuT01/DACTYL-Pretraining huggingface dataset:
It was recently shown by Lubetzky and Peres (2016) and by Sardari (2018) that Ramanujan graphs, i.e., graphs with the optimal spectrum, exhibit cutoff of the simple random walk in an optimal time and have an optimal almost-diameter. We show that this spectral condition can be replaced by a weaker condition, the Sarnak-Xue density property, to deduce similar results. This allows us to prove that some natural families of Schreier graphs of the $SL_2(\mathbb{F}_t)$-action on the projective line exhibit cutoff, thus proving a special case of a conjecture of Rivin and Sardari.
The machinery is suggested to describe the varying spacetime topology on the level of its substitutes by finite topological spaces.
We have developed a model for the N N --> N N pi pi reaction and evaluated cross sections for the different charged channels. The low energy part of those channels where the pions can be in an isospin zero state is dominated by N* excitation, driven by an isoscalar source recently found experimentally, followed by the decay N* --> N (pi pi, T=0, s-wave). At higher energies, and in channels where the pions are not in T=0, Delta excitation mechanisms become relevant. A rough agreement with the experimental data is obtained in most channels. Repercussions of the present findings for the ABC effect and the p p --> p p pi0 reaction close to threshold are also suggested.
We discuss the complete set of one-loop triangle graphs involving the Yang-Mills gauge connection, the \Kahler\ connection and the $\sigma$-model coordinate connection in the effective field theory of $(2,2)$ symmetric $Z_N$ orbifolds. That is, we discuss pure gauge, pure \Kahler\ and pure $\sigma$-model coordinate anomalies as well as the mixed anomalies, such as \Kahler-gauge, some of which have been discussed elsewhere. We propose a mechanism for restoring both \Kahler\ and $\sigma$-model coordinate symmetry based upon the introduction of two types of counterterms. Finally, we enlarge the $\sigma$-model generalization of the Green-Schwarz mechanism to allow the removal of the universal parts of a wider class of anomalies than those previously discussed.
In this work, we demonstrate that the interaction of electromagnetic waves with a microstructured material formed by metallic wires connected to a metallic surface can be described using homogenization methods provided an additional boundary condition is considered. The additional boundary condition is derived by taking into account the specific microstructure of the wire medium. To illustrate the application of the result, we characterize a substrate formed by an array of tilted metallic wires connected to a ground plane, demonstrating that in such configuration the wire medium behaves essentially as a material with extreme optical anisotropy and that in some circumstances the substrate can be seen as an impedance surface.
Two-particle generalized susceptibilities and their irreducible vertex functions play a prominent role in the quantum many-body theory for correlated electron systems. They act as basic building blocks in the parquet formalism which provides a flexible scheme for the calculation of spectral and response functions. The irreducible vertices themselves have recently attracted increased attention as unexpected divergences in these functions have been identified. Remarkably, such singularities appear already for one of the simplest strongly interacting systems: the atomic limit of the half-filled Hubbard model (Hubbard atom). In this paper, we calculate the analytical expressions for all two-particle irreducible vertex functions of the Hubbard atom in all scattering channels as well as the fully irreducible two-particle vertices. We discuss their divergences and classify them by the eigenvalues and eigenvectors of the corresponding generalized susceptibilities. In order to establish a connection to the recently found multivaluedness of the exact self-energy functional $\Sigma[G]$, we show that already an approximation akin to iterated perturbation theory is sufficient to capture, qualitatively, the divergent structure of the vertex functions. Finally, we show that the localized divergences in the disordered binary mixture model are directly linked to a minimum in the single-particle Matsubara Green's function.
We explore and demonstrate the capabilities of LSST to study Type I superluminous supernovae (SLSNe). We first fit the light curves of 58 known SLSNe at z~0.1-1.6, using an analytical magnetar spin-down model implemented in MOSFiT. We then use the posterior distributions of the magnetar and ejecta parameters to generate thousands of synthetic SLSN light curves, and we inject those into the OpSim to generate realistic ugrizy light curves. We define simple, measurable metrics to quantify the detectability and utility of the light curve, and to measure the efficiency of LSST in returning SLSN light curves satisfying these metrics. We combine the metric efficiencies with the volumetric rate of SLSNe to estimate the overall discovery rate of LSST, and we find that ~10^4 SLSNe per year with >10 data points will be discovered in the WFD survey at z<3.0, while only ~15 SLSNe per year will be discovered in each DDF at z<4.0. To evaluate the information content in the LSST data, we refit representative output light curves with the same model that was used to generate them. We correlate our ability to recover magnetar and ejecta parameters with the simple light curve metrics to evaluate the most important metrics. We find that we can recover physical parameters to within 30% of their true values from ~18% of WFD light curves. Light curves with measurements of both the rise and decline in gri-bands, and those with at least fifty observations in all bands combined, are most information rich, with ~30% of these light curves having recoverable physical parameters to ~30% accuracy. WFD survey strategies which increase cadence in these bands and minimize seasonal gaps will maximize the number of scientifically useful SLSN light curves. Finally, although the DDFs will provide more densely sampled light curves, we expect only ~50 SLSNe with recoverable parameters in each field in the decade-long survey.
Let E be an elliptic curve with complex multiplication by R, where R is an order of discriminant D<-4 of an imaginary quadratic field K . If a prime number p is decomposed completely in the ring class field associated with R, then E has good reduction at a prime ideal P of K dividing p and there exist positive integers u and v such that 4p=u^2-Dv^2. It is well known that square of the trace a_P of Frobenius endomorphism of the reduction of E modulo P is equal to u^2. We determine whether a_P=u or a_P=-u in the case the class number of R is 2 or 3 and D is divided by 3,4 or 5. This article is a revised version of the authors' preprint DMIS-RR-02-5,2002.
We present STR (Star-Triangle Relations), a Mathematica package designed to solve Feynman diagrams by means of the method of uniqueness in any Euclidean spacetime dimension. The method of uniqueness is a powerful technique to solve multi-loop Feynman integrals in theories with conformal symmetry imposing some relations between the powers of propagators and the spacetime dimension. In our algorithm we include both identities for scalar and Yukawa type integrals. The package provides a graphical environment in which it is possible to draw the desired diagram with the mouse input and a set of tools to modify and compute it. Throughout the use of a graphic interface, the package should be easily accessible to users with little or no previous experience on diagrams computation. This manual includes some pedagogical examples of computation of Feynman graphs as the scalar two-loop kite master integral and a fermionic diagram appearing in the computation of the spectrum of the $\gamma$-deformed $\mathcal{N}=4$ SYM in the double-scaling limit.
We present an argument for a {\it lower limit} to the Compton-$y$ parameter describing spectral distortions of the cosmic microwave background (CMB). The absence of a detectable Gunn-Peterson signal in the spectra of high redshift quasars demands a high ionization state of the intergalactic medium (IGM). Given an ionizing flux at the lower end of the range indicated by the proximity effect, an IGM representing a significant fraction of the nucleosynthesis-predicted baryon density must be heated by sources other than the photon flux to a temperature $\go {\rm few} \times 10^5\, K$. Such a gas at the redshift of the highest observed quasars, $z\sim 5$, will produce a $y\go 10^{-6}$. This lower limit on $y$ rises if the Universe is open, if there is a cosmological constant, or if one adopts an IGM with a density larger than the prediction of standard Big Bang nucleosynthesis.
In this paper we prove that the PDE $p(D)f=q,$ where $p$ and $q$ are multivariate polynomials, has a solution in the space of polynomials of total degree not exceeding ${n+s},$ where $n$ is the degree of $q$ and $s$ is the zero order of $O=(0,\ldots,0)$ for $p.$
Mechanisms for the production of $^1S_0$ diproton pairs, ${pp}_s$, in the $pd\to {pp}_s n$ reaction are studied at proton beam energies 0.5 -- 2 GeV in kinematics similar to those of backward elastic $pd$ scattering. This reaction provides valuable information on the short-range $NN$ and $pd$ interactions that is complementary to that investigated in the well known $pd\to dp$ and $dp\to p(0^\circ)X$ processes. The $pd\to {pp}_sn$ reaction is related to the subprocesses $\pi^0 d\to pn$ and $pN\to {pp}_s \pi$ using two different one--pion--exchange (OPE) diagrams. Within both these models a reasonable agreement could be obtained with the data below 1GeV. The similar energy dependence of the $pd\to\{pp\}_s n$ and $pd\to dp$ cross sections and the small ratio of about 1.5% in the production of $\{pp\}_s$ to deuteron final states follow naturally within the OPE models.
With the detection of Gravitational waves just about an year ago Einstein`s general theory of relativity- a space-time theory of gravity, got established on a firmer footing than any other theory in physics. Gravitational waves are just propagating disturbances in the gravitational field of extremely strong sources caused by some catastrophic event associated with cosmic bodies, like binary black hole coalescence, or neutron star mergers. As these events happen very far away in cosmos, and the signal strength would be extremely weak, it requires extraordinary detection and analysis technology to observe an event on earth. Luckily the joint collaboration LIGO-VIRGO, have so far detected two events in September and December of 2015 during their analysis of observations made with the laser interferometers over the last few observing sessions. The talk will give a brief theoretical sketch of the analysis required for describing the waves resulting from mass motion in the realm of general relativity, and point out, the serious and sincere efforts of the past fifty years that went into the final success. An attempt will be made to point out the enormous scope that is available for the new generation of students and researchers in pursuing the topic as a new window for possibly viewing the Universe with the implications for the studies of Dark matter, Dark energy and Cosmology as a whole.
Recently, Widrow and collaborators announced the discovery of vertical density waves in the Milky Way disk. Here we investigate a scenario where these waves were induced by the Sagittarius dwarf galaxy as it plunged through the Galaxy. Using numerical simulations, we find that the Sagittarius impact produces North-South asymmetries and vertical wave-like behavior that qualitatively agrees with what is observed. The extent to which vertical modes can radially penetrate into the disc, as well as their amplitudes, depend on the mass of the perturbing satellite. We show that the mean height of the disc is expected to vary more rapidly in the radial than in the azimuthal direction. If the observed vertical density asymmetry is indeed caused by vertical oscillations, we predict radial and azimuthal variations of the mean vertical velocity, correlating with the spatial structure. These variations can have amplitudes as large as 8 km/s.
We develop a low-energy effective theory for spin-1/2 frustrated two-leg Heisenberg spin ladders. We obtain a new type of interchain coupling that breaks parity symmetry. In the presence of an XXZ-type anisotropy, this interaction gives rise to a novel ground state, characterized by incommensurate correlations. In the case of a single ladder, this state corresponds to a spin nematic phase. For a frustrated quasi-one-dimensional system of infinitely many weakly coupled chains, this state develops true three dimensional spiral order. We apply our theory to recent neutron scattering experiments on $Cs_2CuCl_4$.
Even within the Constrained Minimal Supersymmetric Standard Model (CMSSM) it is possible to induce sfermion flavor mixing through the Renormalization Group Equations (RGE) when the full structure of the Yukawa couplings is considered. We analyse the impact of including those effects on the accurate computation of $B$-physics observables, electroweak precision observables (EWPO) and the Higgs boson mass predictions.
We present quantum-mechanical theory of impact ionization in semiconductors with the direct band gap in \$\Gamma\$-point. It is shown that energy dependence of the impact ionization rate \$\mathcal{W}(E)\$ near a threshold \$E_{th}\$ is given by superposition of the two terms, one of which is strongly anisotropic and quadratic in \$E-E_{th}\$, while another one is isotropic and cubic in \$E-E_{th}\$. Explicit form of the coefficients in such representation is derived in the framework of the 14-band \${\bf k\cdot p}\$ model, and we claim the room temperature domination of the cubic contribution for most of the direct-gap materials with \$E_g\$ up to 1.5 eV.
The inner Tutte group of a matroid is a finitely generated abelian group introduced as an algebraic counterpart of Tutte's homotopy theory of matroids. The aim of this work is to provide a new presentation for this group with a set of generators that is smaller than those previously known.
Smoothly varying magnetization textures such as domain walls, skyrmions or hopfions serve as promising candidates for the information bits of the future. Understanding their physical properties is both a major field of interest and a theoretical challenge, involving the physics on different length scales. Here, we apply the phase space formulation of quantum mechanics to magnetic insulators and metals in the limit of zero temperature to obtain a gradient expansion in terms of real-space derivatives of the magnetization. Our primary focus is the anomalous Hall effect in noncollinear magnets which serves as an important proxy in the detection of localized magnetic structures. We formulate the problem in the language of noncommutative fiber bundles and make the central finding that the semiclassical expansion of the density matrix and the Berry curvature is governed by a construction from string theory which is known as the Seiberg-Witten map. Originally discovered in the effective low-energy behavior of D-branes, this map now gives a geometrical underpinning to gradient expansion techniques in noncollinear magnets and offers a radically new perspective on their electronic properties.
We report the discovery of 3.76-s pulsations from a new burst source near Sgr A* observed by the NuSTAR Observatory. The strong signal from SGR J1745-29 presents a complex pulse profile modulated with pulsed fraction 27+/-3 % in the 3-10 keV band. Two observations spaced 9 days apart yield a spin-down rate of Pdot = (6.5+/-1.4)x10^{-12}. This implies a magnetic field B = 1.6x10^14 G, spin-down power Edot = 5x10^33 erg/s, and characteristic age P/2Pdot = 9x10^3 yr, for the rotating dipole model. However, the current Pdot may be erratic, especially during outburst. The flux and modulation remained steady during the observations and the 3-79 keV spectrum is well fitted by a combined blackbody plus power-law model with temperature kT_BB = 0.96+/-0.02 keV and photon index = 1.5+/-0.4, respectively. The neutral hydrogen column density (nH ~ 1.4x10^23 cm^{-2}) measured by NuSTAR and Swift suggests that SGR J1745-29 is located at or near the Galactic Center. The lack of an X-ray counterpart in the published Chandra survey catalog sets a quiescent 2-8 keV luminosity limit of Lx ~< 10^32 erg/s. The bursting, timing, and spectral properties indicate a transient magnetar undergoing an outburst with 2-79 keV luminosity up to 3.5x10^35 erg/s for a distance of 8 kpc. SGR J1745-29 joins a growing subclass of transient magnetars, indicating that many magnetars in quiescence remain undetected in the X-ray band or have been detected as high-B radio pulsars. The peculiar location of SGR J1745-29 has important implications for the formation and dynamics of neutron stars in the Galactic Center region.
In this paper, we prove the propagation of $L^p$ upper bounds for the spatially homogeneous relativistic Boltzmann equation for any $1<p<\infty$. We consider the case of relativistic \textit{hard ball} with Grad's angular cutoff. Our proof is based on a detailed study of the interrelationship between the relative momenta, the regularity and the $L^p$ estimates for the gain operator, the development of the relativistic Carleman representation, and several estimates on the relativistic hypersurface $E^{v_*}_{v'-v}$. We also derive a Pythagorean theorem for the \textit{relative momenta} $g(v,v_*),$ $g(v,v')$, and $g(v',v_*)$, which has a crucial role in the reduction of the momentum singularity.
Recently, the distribution of velocity dispersion as far as 400kpc around red isolated galaxies was derived from statistical studies of satellites in the SDSS (Klypin & Prada 2009). This could help to constrain dark matter models at intermediate scales. We compare the predictions of different DM distributions, LCDM with NFW or cored profiles, and also modified gravity models, with observations. It is shown how the freedom in the various parameters (radial distribution of satellites, velocity anisotropy, external field effect), prevents to disentangle the models, which all can give pretty good fits to the data. In all cases, realistic radial variations of velocity anisotropy are used for the satellites, and a constant stellar-mass to light ratio for the host galaxies.
We study on the third quantization of a Kaluza-Klein toy model. In this model time ($x$) is defined by the scale factor of universe, and the space coordinate ($y$) is defined by the ratio of the scales of the ordinary space and the internal space. We calculate the number density of the universes created from nothing and examine whether the compactification can be explained statistically by the idea of the third quantization.
A method is presented for the identification of high-energy neutrinos from gamma ray bursts by means of a large-scale neutrino telescope. The procedure makes use of a time profile stacking technique of observed neutrino induced signals in correlation with satellite observations. By selecting a rather wide time window, a possible difference between the arrival times of the gamma and neutrino signals may also be identified. This might provide insight in the particle production processes at the source. By means of a toy model it will be demonstrated that a statistically significant signal can be obtained with a km^3 scale neutrino telescope on a sample of 500 gamma ray bursts for a signal rate as low as 1 detectable neutrino for 3% of the bursts.
We give evidence for intrinsic, defect-induced bulk paramagnetism in SiC by means of $^{13}$C and $^{29}$Si nuclear magnetic resonance (NMR) spectroscopy. The temperature dependence of the internal dipole-field distribution, probed by the spin part of the NMR Knight shift and the spectral linewidth, follows a Curie law and scales very well with the macroscopic DC susceptibility. In order to quantitatively analyze the NMR spectra, a microscopic model based on dipole-dipole interactions was developed. The very good agreement between these simulations and the NMR data establishes a direct relation between the frequency distribution of the spectral intensity and the corresponding real-space volumes of nuclear spins. The presented approach by NMR can be applied to a variety of similar materials and, thus, opens a new avenue for the microscopic exploration and exploitation of diluted bulk magnetism in semiconductors.
The thermal-to-nonthermal partition was found to vary greatly from one flare to another resulting in a broad variety of cases from 'heating without acceleration' to 'acceleration without heating'. Recent analysis of microwave data of these differing cases suggests that a similar acceleration mechanism, forming a power-law nonthermal tail up to a few MeV or even higher, operates in all the cases. However, the level of this nonthermal spectrum compared to the original thermal distribution differs significantly from one case to another, implying a highly different thermal-to-nonthermal energy partition in various cases. This further requires a specific mechanism capable of extracting the charged particles from the thermal pool and supplying them to a bulk acceleration process to operate in flares \textit{in addition} to the bulk acceleration process itself, which, in contrast, efficiently accelerates the seed particles, while cannot accelerate the thermal particles. Within this 'microwave' view on the flare energy partition and particle acceleration I present a few contrasting examples of acceleration regions detected with microwave data and compare them with the most popular acceleration mechanisms---in DC fields, in collapsing traps, and stochastic acceleration by a turbulence spectrum - to identify the key elements needed to conform with observations. In particular, I point out that the turbulence needed to drive the particle acceleration is generated in nonpotential magnetic structures, which results in nonzero helicity of the turbulence. This helicity, in its turn, produces a nonzero mean DC electric field on top of stochastic turbulent fields driving the main stochastic acceleration; thus, acceleration by helical turbulence combines properties of the standard stochastic acceleration with some features of acceleration in DC electric fields, exactly what is demanded by observation.
The time delay in gravitational lenses can be used to derive the Hubble constant in a relatively simple way. The results of this method are less dependent on astrophysical assumptions than in many other methods. The most important uncertainty is related to the mass model used. We discuss a family of models with a separable radial power-law and an arbitrary angular dependence for the potential psi = r^beta * F(theta). Isothermal potentials are a special case of these models with beta=1. An additional external shear is used to take into account perturbations from other galaxies. Using a simple linear formalism for quadruple lenses, we can derive H0 as a function of the observables and the shear. If the latter is fixed, the result depends on the assumed power-law exponent according to H0 proportional to (2-beta)/beta. The effect of external shear is quantified by introducing a `critical shear' gamma_c as a measure for the amount of shear that changes the result significantly. The analysis shows, that in the general case H0 and gamma_c do not depend on the position of the lens galaxy. We discuss these results and compare with numerical models for a number of real lens systems.
In this paper we study the drifted Brownian meander, that is a Brownian motion starting from $ u $ and subject to the condition that $ \min_{ 0\leq z \leq t} B(z)> v $ with $ u > v $. The limiting process for $ u \downarrow v $ is analyzed and the sufficient conditions for its construction are given. We also study the distribution of the maximum of the meander with drift and the related first-passage times. The representation of the meander endowed with a drift is provided and extends the well-known result of the driftless case. The last part concerns the drifted excursion process the distribution of which coincides with the driftless case.