ShantanuT01/DACTYL-Pretraining huggingface dataset:
Serre obtained the p-adic limit of the integral Fourier coefficient of modular forms on $SL_2(\mathbb{Z})$ for $p=2,3,5,7$. In this paper, we extend the result of Serre to weakly holomorphic modular forms of half integral weight on $\Gamma_{0}(4N)$ for $N=1,2,4$. A proof is based on linear relations among Fourier coefficients of modular forms of half integral weight. As applications we obtain congruences of Borcherds exponents, congruences of quotient of Eisentein series and congruences of values of $L$-functions at a certain point are also studied. Furthermore, the congruences of the Fourier coefficients of Siegel modular forms on Maass Space are obtained using Ikeda lifting.
The energies and widths of gamma-ray lines emitted by ambient nuclei excited by flare-accelerated protons and alpha particles provide information on the ions directionality and spectra, and on the characteristics of the interaction region. We have measured the energies and widths of strong lines from de-excitations of 12C, 16O, and 20Ne in solar flares as a function of heliocentric angle. The line energies from all three nuclei exhibit ~1% redshifts for flares at small heliocentric angles, but are not shifted near the limb. The lines have widths of ~3% FWHM. We compare the 12C line measurements for flares at five different heliocentric angles with calculations for different interacting-particle distributions. A downward isotropic distribution (or one with a small upward component) provides a good fit to the line measurements. An angular distribution derived for particles that undergo significant pitch angle scattering by MHD turbulence in coronal magnetic loops provides comparably good fits.
We propose a scheme for encoding logical qubits in a subspace protected against collective rotations around the propagation axis using the polarization and transverse spatial degrees of freedom of single photons. This encoding allows for quantum key distribution without the need of a shared reference frame. We present methods to generate entangled states of two logical qubits using present day down-conversion sources and linear optics, and show that the application of these entangled logical states to quantum information schemes allows for alignment-free tests of Bell's inequalities, quantum dense coding and quantum teleportation.
Bishop independence concerns determining the maximum number of bishops that can be placed on a board such that no bishop can attack any other bishop. This paper presents the solution to the bishop independence problem, determining the bishop independence number, for all sizes of boards on the surface of a square prism.
The gadolinium pyrochlores, Gd$_2B_2$O$_7$, are amongst the best realizations of antiferromagnetically coupled Heisenberg spins on a pyrochlore lattice. We present a magnetic characterization of Gd$_2$Pt$_2$O$_7$, a unique member of this family. Magnetic susceptibility, heat capacity, and muon spin relaxation measurements show that Gd$_2$Pt$_2$O$_7$ undergoes an antiferromagnetic ordering transition at $T_N = 1.6$ K. This transition is strongly first order, as indicated by the sharpness of the heat capacity anomaly, thermal hysteresis in the magnetic susceptibility, and a non-divergent relaxation rate in $\mu$SR. The form of the heat capacity below $T_N$ suggests that the ground state is an anisotropic collinear antiferromagnet with an excitation spectrum that is gapped by 0.245(1) meV. The ordering temperature in Gd$_2$Pt$_2$O$_7$, $T_N = 1.6$ K, is a substantial 160% increase from other gadolinium pyrochlores, which have been found to order at 1 K or lower. We attribute this enhancement in $T_N$ to the $B$-site cation, platinum, which, despite being non-magnetic, has a filled $5d$ $t_{2g}$ orbital and an empty $5d$ $e_g$ orbital that can facilitate superexchange. Thus, the magnetic frustration in Gd$_2$Pt$_2$O$_7$ is partially "relieved", thereby promoting magnetic order.
While both X-ray emission and Sunyaev-Zel'dovich (SZ) temperature fluctuations are generated by the warm-hot gas in dark matter halos, the two observables have different dependence on the underlying physical properties, including the gas distribution. A cross-correlation between the soft X-ray background (SXRB) and the SZ sky may allow an additional probe on the distribution of warm-hot gas at intermediate angular scales and redshifts complementing studies involving clustering within SXRB and SZ separately. Using a halo approach, we investigate this cross-correlation analytically. The two contributions are correlated mildly with a correlation coefficient of $\sim0.3$, and this relatively low correlation presents a significant challenge for its detection. The correlation, at small angular scales, is affected by the presence of radiative cooling or preheating and provides a probe on the thermal history of the hot gas in dark halos. While the correlation remains undetectable with CMB data from the WMAP satellite and X-ray background data from existing catalogs, upcoming observations with CMB missions such as Planck, for the SZ side, and an improved X-ray map of the large scale structure, such as the one planned with DUET mission, may provide a first opportunity for a reliable detection of this cross-correlation.
By combining the tetrahedron method with the cluster perturbation theory (CPT), we present an accurate method to numerically calculate the density of states of interacting fermions without introducing the Lorentzian broadening parameter $\eta$ or the numerical extrapolation of $\eta \to 0$. The method is conceptually based on the notion of the effective single-particle Hamiltonian which can be subtracted in the Lehmann representation of the single-particle Green's function within the CPT. Indeed, we show the general correspondence between the self-energy and the effective single-particle Hamiltonian which describes exactly the single-particle excitation energies of interacting fermions. The detailed formalism is provided for two-dimensional multi-orbital systems and a benchmark calculation is performed for the two-dimensional single-band Hubbard model. The method can be adapted straightforwardly to symmetry broken states, three-dimensional systems, and finite-temperature calculations.
In this paper, we present the tools used to search for galaxy clusters in the Kilo Degree Survey (KiDS), and our first results. The cluster detection is based on an implementation of the optimal filtering technique that enables us to identify clusters as over-densities in the distribution of galaxies using their positions on the sky, magnitudes, and photometric redshifts. The contamination and completeness of the cluster catalog are derived using mock catalogs based on the data themselves. The optimal signal to noise threshold for the cluster detection is obtained by randomizing the galaxy positions and selecting the value that produces a contamination of less than 20%. Starting from a subset of clusters detected with high significance at low redshifts, we shift them to higher redshifts to estimate the completeness as a function of redshift: the average completeness is ~ 85%. An estimate of the mass of the clusters is derived using the richness as a proxy. We obtained 1858 candidate clusters with redshift 0 < z_c < 0.7 and mass 13.5 < log(M500/Msun) < 15 in an area of 114 sq. degrees (KiDS ESO-DR2). A comparison with publicly available Sloan Digital Sky Survey (SDSS)-based cluster catalogs shows that we match more than 50% of the clusters (77% in the case of the redMaPPer catalog). We also cross-matched our cluster catalog with the Abell clusters, and clusters found by XMM and in the Planck-SZ survey; however, only a small number of them lie inside the KiDS area currently available.
The pre-transitional disk around the Herbig Ae star HD 169142 shows a complex structure of possible ongoing planet formation in dust thermal emission from the near infrared (IR) to millimeter wavelength range. Also, a distinct set of broad emission features at 3.3, 6.2, 7.7, 8.6, 11.3, and 12.7 $\mu$m, commonly attributed to polycyclic aromatic hydrocarbons (PAHs), are detected prominently in the HD 169142 disk. We model the spectral energy distribution (SED) as well as the PAH emission features of the HD 169142 disk simultaneously with porous dust and astronomical-PAHs taking into account the spatially resolved disk structure. Our porous dust model consisting of three distinct components that are primarily concentrated in the inner ring, middle ring, and outer disk, respectively, provides an excellent fit to the entire SED, and the PAH model closely reproduces the observed PAH features. The accretion of ice mantles onto porous dust aggregates occurs between ~16 AU and 60 AU, which overlaps with the spatial extent (~50 AU) of the observed PAH emission features. Finally, we discuss the role of PAHs in the formation of planets possibly taking place in the HD 169142 system.
We reconsider semiclassical quantization of folded string spinning in AdS_3 part of AdS_5 X S^5 using integrability-based (algebraic curve) method. We focus on the "short string" (small spin S) limit with the angular momentum J in S^5 scaled down according to \cal J = rho \sqrt \cal S in terms of the variables \cal J = J/\sqrt\lambda, \cal S = S/\sqrt\lambda. The semiclassical string energy in this particular scaling limit admits the double expansion E = \sum_{n=0}^{\infty}\sum_{p=0}^{\infty} (\sqrt\lambda)^{1-n}\,a_{n,p}(rho)\, \cal S^{p+1/2}. It behaves smoothly as J -> 0 and partially resums recent results by Gromov and Valatka. We explicitly compute various one-loop coefficients a_{1,p}(rho) by summing over the fluctuation frequencies for integrable perturbations around the classical solution. For the simple folded string, the result agrees with what could be derived exploiting a recent conjecture of Basso. However, the method can be extended to more general situations. As an example, we consider the m-folded string where Basso's conjecture fails. For this classical solution, we present the exact values of a_{1,0}(rho) and a_{1,1}(rho) for m=2, 3, 4, 5 and explain how to work out the general case.
We present an investigation of magnetic ordering in the two-dimensional S=1/2 quantum magnet Cu(Pz)_2(ClO_4)_2 using specific heat and zero field muon-spin relaxation (\mu^+SR). The magnetic contribution to the specific heat is consistent with an exchange strength of 17.7(3) K. We find unambiguous evidence for a transition to a state of three-dimensional long range order below a critical temperature T_N=4.21(1) K using \mu^+SR even though there is no feature in the specific heat at that temperature. The absence of a specific heat anomaly at T_N is consistent with recent theoretical predictions. The ratio of T_N/J=0.24 corresponds to a ratio of intralayer to interlayer exchange constants of |J'/J|=6.8x10^-4, indicative of excellent two-dimensional isolation. The scaled magnetic specific heat of [Cu(Pz)_2(HF_2)]BF_4, a compound with an analogous structure, is essentially identical to that of Cu(Pz)_2(ClO_4)_2 although both differ slightly from the predicted value for an ideal 2D S=1/2 Heisenberg antiferromagnet.
We address two issues in the thermodynamic model for nuclear disassembly. Surprisingly large differences in results for specific heat were seen in predictions from the canonical and grand canonical ensembles when the nuclear system passes from liquid-gas co-existence to the pure gas phase. We are able to pinpoint and understand the reasons for such and other discrepancies when they appear. There is a subtle but important difference in the physics addressed in the two models. In particular if we reformulate the parameters in the canonical model to better approximate the physics addressed in the grand canonical model, calculations for observables converge. Next we turn to the issue of bimodality in the probability distribution of the largest fragment in both canonical and grand canonical ensembles. We demonstrate that this distribution is very closely related to average multiplicities. The relationship of the bimodal distribution to phase transition is discussed.
Low-temperature resistivity of half-metals is investigated. To date it has been discussed that the one-magnon scattering process in half-metals is irrelevant for low-temperature resistivity, due to the fully spin-polarized electronic structure at the ground state. If one takes into account the non-rigid-band behavior of the minority band due to spin fluctuations at finite temperatures, however, the unconventional one-magnon scattering process is shown to be most relevant and gives T^3 dependence in resistivity. This behavior may be used as a crucial test in the search for half-metallic materials which are potentially important for applications. Comparison with resistivity data of   La_1-x Sr_x MnO_3 as candidates for half-metals shows good agreement.
We present a kinematic study of the Herbig-Haro objects HH 202, 203 and 204 using Halpha and [NII] Fabry-Perot velocity maps. For HH 202 we find new features that could belong to this HH object or that perhaps are associated with an outflow different from HH 202. Because of its high velocity (up to 100 km/seg) this outflow probably can be a HH flow not catalogued previously. Large internal motions are found in the fainter regions of HH 203-204, as well as evidence of transverse density gradients. We show that the apex of HH 204 is the zone of maximum velocity in agreement with bow shock models. From our studies, we find kinematic evidence that suggests that HH 203-204 and HH 202 are part of a single and large (approx 0.55 pc) HH flow.
We report extremely large magnetoresistance (MR) in an extended temperature regime from 1.5 K to 300 K in non-magnetic binary compounds TaP and NbP. TaP exhibits linear MR around $1.8\times 10^4$ at 2 K in a magnetic field of 9 Tesla, which further follows its linearity up to $1.4\times 10^5$ in a magnetic field of 56 Tesla at 1.5 K. At room temperature the MR for TaP and NbP follows a power law of the exponent about $1.5$ with the values larger than $300\%$ in a magnetic field of 9 Tesla. Such large MR in a wide temperature regime is not likely only due to a resonance of the electron-hole balance, but indicates a complicated mechanism underneath.
In central collisions at relativistic heavy ion colliders like the Relativistic Heavy Ion Collider RHIC/Brookhaven and the Large Hadron Collider LHC (in its heavy ion mode) at CERN/Geneva, one aims at detecting a new form of hadronic matter --- the Quark Gluon Plasma. We discuss here a complementary aspect of these collisions, the very peripheral ones. Due to coherence, there are strong electromagnetic fields of short duration in such collisions. They give rise to photon-photon and photon-nucleus collisions with high flux up to an invariant mass region hitherto unexplored experimentally. After a general survey photon-photon luminosities in relativistic heavy ion collisions are discussed. Then photon-photon physics at various gamma-gamma-invariant mass scales is discussed. The region of several GeV, relevant for RHIC is dominated by QCD phenomena (meson and vector meson pair production). Invariant masses of up to about 100 GeV can be reached at LHC, and the potential for new physics is discussed. Lepton-pair production, especially electron-positron pair production is copious. Due to the strong fields there will be new phenomena, especially multiple e+e- pair production.
We show in this article how the usual hamiltonian formalism of General Relativity should be modified in order to allow the inclusion of the Euclidean classical solutions of Einstein's equations. We study the effect that the dynamical change of signature has on the superspace and we prove that it induces a passage of the signature of the supermetric from ($-+++++$) to ($+-----$). Next, all these features are more particularly studied on the example of minisuperspaces. Finally, we consider the problem of quantization of the Euclidean solutions. The consequences of different choices of boundary conditions are examined.
We introduce several classes of monoids satisfying up to five axioms and establish basic theories on their arithmetics. The one satisfying all the axioms is named natural monoid. Two typical examples are 1) the monoid $\mathbb{N}$ of natural numbers in the group of positive rationals and 2) a certain monoid $\mathbb{S}$ in one of Thompson's groups. The latter one is non-abelian, which serves as an important example for non-commutative arithmetics.   Defining primes in a non-abelian monoid $S$ is highly non-trivial, which relies on a concept we called `castling'. Three types of castlings are essential to grasp the arithmetics on $S$. Multiplicative and completely multiplicative functions are defined. In particular, M\"obius function is multiplicative, and Liouville function on a natural monoid is completely multiplicative. The divisor function has a sub-multiplicative property, which induces a non-trivial quantity $\tau_0(u)=\lim\nolimits_{n\rightarrow \infty}(\tau(u^n))^{1/n}$ in a non-abelian monoid $S$. Moreover, the quantity $\c{C}(S)=\sup\nolimits_{1\neq u\in S}\tau_0(u)/\tau(u)$ describes the complexity for castlings in $S$. We show that $\c{C}(\mathbb{N})=1/2$ and $\c{C}(\mathbb{S})=1$. The reduced $C^\ast$-algebra of $S$, on which a particular trace can be defined, is also studied. Furthermore, we prove that a natural monoid having finitely many primes is amenable.
We examine the competition between the charge-density wave (CDW) instability and the excitonic condensate (EC) in spatially separated layers of electrons and holes. The CDW and the EC order parameters (OPs), described by two different mechanisms and hence two different transition temperatures $T^{CDW}_c$ and $T^{EC}_c$, are self-consistently coupled by a microscopic mean field theory. We discuss the results in our model specifically focusing on the transition-metal dichalcogenides which are considered as the most typical examples of strongly coupled CDW/EC systems with atomic layer separations where the electronic energy scales are large with the critical temperatures in the range $T^{EC}_c \sim T^{CDW}_c \sim 100-200 K$. An important consequence of this is that the excitonic energy gap, hence the condensed free energy, vary with the layer separation resulting in a new type of force ${\cal F}_{EC}$. We discuss the possibility of this force as the possible driver of the structural lattice deformation observed in some TMDCs with a particular attention on the $ 1 {\it T}$-$TiSe_2$ below $200 K$.
L. K. Grover's search algorithm in quantum computing gives an optimal, square-root speedup in the search for a single object in a large unsorted database. In this paper, we expound Grover's algorithm in a Hilbert-space framework that isolates its geometrical essence, and we generalize it to the case where more than one object satisfies the search criterion.
An edge-colored graph $G$ is \emph{conflict-free connected} if, between each pair of distinct vertices, there exists a path containing a color used on exactly one of its edges. The \emph{conflict-free connection number} of a connected graph $G$, denoted by $cfc(G)$, is defined as the smallest number of colors that are needed in order to make $G$ conflict-free connected. In this paper, we determine all trees $T$ of order $n$ for which $cfc(T)=n-t$, where $t\geq 1$ and $n\geq 2t+2 $. Then we prove that $1\leq cfc(G)\leq n-1$ for a connected graph $G$, and characterize the graphs $G$ with $cfc(G)=1,n-4,n-3,n-2,n-1$, respectively. Finally, we get the Nordhaus-Gaddum-type theorem for the conflict-free connection number of graphs, and prove that if $G$ and $\overline{G}$ are connected, then $4\leq cfc(G)+cfc(\overline{G})\leq n$ and $4\leq cfc(G)\cdot cfc(\overline{G})\leq2(n-2)$, and moreover, $cfc(G)+cfc(\overline{G})=n$ or $cfc(G)\cdot cfc(\overline{G})=2(n-2)$ if and only if one of $G$ and $\overline{G}$ is a tree with maximum degree $n-2$ or a $P_5$, and the lower bounds are sharp.
We report on the discovery and localization of fast radio bursts (FRBs) from the MeerTRAP project, a commensal fast radio transient-detection programme at MeerKAT in South Africa. Our hybrid approach combines a coherent search with an average field-of-view of 0.4 $\rm deg^{2}$ with an incoherent search utilizing a field-of-view of $\sim$1.27 $\rm deg^{2}$ (both at 1284~MHz). Here, we present results on the first three FRBs: FRB 20200413A (DM=1990.05 pc cm$^{-3}$), FRB 20200915A (DM=740.65 pc cm$^{-3}$), and FRB 20201123A (DM=433.55 pc cm$^{-3}$). FRB 20200413A was discovered only in the incoherent beam. FRB 20200915A (also discovered only in the incoherent beam) shows speckled emission in the dynamic spectrum which cannot be explained by interstellar scintillation in our Galaxy or plasma lensing, and might be intrinsic to the source. FRB 20201123A shows a faint post-cursor burst about 200 ms after the main burst and warrants further follow-up to confirm whether it is a repeating FRB. FRB 20201123A also exhibits significant temporal broadening consistent with scattering by a turbulent medium. The broadening exceeds that predicted for medium along the sightline through our Galaxy. We associate this scattering with the turbulent medium in the environment of the FRB in the host galaxy. Within the approximately $1'$ localization region of FRB 20201123A, we identify one luminous galaxy ($r \approx 15.67$; J173438.35$-$504550.4) that dominates the posterior probability for a host association. The galaxy's measured properties are consistent with other FRB hosts with secure associations.
In this paper we continue the study of the Griffith brittle fracture energy minimisation under Dirichlet boundary conditions, suggested by Francfort and Marigo in 1998. In a recent paper, we proved the existence of weak minimisers of the problem. Now we show that these minimisers are indeed strong solutions, namely their jump set is closed and they are smooth away from the jump set and continuous up to the Dirichlet boundary. This is obtained by extending up to the boundary the recent regularity results of Conti, Focardi, Iurlano, and of Chambolle, Conti, Iurlano.
We present an analytical and phenomenological model for metal enrichment in halos based on hierarchical structure formation. This model assumes that astration of normal stellar populations along with SNe II already occurs at very high redshift. For halos that are not disrupted by SN II explosions, the chemical evolution of the gas and stars is explicitly determined by the rate of gas infall as compared with the astration rate and the corresponding rate of metal production by SNe II per H atom in the gas. This model provides a good description of the data on [Fe/H] for damped Ly alpha systems over a wide range of redshift 0.5 < z < 5. For all halos not disrupted by SN II explosions, if there is a cessation of gas infall, the metallicities of stars follow a bimodal distribution. This distribution is characterized by a sharp peak at the value of [Fe/H] corresponding to the time of infall cessation and by a broad peak at a higher value of [Fe/H] corresponding to the subsequent period of astration during which the bulk of the remaining gas forms stars. Such a distribution may be compared to that observed for the Galactic halo stars. If the gas in a halo is rapidly lost upon cessation of infall, then an assemblage of stars with a very sharply-defined [Fe/H] value will be left behind. This assemblage of stars may be accreted by a larger system and become a globular cluster of the larger system. We also discuss the masses and metallicities of the globular clusters in this model. (Abridged)