ShantanuT01/DACTYL-Pretraining huggingface dataset:
Both the Rys F-model and antiferromagnetic square ice posses the same ordered, antiferromagnetic ground state, but the ordering transition is of second order in the latter, and of infinite order in the former. To tie this difference to topological properties and their breakdown, we introduce a Faraday line representation where loops carry the energy and magnetization of the system. Because of the absence of monopoles in the F-model, its loops have distinct topological properties, absent in square ice, and which allow for a natural partition of its phase space into topological sectors. Then the N\'eel temperature corresponds to a transition from trivial to non-trivial topological sectors. Moreover, its zero susceptibility below a critical field is explained by the homotopy invariance of its magnetization. In spin ices, instead, monopoles destroy the homotopy invariance of the magnetization, and thus erase this rich topological structure. Consequently, even trivial loops can be magnetized, and their susceptibility is never zero.
A study of the use of fractals in top non-leptonic decays for the sake of discrimination against background is presented. Preliminary results show that fractals may provide a useful check for top event enrichment techniques.
Geometric phases are robust against certain types of local noises, and thus provide a promising way towards high-fidelity quantum gates. However, comparing with the dynamical ones, previous implementations of nonadiabatic geometric quantum gates usually require longer evolution time, due to the needed longer evolution path. Here, we propose a scheme to realize nonadiabatic geometric quantum gates with short paths based on simple pulse control techniques, instead of deliberated pulse control in previous investigations, which can thus further suppress the influence from the environment induced noises. Specifically, we illustrate the idea on a superconducting quantum circuit, which is one of the most promising platforms for realizing practical quantum computer. As the current scheme shortens the geometric evolution path, we can obtain ultra-high gate fidelity, especially for the two-qubit gate case, as verified by our numerical simulation. Therefore, our protocol suggests a promising way towards high-fidelity and roust quantum computation on a solid-state quantum system.
We present a theoretical analysis of the capacitance of a double quantum dot in the charge and spin qubit configurations probed at high-frequencies. We find that in general the total capacitance of the system consists of two state-dependent terms: The quantum capacitance arising from adiabatic charge motion and the tunnelling capacitance that appears when repopulation occurs at a rate comparable or faster than the probing frequency. The analysis of the capacitance lineshape as a function of externally controllable variables offers a way to characterize the qubits' charge and spin state as well as relevant system parameters such as charge and spin relaxation times, tunnel coupling, electron temperature and electron g-factor. Overall, our analysis provides a formalism to understand dispersive qubit-resonator interactions which can be applied to high-sensitivity and non-invasive quantum-state readout.
Let n be a square-free polynomial over F_q, where q is an odd prime power. In this paper, we determine which irreducible polynomials p in F_q[x] can be represented in the form X^2+nY^2 with X, Y in F_q[x]. We restrict ourselves to the case where X^2+nY^2 is anisotropic at infinity. As in the classical case over Z, the representability of p by the quadratic form X^2+nY^2 is governed by conditions coming from class field theory. A necessary (and almost sufficient) condition is that the ideal generated by p splits completely in the Hilbert class field H of K = F_q(x,sqrt{-n}) (for the appropriate notion of Hilbert class field in this context). In order to get explicit conditions for p to be of the form X^2+nY^2, we use the theory of sgn-normalized rank-one Drinfeld modules. We present an algorithm to construct a generating polynomial for H/K. This algorithm generalizes to all situations an algorithm of D.S. Dummit and D.Hayes for the case where -n is monic of odd degree.
A Latin array is a matrix of symbols in which no symbol occurs more than once within a row or within a column. A diagonal of an $n\times n$ array is a selection of $n$ cells taken from different rows and columns of the array. The weight of a diagonal is the number of different symbols on it. We show via computation that every Latin array of order $n\le11$ has a diagonal of weight at least $n-1$. A corollary is the existence of near transversals in Latin squares of these orders.   More generally, for all $k\le20$ we compute a lower bound on the order of any Latin array that does not have a diagonal of weight at least $n-k$.
We take an ordered, anharmonic crystal in the form of slab geometry in three dimensions. Apart from attaching baths of Langevin type to the extreme surfaces, we also attach baths of same type to the intermediate surfaces of the slab to simulate the environment surrounding the system. We assume noise functions to be Gaussian and their widths to be site dependent. We find that the radiated heat from the slab does not receive any correction at the leading order of anharmonic coupling and the Newton's law of cooling holds for an appropriate choice of the widths. We observe that in the steady state limit entire slab becomes an assembly of $N$ different thermally equilibriated layers, where $N$ is the number of sites in the direction of conduction current flow. We find an exponentially falling nature of the temperature profile as its leading behaviour and its non-leading behaviour is governed by the two site dependent functions. Our evaluation suggests that in the thermodynamic limit thermal conductivity remains independent of the environment temperature and is dependent only on the difference of temperature of the extreme surfaces linearly at the leading order of anharmonic coupling. We find that owing to finiteness of conductivity in the thermodynamic limit, Fourier's law holds to leading order in anharmonic coupling.
In this paper, we establish a central limit theorem and a moderate deviations for 2D stochastic primitive equations with multiplicative noise. The proof is mainly based on the weak convergence approach.
We consider the emission of photons from the inner parts of a relativistically expanding plasma outflow, characterized by a constant Lorentz factor, Gamma. Photons that are injected in regions of high optical depth are advected with the flow until they escape at the photosphere. Due to multiple scattering below the photosphere, the locally emerging comoving photon distribution is thermal. However, as an observer sees simultaneously photons emitted from different angles, hence with different Doppler boosting, the observed spectrum is a multi-color black-body. We calculate here the properties of the observed spectrum at different observed times. Due to the strong dependence of the photospheric radius on the angle to the line of sight, for parameters characterizing gamma-ray bursts (GRBs) thermal photons are seen up to tens of seconds following the termination of the inner engine. At late times, following the inner engine termination, both the number flux and energy flux of the thermal spectrum decay as F ~ t^{-2}. At these times, the multicolor black body emission results in a power law at low energies (below the thermal peak), with power law index F_\nu ~ \nu^{0}. This result is remarkably similar to the average value of the low energy spectral slope index (``\alpha'') seen in fitting the spectra of large GRB sample.
Following the discovery of high-energy (HE; $E>10\,{\rm MeV}$) and very-high-energy (VHE; $E>100\,{\rm GeV}$) $\gamma$-ray emission from the low-frequency-peaked BL~Lac (LBL) object AP Librae, its electromagnetic spectrum is studied over 60 octaves in energy. Contemporaneous data in radio, optical and UV together with the $\gamma$-ray data are used to construct the most precise spectral energy distribution of this source. The data have been found to be modeled with difficulties with single zone homogeneous leptonic synchrotron self-Compton (SSC) radiative scenarios due to the unprecedented width of the high-energy component when compared to the lower-energy component. The two other LBL objects also detected at VHE appear to have similar modeling difficulties. Nevertheless, VHE $\gamma$ rays produced in the extended jet could account for the VHE flux observed by H.E.S.S.
We compute the degree of the variety parametrizing rational ruled surfaces of degree d in the projective space by relating the problem to Gromov-Witten invariants and Quantum cohomology.
A numerical algorithm to calculate exact finite-temperature spectra of many-body lattice Hamiltonians is formulated by combining the typicality approach and the shifted Krylov subspace method. The combined algorithm, which we name finite-temperature shifted Krylov subspace method for simulating spectra (FTK$\omega$), efficiently reproduces the canonical-ensemble probability distribution at finite temperatures with the computational cost proportional to the Fock space dimension. The present FTK$\omega$ enables us to exactly calculate finite-temperature spectra of many-body systems whose system sizes are twice larger than those handled by the canonical ensemble average and allows us to access the frequency domain without sequential real-time evolution often used in previous studies. By employing the reweighting method with the present algorithm, we obtain significant reduction of the numerical costs for temperature sweeps. Application to the Kiteav-Heisenberg model (KHM) on a honeycomb lattice demonstrates the capability of the FTK$\omega$. The KHM shows quantum phase transitions from the quantum spin liquid (QSL) phase to magnetically ordered phases when the finite Heisenberg exchange coupling is introduced. We examine temperature dependence of dynamical spin structure factors of the KHM in proximity to the QSL. It is clarified that the crossover from a spin-excitation continuum, which is a characteristic of the QSL, to a damped high-energy magnon mode occurs at temperatures higher than the energy scale of the Heisenberg couplings or the spin gap that is a signature of the QSL at zero temperature. The crossover and the closeness to the Kitaev's QSL are quantitatively measured by the width of the excitation continuum or the magnon spectrum. The present results shed new light on analysis of neutron scattering and other spectroscopy measurements on QSL candidates.
It will be shown that the peaks in the (Lambda p) and (Lambda d) invariant mass distributions, observed in recent FINUDA experiments and claimed to be signals of deeply bound kaonic states, are naturally explained in terms of K- absorption by two or three nucleons leaving the rest of the original nuclei as spectator. For reactions on heavy nuclei, the subsequent interactions of the particles produced in the primary absorption process with the residual nucleus play an important role. Our analyses leads to the conclusion that at present there is no experimental evidence of deeply bound K- state in nuclei. Although the FINUDA experiments have been done for reasons which are not supported a posteriori, some new physics can be extracted from the data.
Tur\'an's Theorem says that an extremal $K_{r+1}$-free graph is $r$-partite. The Stability Theorem of Erd\H{o}s and Simonovits shows that if a $K_{r+1}$-free graph with $n$ vertices has close to the maximal $t_r(n)$ edges, then it is close to being $r$-partite. In this paper we determine exactly the $K_{r+1}$-free graphs with at least $m$ edges that are farthest from being $r$-partite, for any $m\ge t_r(n) - \delta_r n^2$. This extends work by Erd\H{o}s, Gy\H{o}ri and Simonovits, and proves a conjecture of Balogh, Clemen, Lavrov, Lidick\'y and Pfender.
In this letter, we address the thermal processes occurring in plasmonic nanoparticles. We determine constrains imposed upon the plasmonic excitation in such nanoparticle by the resulting heat generation. Taking into account temperature dependence of the metal losses, we predict the existence of the critical number of plasmons in the nanoparticle. We also allow for the temperature dependencies of the thermal-conductivity coefficient of the environment and the Kapitza heat boundary resistance. We show that the latter can dominate the overall heat resistance in the system. Strength limitations caused by the action of electric forces are also considered. Obtained results provide instruments for the heat and strength management in the plasmonic engineering.
The Mott metal-insulator transition in the two-band Hubbard model in infinite dimensions is studied by using the linearized dynamical mean-field theory recently developed by Bulla and Potthoff. The phase boundary of the metal-insulator transition is obtained analytically as a function of the on-site Coulomb interaction at the $d$-orbital, the charge-transfer energy between the $d$- and $p$-orbitals and the hopping integrals between $p-d$, $d-d$ and $p-p$ orbitals. The result is in good agreement with the numerical results obtained from the exact diagonalization method.
The presence of photospheric magnetic reconnection has long been thought to give rise to short and impulsive events, such as Ellerman bombs (EBs) and Type II spicules. In this article, we combine high-resolution, high-cadence observations from the Interferometric BIdimensional Spectrometer (IBIS) and Rapid Oscillations in the Solar Atmosphere (ROSA) instruments at the Dunn Solar Telescope, National Solar Observatory, New Mexico with co-aligned Atmospheric Imaging Assembly (SDO/AIA) and Solar Optical Telescope (Hinode/SOT) data to observe small-scale events situated within an active region. These data are then compared with state-of-the-art numerical simulations of the lower atmosphere made using the MURaM code. It is found that brightenings, in both the observations and the simulations, of the wings of the H alpha line profile, interpreted as EBs, are often spatially correlated with increases in the intensity of the FeI 6302.5A line core. Bi-polar regions inferred from Hinode/SOT magnetic field data show evidence of flux cancellation associated, co-spatially, with these EBs, suggesting magnetic reconnection could be a driver of these high-energy events. Through the analysis of similar events in the simulated lower atmosphere, we are able to infer that line profiles analogous to the observations occur co-spatially with regions of strong opposite polarity magnetic flux. These observed events and their simulated counterparts are interpreted as evidence of photospheric magnetic reconnection at scales observable using current observational instrumentation.
Galaxy bispectrum is a promising probe of inflationary physics in the early universe as a measure of primordial non-Gaussianity (PNG), whereas its signal-to-noise ratio is significantly affected by the mode coupling due to non-linear gravitational growth. In this paper, we examine the standard reconstruction method of linear cosmic mass density fields from non-linear galaxy density fields to de-correlate the covariance in redshift-space galaxy bispectra. In particular, we evaluate the covariance of the bispectrum for massive-galaxy-sized dark matter halos with reconstruction by using 4000 independent $N$-body simulations. Our results show that the bispectrum covariance for the post-reconstructed field approaches the Gaussian prediction at scale of $k<0.2\, h\, {\rm Mpc}^{-1}$. We also verify the leading-order PNG-induced bispectrum is not affected by details of the reconstruction with perturbative theory. We then demonstrate the constraining power of the post-reconstructed bispectrum for PNG at redshift of $\sim0.5$. Further, we perform a Fisher analysis to make a forecast of PNG constraints by galaxy bispectra including anisotropic signals. Assuming a massive galaxy sample in the SDSS Baryon Oscillation Spectroscopic Survey, we find that the post-reconstructed bispectrum can constrain the local-, equilateral- and orthogonal-types of PNG with $\Delta f_{\rm NL} \sim$13, 90 and 42, respectively, improving the constraints with the pre-reconstructed bispectrum by a factor of $1.3-3.2$. In conclusion, the reconstruction plays an essential role in constraining various types of PNG signatures with a level of $\Delta f_{\rm NL}<1$ from the galaxy bispectrum based on upcoming galaxy surveys.
We analyze the properties of deuteron-like structures in infinite, correlated nuclear matter, described by a realistic hamiltonian containing the Urbana $v_{14}$ two-nucleon and the Urbana TNI many-body potentials. The distribution of neutron-proton pairs, carrying the deuteron quantum numbers, is obtained as a function of the total momentum by computing the overlap between the nuclear matter in its ground state and the deuteron wave functions in correlated basis functions theory. We study the differences between the S- and D-wave components of the deuteron and those of the deuteron-like pair in the nuclear medium. The total number of deuteron type pairs is computed and compared with the predictions of Levinger's quasideuteron model. The resulting Levinger's factor in nuclear matter at equilibrium densityis 11.63. We use the local density approximation to estimate the Levinger's factor for heavy nuclei, obtaining results which are consistent with the available experimental data from photoreactions.
The density functional theory with generalized gradient approximation has been used to investigate the electronic structure of gadolinium pyrochlore A2Zr2O7 (A=Gd, Nd) ceramic synthesized in polycrystalline form by solid state reaction. Structural characterization of the compound was done through X-ray diffraction (XRD) followed by Rietveld analysis of the XRD pattern. The Zr-K edge X-ray absorption (XAFS) spectra of A2Zr2O7 (A=Gd, Nd) were analysed together with those Zr-foil, which was used as reference compounds. X-ray photoemission spectroscopy (XPS), X-ray absorption near edge structure (XANES) and extended X-ray absorption fine structure (EXAFS) for A2Zr2O7 (A=Gd, Nd) has been employed to obtain quantitative structural information on the Zr-local environment. The band gap is estimated using UV-Vis spectroscopy. The crystal structure is face centered cubic, space group being Fd-3m (No. 227). The total energies in this work were calculated using the generalized gradient approximation to DFT plus on-site repulsion (U) method.
We provide sufficient conditions which ensure that the intrinsic martingale in the supercritical branching random walk converges exponentially fast to its limit. The case of Galton-Watson processes is particularly included so that our results can be seen as a generalization of a result given in the classical treatise by Asmussen and Hering. As an auxiliary tool, we prove ultimate versions of two results concerning the exponential renewal measures which may be interesting on its own and which correct, generalize and simplify some earlier works.
The article investigates several questions about field generated by certain formal group laws. This is continuation of a study initiated by the author in prior article titled 'Field Generated by Division Points of Certain Formal Group Laws'.
Electron capture and emission by Coulomb scattering in self-assembled quantum dot (QD) devices is studied theoretically. While the dependence of the Coulomb scattering (Auger) rates on the local wetting layer electron density has been a topic of intense research, we put special interest on the remote scattering between QD electrons and continuum electrons originating from a quantum well, doped bulk layers or metal contacts. Numerical effort is made to include all microscopic transitions between the Fermi distributed continuum states. The remote Coulomb scattering is investigated as a function of the electron density, the distance from the QDs and the temperature. Our results are compared with experimental observations, considering lifetime limitations in QD memory structures as well as the electron emission in pn-diodes.
We observed an arch filament system (AFS) in a sunspot group with the GREGOR Infrared Spectrograph attached to the GREGOR solar telescope. The AFS was located between the leading sunspot of negative polarity and several pores of positive polarity forming the following part of the sunspot group. We recorded five spectro-polarimetric scans of this region. The spectral range included the spectral lines Si I 1082.7 nm, He I 1083.0 nm, and Ca I 1083.9 nm. In this work we concentrate on the silicon line which is formed in the upper photosphere. The line profiles are inverted with the code `Stokes Inversion based on Response functions' to obtain the magnetic field vector. The line-of-sight velocities are determined independently with a Fourier phase method. Maximum velocities are found close to the ends of AFS fibrils. These maximum values amount to 2.4 km/s next to the pores and to 4 km/s at the sunspot side. Between the following pores, we encounter an area of negative polarity that is decreasing during the five scans. We interpret this by new emerging positive flux in this area canceling out the negative flux. In summary, our findings confirm the scenario that rising magnetic flux tubes cause the AFS.
We show how spectra of Type Ia supernovae (SNe Ia) at maximum light can be used to improve cosmological distance estimates. In a companion article, we used manifold learning to build a three-dimensional parameterization of the intrinsic diversity of SNe Ia at maximum light that we call the "Twins Embedding". In this article, we discuss how the Twins Embedding can be used to improve the standardization of SNe Ia. With a single spectrophotometrically-calibrated spectrum near maximum light, we can standardize our sample of SNe Ia with an RMS of $0.101 \pm 0.007$ mag, which corresponds to $0.084 \pm 0.009$ mag if peculiar velocity contributions are removed and $0.073 \pm 0.008$ mag if a larger reference sample were obtained. Our techniques can standardize the full range of SNe Ia, including those typically labeled as peculiar and often rejected from other analyses. We find that traditional light curve width + color standardization such as SALT2 is not sufficient. The Twins Embedding identifies a subset of SNe Ia including but not limited to 91T-like SNe Ia whose SALT2 distance estimates are biased by $0.229 \pm 0.045$ mag. Standardization using the Twins Embedding also significantly decreases host-galaxy correlations. We recover a host mass step of $0.040 \pm 0.020$ mag compared to $0.092 \pm 0.024$ mag for SALT2 standardization on the same sample of SNe Ia. These biases in traditional standardization methods could significantly impact future cosmology analyses if not properly taken into account.
We study the composite Skyrme model, proposed by Cheung and G\"{u}rsey, introducing vector mesons in a chiral Lagrangian. We calculate the static properties of baryons and compare with results obtained from models without vector mesons.
Topological electrons in semimetals are usually vulnerable to chemical doping and environment change, which restricts their potential application in future electronic devices. In this paper we report that the type-II Dirac semimetal $\mathbf{VAl_3}$ hosts exceptional, robust topological electrons which can tolerate extreme change of chemical composition. The Dirac electrons remain intact even after a substantial part of V atoms have been replaced in the $\mathbf{V_{1-x}Ti_xAl_3}$ solid solutions. This Dirac semimetal state ends at $x=0.35$ where a Lifshitz transition to $p$-type trivial metal occurs. The V-Al bond is completely broken in this transition as long as the bonding orbitals are fully depopulated by the holes donated from Ti substitution. In other words, the Dirac electrons in $\mathbf{VAl_3}$ are protected by the V-Al bond whose molecular orbital is their bonding gravity center. Our understanding on the interrelations among electron count, chemical bond and electronic properties in topological semimetals suggests a rational approach to search robust, chemical-bond-protected topological materials.