ShantanuT01/DACTYL-Pretraining huggingface dataset:
In the context of solar neutrino oscillations among active states, we briefly discuss the current likelihood of Mikheyev-Smirnov-Wolfenstein (MSW) solutions to the solar neutrino problem, which appear to be currently favored at large mixing, where small Earth regeneration effects might still be observable in Super-Kamiokande (SK) and in the Sudbury Neutrino Observatory (SNO). We point out that, since such effects are larger at high (low) solar neutrino energies for high (low) values of the mass square difference \delta m^2, it may be useful to split the night-day rate asymmetry in two separate energy ranges. We show that the difference \Delta of the night-day asymmetry at high and low energy may help to discriminate the two large-mixing solutions at low and high \delta m^2 through a sign test, both in SK and in SNO, provided that the sensitivity to \Delta can reach the (sub)percent level.
We predict that spin-waves in an ordered quantum antiferromagnet (AFM) in a strong magnetic field become unstable with respect to spontaneous two-magnon decays. At zero temperature, the instability occurs between the threshold field $H^*$ and the saturation field $H_c$. As an example, we investigate the high-field dynamics of a Heisenberg antiferromagnet on a square lattice and show that the single-magnon branch of the spectrum disappears in the most part of the Brillouin zone.
In this paper, we derive sufficient conditions for each component of the solution to a general backward stochastic differential equation to have a density for which upper and lower Gaussian estimates can be obtained.
We are studying quantum corrections in the earlier proposed string theory based on world-sheet action which measures the linear sizes of the surfaces. At classical level the string tension is equal to zero and as it was demonstrated in the previous studies one loop correction to the classical world-sheet action generates Nambu-Goto area term, that is nonzero string tension. We extend this analysis computing the world-sheet effective action in the second order of the loop expansion.
The three-dimensional bimodal random-field Ising model is studied via a new finite temperature numerical approach. The methods of Wang-Landau sampling and broad histogram are implemented in a unified algorithm by using the N-fold version of the Wang-Landau algorithm. The simulations are performed in dominant energy subspaces, determined by the recently developed critical minimum energy subspace technique. The random fields are obtained from a bimodal distribution, that is we consider the discrete $(\pm\Delta)$ case and the model is studied on cubic lattices with sizes $4\leq L \leq 20$. In order to extract information for the relevant probability distributions of the specific heat and susceptibility peaks, large samples of random field realizations are generated. The general aspects of the model's scaling behavior are discussed and the process of averaging finite-size anomalies in random systems is re-examined under the prism of the lack of self-averaging of the specific heat and susceptibility of the model.
It is shown that the elliptic Ruijsenaars-Schneider model can be obtained from the cotangent bundle over the two-dimensional current group by means of the Hamiltonian reduction procedure.
The generation of high-order harmonics in quasi-one-dimensional graphene nanoribbons (GNRs) initiated by intense coherent radiation is investigated. A microscopic theory describing the extreme nonlinear optical response of GNRs is developed. The closed set of differential equations for the single-particle density matrix at the GNR-strong laser field multiphoton interaction is solved numerically. The obtained solutions indicate the significance of the bandgap width and Fermi energy level on the high-order harmonic generation process in GNRs.
Full investigation of deep defect states and impurities in wide-bandgap materials by employing commercial transient capacitance spectroscopy is a challenge, demanding very high temperatures. Therefore, a high-temperature deep-level transient spectroscopy (HT-DLTS) system was developed for measurements up to 1100 K. The upper limit of the temperature range allows for the study of deep defects and trap centers in the bandgap, deeper than previously reported by DLTS characterization in any material. Performance of the system was tested by conducting measurements on the well-known intrinsic defects in n-type 4H-SiC in the temperature range 300-950 K. Experimental observations performed on 4H-SiC Schottky diodes were in good agreement with the literatures. However, the DLTS measurements were restricted by the operation and quality of the electrodes.
We use Ward identities of broken scale invariance to infer the amount of scalar glueball--$\bar{q}q$ meson mixing from the ratio of quark and gluon condensates in the QCD vacuum. Assuming dominance by a single scalar state, as suggested by a phase-shift analysis, we find a mixing angle $\gamma \sim 36^{\circ}$, corresponding to near-maximal mixing of the glueball and $\bar{s}s$ components.
The Klein-Gordon equation in the presence of a spatially one-dimensional Hulth\'en potential is solved exactly and the scattering solutions are obtained in terms of hypergeometric functions. The transmission coefficient is derived by the matching conditions on the wavefunctions and the condition for the existence of transmission resonances are investigated. It is shown how the zero-reflection condition depends on the shape of the potential.
The nonclassical behaviors of a two-level system coupled to a harmonic oscillator is investigated in the ultrastrong coupling regime. We revisit the variational solution of the ground state and find that the existing solution do not account accurately for nonclassical effects such squeezing. We suggest a new trial wave function and demonstrate that it has an excellent accuracy on the quantum correlation effects as well as on energy.
Assuming a new interaction with a $\theta$ term for the third generation of quarks, a value of $\theta$ different from zero dynamically induces the top- bottom mass splitting and a large CP-violating phase.
We aim at measuring the stellar parameters of the two Chemically Peculiar components of the B9.5Vp HgMn + A2 Vm double-lined spectroscopic binary HD141556, whose period is 15.25 days. We combined historical radial velocity measurements with new spatially resolved astrometric observations from PIONIER/VLTI to reconstruct the three-dimensional orbit of the binary, and thus obtained the individual masses. We fit the available photometric points together with the flux ratios provided by interferometry to constrain the individual sizes, which we compared to predictions from evolutionary models.The individual masses of the components are $\Ma = 2.84 \pm 0.12\ \Msun$ and $\Mb = 1.94 \pm 0.09\ \Msun$. The dynamical distance is compatible with the Hipparcos parallax. We find linear stellar radii of $\Ra=2.85 \pm 0.15\ \Rsun$ and $\Rb=1.75 \pm 0.18\ \Rsun$. This result validates a posteriori the flux ratio used in previous detailed abundance studies. We determine a sub-solar initial metallicity $Z=0.012\pm0.003$ and an age of $(2.8\pm0.3)\times10^8\ $years. Our results imply that the primary rotates more slowly than its synchronous velocity, while the secondary is probably synchronous. We show that strong tidal coupling during the pre-main sequence evolution followed by a full decoupling at zero-age main sequence provides a plausible explanation for these very low rotation rates.
The Kuramoto model is a classical model used in the study of spontaneous synchronizations in networks of coupled oscillators. In this model, frequency synchronization configurations can be formulated as complex solutions to a system of algebraic equations. Recently, upper bounds to the number of frequency synchronization configurations in cycle networks of N oscillators were calculated under the assumption of generic non-uniform coupling. In this paper, we refine these results for the special cases of uniform coupling. In particular, we show that when, and only when, N is divisible by 4, the upper bound for the number of synchronization configurations in the uniform coupling cases is significantly less than the bound in the non-uniform coupling cases. This result also establishes an explicit formula for the gap between the birationally invariant intersection index and the Bernshtein-Kushnirenko-Khovanskii bound for the underlying algebraic equations.
We study the composite fermion construction at and below the single vortex ($L=N$) state of weakly interacting rotating Bose gases, presenting a new method for handling the large number of derivatives typically occurring via the Slater determinant. Remarkably, the CF wave function at $L=N$ becomes {\em exact} in the large $N$ limit, even though this construction is not, {\em a priori}, expected to work in the low angular momentum regime. This implies an interesting mathematical identity which may be useful in other contexts.
We consider the Gribov-Zwanziger (GZ) theory with appropriate horizon term which exhibits the nilpotent BRST invariance. This infinitesimal BRST transformation has been generalized by allowing the parameter to be finite and field dependent (FFBRST). By constructing appropriate finite field dependent parameter we show that the generating functional of GZ theory with horizon term is related to that of Yang-Mills (YM) theory through FFBRST transformation.
Since the launch of Chandra and XMM-Newton, high-resolution X-ray spectra of cosmic sources of all kinds have become available. These spectra have resulted in major scientific breakthroughs. However, due to the techniques used, in general high-quality spectra can only be obtained for the brightest few sources of each class. Moreover, except for the most compact extended sources, like cool core clusters, grating spectra are limited to point sources. Hitomi made another major step forward, in yielding for the first time a high-quality spectrum of an extended source, and improved spectral sensitivity in the Fe-K band. For point sources with the proposed Arcus mission, and for all sources with the launch of Athena, X-ray spectroscopy will become mature. It allows us to extend the investigations from the few handful of brightest sources of each category to a large number of sources far away in space and time, or to get high time-resolution, high-spectral resolution spectra of bright time variable sources.
Observational evidence for dark matter can be explained by Weakly Interacting Massive Particles (WIMPs). These dark matter particle candidates could indirectly be detected through the observation of signals produced as part of WIMP annihilations or decays. Latest results from indirect searches for WIMPs are reviewed. Current and planned experiments are presented and their prospects and discovery potential discussed.
Extending the idea of \cite{dab2} and using the 2-descent method, we provide three general families of elliptic curves over Q such that a positive proportion of prime-twists of such elliptic curves have rank zero simultaneously.
The First Fermi-LAT catalog (1FGL) represents the most complete list of sources in the GeV sky to date. We use the reported 1FGL spectral parameters to extrapolate Fermi AGN spectra to the very-high energy (VHE) range (15 GeV - 300 TeV). The extrapolated VHE spectra are then attenuated using current estimations of the extragalactic background light (EBL) absorption as a function of redshift. Using the expected effective areas and background rates of the Cherenkov Telescope Array (CTA) from Monte Carlo simulations, we make a first order prediction of the AGN population accessible to CTA in the VHE sky. We find that CTA should easily triple the AGN detection rate of current ground-based Cherenkov telescopes. In addition, CTA will allow unprecedented access to high-redshift blazars out to z ~ 2, and hence will start to reveal the EBL shape with gamma-ray observations.
We study angular momentum in non-relativistic quantum electrodynamics (NRQED). We construct the effective total angular momentum operator by applying Noether's theorem to the NRQED lagrangian. We calculate the NRQED matching for the individual components of the QED angular momentum up to one loop. We illustrate an application of our results by the first calculation of the angular momentum of the ground state hydrogen atom carried in radiative photons, $\alpha_{\rm em}^3/18\pi$, which might be measurable in future atomic experiments.
A major advantage in using Szegedy's formalism over discrete-time and continuous-time quantum walks lies in its ability to define a unitary quantum walk on directed and weighted graphs. In this paper, we present a general scheme to construct efficient quantum circuits for Szegedy quantum walks that correspond to classical Markov chains possessing transformational symmetry in the columns of the transition matrix. In particular, the transformational symmetry criteria do not necessarily depend on the sparsity of the transition matrix, so this scheme can be applied to non-sparse Markov chains. Two classes of Markov chains that are amenable to this construction are cyclic permutations and complete bipartite graphs, for which we provide explicit efficient quantum circuit implementations. We also prove that our scheme can be applied to Markov chains formed by a tensor product. We also briefly discuss the implementation of Markov chains based on weighted interdependent networks. In addition, we apply this scheme to construct efficient quantum circuits simulating the Szegedy walks used in the quantum Pagerank algorithm for some classes of non-trivial graphs, providing a necessary tool for experimental demonstration of the quantum Pagerank algorithm.
We study the size and the external path length of random tries and show that they are asymptotically independent in the asymmetric case but strongly dependent with small periodic fluctuations in the symmetric case. Such an unexpected behavior is in sharp contrast to the previously known results on random tries that the size is totally positively correlated to the internal path length and that both tend to the same normal limit law. These two dependence examples provide concrete instances of bivariate normal distributions (as limit laws) whose correlation is $0$, $1$ and periodically oscillating. Moreover, the same type of behaviors is also clarified for other classes of digital trees such as bucket digital trees and Patricia tries.
The rate at which interstellar gas is converted into stars, and its dependence on environment, is one of the pillars on which our understanding of the visible Universe is build. We present a comparison of the surface density of young stars (Sigma_*) and dust surface density (Sigma_d) across NGC346 (N66) in 115 independent pixels of 6x6 pc^2. We find a correlation between Sigma_* and Sigma_d with a considerable scatter. A power law fit to the data yields a steep relation with an exponent of 2.6+-0.2. We convert Sigma_d to gas surface density (Sigma_g) and Sigma_* to star formation rate (SFR) surface densities (Sigma_SFR), using simple assumptions for the gas-to-dust mass ratio and the duration of star formation. The derived total SFR (4+-1 10^-3 M_sun/yr) is consistent with SFR estimated from the Ha emission integrated over the Ha nebula. On small scales the Sigma_SFR derived using Ha systematically underestimates the count-based Sigma_SFR, by up to a factor of 10. This is due to ionizing photons escaping the area, where the stars are counted. We find that individual 36 pc^2 pixels fall systematically above integrated disc-galaxies in the Schmidt-Kennicutt diagram by on average a factor of ~7. The NGC346 average SFR over a larger area (90 pc radius) lies closer to the relation but remains high by a factor of ~3. The fraction of the total mass (gas plus young stars) locked in young stars is systematically high (~10 per cent) within the central 15 pc and systematically lower outside (2 per cent), which we interpret as variations in star formation efficiency. The inner 15 pc is dominated by young stars belonging to a centrally condensed cluster, while the outer parts are dominated by a dispersed population. Therefore, the observed trend could reflect a change of star formation efficiency between clustered and non-clustered star-formation.
In this note we prove that for every integer $k$, there exist constants $g_{1}(k)$ and $g_{2}(k)$ such that the following holds. If $G$ is a graph on $n$ vertices with maximum degree $\Delta$ then it contains an induced subgraph $H$ on at least $n - g_{1}(k)\sqrt{\Delta}$ vertices, such that $H$ has $k$ vertices of the same degree of order at least $\Delta(H)-g_{2}(k)$. This solves a conjecture of Caro and Yuster up to the constant $g_{2}(k)$.
We consider the energetic description of a visco-plastic evolution and derive an existence result. The energies are convex, but not necessarily quadratic. Our model is a strain gradient model in which the curl of the plastic strain contributes to the energy. Our existence results are based on a time-discretization, the limit procedure relies on Helmholtz decompositions and compensated compactness.
We explore the idea of higher-order flavor sum rules, i.e. sum rules that hold to higher orders in the flavor symmetry-breaking parameters. In particular, we consider isospin sum rules based on $B \to n\pi$ decays, and U-spin sum rules based on $B_d$ and $B_s$ decays to $n$ charged pions and/or kaons. We also demonstrate that sum rules exist to arbitrary orders by considering decay modes with increasing number of final state mesons $n$. Finally, we identify various theoretical and practical issues that need to be addressed in utilizing these sum rules.
Let $X,Y$ be algebraic varieties defined over $\Bbb R$. Assume $Y$ is smooth and $X$ is Gorenstein. Suppose $\varphi:X\to Y$ is a flat $\Bbb R$-morphism such that all the fibers have rational singularities. We show that the pushforward of any smooth, compactly supported measure on $X$ has a continuous density with respect to any smooth measure with non-vanishing density on $Y$. This extends a result of Aizenbud and Avni from the $p$-adic case to the archimedean case.
We review the most recent evidence for the amazing properties of the density distribution of dark matter around spiral galaxies. Their rotation curves, coadded according to the galaxy luminosity, conform to an universal profile which can be represented as the sum of an exponential thin disk plus a spherical halo with a flat density core. From dwarfs to giants, these halos feature an inner constant density region. The fine structure of dark matter halos is obtained from the kinematics of a number of suitable low-luminosity disk galaxies. The halo circular velocity increases linearly with radius out to the edge of the stellar disk, implying a constant dark halo density over the entire disk region. The properties of halos around normal spirals provide substantial evidence of a discrepancy between the mass distributions predicted in the Cold Dark Matter scenario and those actually detected around galaxies.
We produce a canonical filtration for locally free sheaves on an open p-adic annulus equipped with a Frobenius structure. Using this filtration, we deduce a conjecture of Crew on p-adic differential equations, analogous to Grothendieck's local monodromy theorem (also a consequence of results of Andre and of Mebkhout). Namely, given a finite locally free sheaf on an open p-adic annulus with a connection and a compatible Frobenius structure, the corresponding module admits a basis over a finite cover of the annulus on which the connection acts via a nilpotent matrix.   Note: this preprint improves on results from our previous preprints math.AG/0102173, math.AG/0105244, math.AG/0106192, math.AG/0106193 but does not explicitly invoke any results from these preprints.
We propose a nano-scale realization of a phonon laser utilizing phonon-assisted spin flips in quantum dots to amplify sound. Owing to a long spin relaxation time, the device can be operated in a strong pumping regime, in which the population inversion is close to its maximal value allowed under Fermi statistics. In this regime, the threshold for stimulated emission is unaffected by spontaneous spin flips. Considering a nanowire with quantum dots defined along its length, we show that a further improvement arises from confining the phonons to one dimension, and thus reducing the number of phonon modes available for spontaneous emission. Our work calls for the development of nanowire-based, high-finesse phonon resonators.
In this note we study the growth of \sum_{m=1}^M\frac1{\|m\alpha\|} as a function of M for different classes of \alpha\in[0,1). Hardy and Littlewood showed that for numbers of bounded type, the sum is \simeq M\log M. We give a very simple proof for it. Further we show the following for generic \alpha. For a non-decreasing function \phi tending to infinity, \limsup_{M\to\infty}\frac1{\phi(\log M)}\bigg[\frac1{M\log M}\sum_{m=1}^M\frac1{\|m\alpha\|}\bigg] is zero or infinity according as \sum\frac1{k\phi(k)} converges or diverges.
We have characterized CdS/CdSe/CdS quantum-dot quantum wells using time-resolved Faraday rotation (TRFR). The spin dynamics show that the electron g-factor varies as a function of quantum well width and the transverse spin lifetime of several nano-seconds is robust up to room temperature. As a function of probe energy, the amplitude of the TRFR signal shows pronounced resonances, which allow one to identify individual exciton transitions. While the TRFR data are inconsistent with the conduction and valence band level scheme of spherical quantum-dot quantum wells, a model in which broken spherical symmetry is taken into account captures the essential features.
We examine the relation between two known classes of solutions of the sine--Gordon equation, which are expressed by theta functions on hyperelliptic Riemann surfaces. The first one is a consequence of the Fay's trisecant identity. The second class exists only for odd genus hyperelliptic Riemann surfaces which admit a fixed--point--free automorphism of order two. We show that these two classes of solutions coincide. The hyperelliptic surfaces corresponding to the second class appear to be double unramified coverings of the Riemann surfaces corresponding to the first class of solutions. We also discuss the soliton limits of these solutions.
The quantum theory of General Relativity at low energy exists and is of the form called "effective field theory". In this talk I describe the ideas of effective field theory and its application to General Relativity.
We study the capitulation of $2$-ideal classes of an infinite family of imaginary biquadratic number fields consisting of fields $k =Q(\sqrt{pq_1q_2}, i)$, where $i=\sqrt{-1}$ and $q_1\equiv q_2\equiv-p\equiv-1 \pmod 4$ are different primes. For each of the three quadratic extensions $K/k$ inside the absolute genus field $k^{(*)}$ of $k$, we compute the capitulation kernel of $K/k$. Then we deduce that each strongly ambiguous class of $k/Q(i)$ capitulates already in $k^{(*)}$.