ShantanuT01/DACTYL-Pretraining huggingface dataset:
Reiman produced a quadratic inequality for the size of bipartite graphs of girth six. We get its counterpart for girth eight, a cubic inequality. It is optimal in as far as it admits the algebraic structure of generalized quadrangles as case of equality. This enables us to obtain the optimal estimate e ~ v^(4/3) for balanced bipartite graphs. We also get an optimal estimate for very unbalanced graphs.
We review the present status of CP violation in the standard model. Subsequently we make an excursion in the future in order to see what we could expect in this field in this and the next decade. We present various strategies for the determination of the CKM parameters and divide the decays into four classes with respect to theoretical uncertainties. We emphasize that the definitive tests of the Kobayashi-Maskawa picture of CP violation will come through a {\it simultaneous} study of CP asymmetries in $B_{d,s}^o$ decays, the rare decays $K^+ \to \pi^+\nu \bar\nu$ and $K_L \to \pi^o\nu\bar\nu$, and $x_d/x_s$. We illustrate how the measurements of the CP asymmetries in $B^0_{d,s}$-decays together with a measurement of $Br(K_L\to \pi^\circ\nu\bar\nu)$ or $Br(\kpnn)$ and the known value of $\mid V_{us}\mid $ can determine {\it all} elements of the Cabibbo-Kobayashi-Maskawa matrix essentially without any hadronic uncertainties.
A pseudo-velocity concept, based on the extension of a linear body, is defined by a special relativity experiment. It suggests an analogy with the covariance properties of Wiener's process, ultimately implying that the scaling behavior of (Gaussian) polymer solutions can be derived from a Brownian Relativity theory, as it was formerly put forward. An ad-hoc statistical interpretation of the resulting spacetime transforms may be given by the central limit theorem.
Let $h(d)$ be the class number of indefinite binary quadratic forms of discriminant $d$, and let $\varepsilon_d$ be the corresponding fundamental unit. In this paper, we obtain an asymptotic formula for the $k$-th moment of $h(d)$ over positive discriminants $d$ with $\varepsilon_d\leq x$, uniformly for real numbers $k$ in the range $0<k\leq (\log x)^{1-o(1)}$. This improves upon the work of Raulf, who obtained such an asymptotic for a fixed positive integer $k$. We also investigate the distribution of large values of $h(d)$ when the $d$'s are ordered according to the size of their fundamental units $\varepsilon_d$. In particular, we show that the tail of this distribution has the same shape as that of class numbers of imaginary quadratic fields ordered by the size of their discriminants. As an application of these results, we prove that there are many positive discriminants $d$ with class number $h(d)\geq (e^{\gamma}/3+o(1))\cdot\varepsilon_d (\log\log \varepsilon_d)/\log \varepsilon_d$, a bound that we believe is best possible. We also obtain an upper bound for $h(d)$ that is twice as large, assuming the generalized Riemann hypothesis.
Diazonium reactions with carbon nanotubes form optical $sp^3$ defects that can be used in optical and electrical circuits. We investigate a direct on-device reaction supported by confined laser irradiation and present a technique where an arbitrary carbon nanotube can be preferentially functionalized within a device by matching the light frequency with its transition energy. An exemplary reaction was carried out between (9,7) nanotube and 4-bromobenzenediazonium tetrafluoroborate. The substrate supported nanotubes of multiple semiconducting chiralities were locally exposed to laser light while monitoring the reaction kinetics in-situ via Raman spectroscopy. The chiral selectivity of the reaction was confirmed by resonant Raman spectroscopy, reporting a 10 meV $E_{22}$ transition energy red-shift only of the targeted species. We further demonstrated this method on a single tube (9,7) electroluminescent device and show a 25 meV red-shifted emission of the ground state $E_{11}$ compared to the emission from the pristine tubes.
Products of large-N conformal field theories coupled by multi-trace interactions in diverse dimensions are used to define quantum multi-gravity (multi-string theory) on a union of (asymptotically) AdS spaces. One-loop effects generate a small O(1/N) mass for some of the gravitons. The boundary gauge theory and the AdS/CFT correspondence are used as guiding principles to study and draw conclusions on some of the well known problems of massive gravity - classical instabilities and strong coupling effects. We find examples of stable multi-graviton theories where the usual strong coupling effects of the scalar mode of the graviton are suppressed. Our examples require a fine tuning of the boundary conditions in AdS. Without it, the spacetime background backreacts in order to erase the effects of the graviton mass.
In layered semiconductors with spin-orbit interaction (SOI) a persistent spin helix (PSH) state with suppressed spin relaxation is expected if the strengths of the Rashba and Dresselhaus SOI terms, alpha and beta, are equal. Here we demonstrate gate control and detection of the PSH in two-dimensional electron systems with strong SOI including terms cubic in momentum. We consider strain-free InGaAs/InAlAs quantum wells and first determine alpha/beta ~ 1 for non-gated structures by measuring the spin-galvanic and circular photogalvanic effects. Upon gate tuning the Rashba SOI strength in a complementary magneto-transport experiment, we then monitor the complete crossover from weak antilocalization via weak localization to weak antilocalization, where the emergence of weak localization reflects a PSH type state. A corresponding numerical analysis reveals that such a PSH type state indeed prevails even in presence of strong cubic SOI, however no longer at alpha = beta.
We describe and execute a novel approach to observationally estimate the lifetimes of giant molecular clouds (GMCs). We focus on the cloud population between the two main spiral arms in M51 (the inter-arm region) where cloud destruction via shear and star formation feedback dominates over formation processes. By monitoring the change in GMC number densities and properties from one side of the inter-arm to the other, we estimate the lifetime as a fraction of the inter-arm travel time. We find that GMC lifetimes in M51's inter-arm are finite and short, 20 to 30 Myr. Such short lifetimes suggest that cloud evolution is influenced by environment, in which processes can disrupt GMCs after a few free-fall times. Over most of the region under investigation shear appears to regulate the lifetime. As the shear timescale increases with galactocentric radius, we expect cloud destruction to switch primarily to star formation feedback at larger radii. We identify a transition from shear- to feedback-dominated disruption through a change in the behavior of the GMC number density. The signature suggests that shear is more efficient at completely dispersing clouds, whereas feedback transforms the population, e.g. by fragmenting high mass clouds into lower mass pieces. Compared to the characteristic timescale for molecular hydrogen in M51, our short lifetimes suggest that gas can remain molecular while clouds disperse and reassemble. We propose that galaxy dynamics regulates the cycling of molecular material from diffuse to bound (and ultimately star-forming) objects, contributing to long observed molecular depletion times in normal disk galaxies. We also speculate that, in more extreme environments such as elliptical galaxies and concentrated galaxy centers, star formation can be suppressed when the shear timescale becomes so short that some clouds can not survive to collapse and form stars.
We consider $(p+1)$-form gauge fields in flat $(2p+4)$-dimensions for which the radiation and the Coulomb solutions have the same asymptotic falloff behavior. Imposing appropriate falloff behavior on fields and adopting a Maxwell-type action, we construct the boundary term which renders the action principle well-defined in the Lorenz gauge. We then compute conserved surface charges and the corresponding asymptotic charge algebra associated with nontrivial gauge transformations. We show that for $p\geq 1$ cases we have three sets of conserved asymptotic charges associated with exact, coexact and zero-mode parts of the corresponding $p$-form gauge transformations on the asymptotic $S^{2p+2}$. The coexact and zero-mode charges are higher form extensions of the four dimensional electrodynamics case $(p=0)$, and are commuting. Charges associated with exact gauge transformations have no counterparts in four dimensions and form infinite copies of Heisenberg algebras. We briefly discuss physical implications of these charges and their algebra.
A B\"acklund transformation yielding the static non-relativistic Chern-Simons vortices of Jackiw and Pi is presented.
This work represents a systematic computational study of the distribution of the Fourier coefficients of cuspidal Hecke eigenforms of level $\Gamma_0(4)$ and half-integral weights. Based on substantial calculations, the question is raised whether the distribution of normalised Fourier coefficients with bounded indices can be approximated by a generalised Gaussian distribution. Moreover, it is argued that the apparent symmetry around zero of the data lends strong evidence to the Bruinier-Kohnen Conjecture on the equidistribution of signs and even suggests the strengthening that signs and absolute values are distributed independently.
We make an exploratory study of how well dark energy models can be constrained using lensed arcs at different redshifts behind cluster lenses. Arcs trace the critical curves of clusters, and the growth of critical curves with source redshift is sensitive to the dark-energy equation of state. Using analytical models and numerically simulated clusters, we explore the key factors involved in using cluster arcs as a probe of dark energy. We quantify the sensitivity to lens mass, concentration and ellipticity with analytical models that include the effects of dark energy on halo structure. We show with simple examples how degeneracies between mass models and cosmography may be broken using arcs at multiple redshifts or additional constraints on the lens density profile. However we conclude that the requirements on the data are so stringent that it is very unlikely that robust constraints can be obtained from individual clusters. We argue that surveys of clusters, analyzed in conjunction with numerical simulations, are a more promising prospect for arc-cosmography.   We use such numerically simulated clusters to estimate how large a sample of clusters/arcs could provide interesting constraints on dark energy models. We focus on the scatter produced by differences in the mass distribution of individual clusters. We find from our sample of simulated clusters that at least 1000 pairs of arcs are needed to obtain constraints if the mass distribution of individual clusters is taken to be undetermined. We discuss several unsolved problems that need study to fully develop this method for precision studies with future surveys.
We investigate the interplay of electronic correlations and spin-orbit coupling (SOC) for a one-band and a two-band honeycomb lattice model. The main difference between the two models concerning SOC is that in the one-band case the SOC is a purely non-local term in the basis of the $p_z$ orbitals, whereas in the two-band case with $p_x$ and $p_y$ as basis functions it is purely local. In order to grasp the correlation effects on non-local spin-orbit coupling, we apply the TRILEX approach that allows to calculate non-local contributions to the self-energy approximatively. For the two-band case we apply dynamical mean-field theory. In agreement with previous studies, we find that for all parameter values in our study, the effect of correlations on the spin-orbit coupling strength is that the bare effective SOC parameter is increased. However, this increase is much weaker in the non-local than in the local SOC case. Concerning the TRILEX method, we introduce the necessary formulas for calculations with broken SU(2) symmetry.
We study a holographic model of a relativistic quantum system with a global U(1) symmetry, at non-zero temperature and density. When the temperature falls below a critical value, we find a second-order superfluid phase transition with mean-field critical exponents. In the symmetry-broken phase, we determine the speed of second sound as a function of temperature. As the velocity of the superfluid component relative to the normal component increases, the superfluid transition goes through a tricritical point and becomes first-order.
By using Girsanov transformation and martingale representation,   Talagrand-type transportation cost inequalities, with respect to both the uniform and the $L^2$ distances on the global free path space, are established for the segment process associated to a class of neutral functional stochastic differential equations. Neutral functional stochastic partial differential equations are also investigated.
WLM is a dwarf irregular that is seen almost edge-on that has prompted a number of kinematical studies investigating its rotation curve and its dark matter content. In this paper, we investigate the origin of the strong asymmetry of the rotation curve, which shows a significant discrepancy between the approaching and the receding side. We first examine whether an $m = 1$ perturbation (lopsidedness) in the halo potential could be a mechanism creating such kinematical asymmetry. To do so, we fit a theoretical rotational velocity associated with an $m = 1$ perturbation in the halo potential model to the observed data via a $\chi-$squared minimization method. We show that a lopsided halo potential model can explain the asymmetry in the kinematic data reasonably well. We then verify that the kinematical classification of WLM shows that its velocity field is significantly perturbed due to both its asymmetrical rotation curve and also its peculiar velocity dispersion map. In addition, based on a kinemetry analysis, we find that it is possible for WLM to lie in the transition region, where the disk and merger coexist. In conclusion, it appears that the rotation curve of WLM diverges significantly from that of an ideal rotating disk, which may significantly affect investigations of its dark matter content.
It is found that for on-site interaction $U\neq 0$ the local $SU(2)\times SU(2) \times U(1)$ gauge symmetry of the Hubbard model on a bipartite lattice with vanishing transfer integral $t=0$ can be lifted to a global $[SU(2)\times SU(2)\times U(1)]/Z_2^2=SO(3)\times SO(3)\times U(1)$ symmetry in the presence of the kinetic-energy hopping term of the Hamiltonian with $t>0$. The generator of the new found hidden independent charge global U(1) symmetry is one half the rotated-electron number of singly-occupied sites operator. It is confirmed elsewhere that our results have important physical consequences concerning the further understanding of the unusual properties of the hole-doped cuprates.
We construct a radiation-hydrodynamics model for the obscuring toroidal structure in active galactic nuclei. In this model the obscuration is produced at parsec scale by a dense, dusty wind which is supported by infrared radiation pressure on dust grains. To find the distribution of radiation pressure, we numerically solve the 2D radiation transfer problem in a flux limited diffusion approximation. We iteratively couple the solution with calculations of stationary 1D models for the wind, and obtain the z-component of the velocity. Our results demonstrate that for AGN luminosities greater than 0.1 Ledd external illumination can support a geometrically thick obscuration via outflows driven by infrared radiation pressure. The terminal velocity of marginally Compton-thin models (0.2<tau_T<0.6), is comparable to or greater than the escape velocity. In Compton thick models the maximum value of the vertical component of the velocity is lower than the escape velocity, suggesting that a significant part of our torus is in the form of failed wind. The results demonstrate that obscuration via normal or failed infrared-driven winds is a viable option for the AGN torus problem and AGN unification models. Such winds can also provide an important channel for AGN feedback.
Recent work has extended Bell's theorem by quantifying the amount of communication required to simulate entangled quantum systems with classical information. The general scenario is that a bipartite measurement is given from a set of possibilities and the goal is to find a classical scheme that reproduces exactly the correlations that arise when an actual quantum system is measured. Previous results have shown that, using local hidden variables, a finite amount of communication suffices to simulate the correlations for a Bell state. We extend this in a number of ways. First, we show that, when the communication is merely required to be finite {\em on average}, Bell states can be simulated {\em without} any local hidden variables. More generally, we show that arbitrary positive operator valued measurements on systems of $n$ Bell states can be simulated with $O(n 2^n)$ bits of communication on average (again, without local hidden variables). On the other hand, when the communication is required to be {\em absolutely bounded}, we show that a finite number of bits of local hidden variables is insufficent to simulate a Bell state. This latter result is based on an analysis of the non-deterministic communication complexity of the NOT-EQUAL function, which is constant in the quantum model and logarithmic in the classical model.
We estimate the resources required to prepare the ground state of a quantum many-body system on a quantum computer of intermediate size. This estimate is made possible using a combination of quantum many-body methods and analytic upper bounds. Our routine can also be used to optimize certain design parameters for specific problem instances. Lastly, we propose and benchmark an improved quantum state preparation procedure. We find that it reduces the circuit T-depth by a factor as large as $10^6$ for intermediate-size lattices.
We present line and continuum observations made with the Submillimeter Array (SMA) of the young stellar object Barnard 5 - IRS1 located in the Perseus molecular cloud. Our $^{12}$CO(2-1) line observations resolve the high-velocity bipolar northeast-southwest outflow associated with this source. We find that the outflowing gas shows different structures at three different velocity regimes, in both lobes, resulting in a spider-like morphology. In addition to the low-velocity, cone-like (wide-angle) lobes that have previously been observed, we report the presence of intermediate-velocity parabolic shells emerging very close to the Class I protostar, as well as high velocity molecular bullets that appear to be associated to the optical/IR jet emanating from this source. These compact high-velocity features reach radial velocities of about 50 km s$^{-1}$ away from the cloud velocity. We interpret the peculiar spider-like morphology is a result of the molecular material being entrained by a wind with both a collimated jet-like component and a wide-angle component. We suggest the outflow is in a transitional evolutionary phase between a mostly jet-driven flow and an outflow in which the entrainment is dominated by the wide-angle wind component. We also detect 1300 $\mu$m continuum emission at the position of the protostar, which likely arises from the dusty envelope and disk surrounding the protostar. Finally, we report the detection of $^{13}$CO(2-1) and SO(6$_5$-5$_4$) emission arising from the outflow and the location of the young stellar object.
We perform a detailed study of the renormalization group equations in the inverse seesaw model. Especially, we derive compact analytical formulas for the running of the neutrino parameters in the standard model and the minimal supersymmetric standard model, and illustrate that, due to large Yukawa coupling corrections, significant running effects on the leptonic mixing angles can be naturally obtained in the proximity of the electroweak scale, perhaps even within the reach of the LHC. In general, if the mass spectrum of the light neutrinos is nearly degenerate, the running effects are enhanced to experimentally accessible levels, well suitable for the investigation of the underlying dynamics behind the neutrino mass generation and the lepton flavor structure. In addition, the effects of the seesaw thresholds are discussed, and a brief comparison to other seesaw models is carried out.
In this paper, we study the dynamics of the Chern-Simons Inflation Model proposed by Alexander, Marciano and Spergel. According to this model, inflation begins when a fermion current interacts with a turbulent gauge field in a space larger than some critical size. This mechanism appears to work by driving energy from the initial random spectrum into a narrow band of frequencies, similar to the inverse energy cascade seen in MHD turbulence. In this work we focus on the dynamics of the interaction using phase diagrams and a thorough analysis of the evolution equations. We show that in this model inflation is caused by an over-damped harmonic oscillator driving waves in the gauge field at their resonance frequency.
A detailed numerical analysis of the magnetization reversal processes in multisegmented nanowire arrays was developed. The nanowires have a long aspect ratio and are formed by magnetic and non-magnetic sections alternately arranged in such a way that the array resembles magnetic layers separated by non-magnetic layers. Attention has been focused on the influence of magnetostatic interaction in the magnetic pattern formation of these magnetic nanostructures. Results from a magnetic correlation function among layers show that three different reversal modes can be detected depending on the number and distance between the magnetic segments. As a consequence of the different reversal modes, a non-monotonic behavior of the annihilation field in function of the distance between the layers is evidenced. Thus, these results are important for the production of magnetic devices with multisegmented nanowire arrays.
The nonrelativistic full-folding optical model approach for nucleon-nucleus scattering is extended into the relativistic regime. In doing so, kinematical issues involving the off-shell Lorentz boost of the colliding particles between the two nucleons and the projectile-nucleus center-of-mass reference frames have been taken into account. The two-body effective interaction is obtained in the framework of the nuclear matter g-matrix using nucleon-nucleon optical model potentials that fully account for the inelasticities and isobar resonances in the continuum at nucleon energies up to 3 GeV. Diverse nucleon-nucleon potential models were constructed by supplementing the basic Paris, Nijmegen, Argonne or Gel'fand-Levitan-Marchenko inversion potentials with complex separable terms. In each case the additional separable terms ensured that the combination led to NN scattering phase shifts in excellent agreement with experimental values. With each phase shift fitting potential nuclear matter g-matrices have been formed and with each of those relativistic full-folding optical potentials for nucleon-nucleus elastic scattering determined. Application to such scattering for projectile energies to 1.5 GeV have been made. Good and systematic agreement is obtained between the calculated and measured observables, both differential and integrated quantities, over the whole energy range of our study. A moderate sensitivity to off-shell effects in the differential scattering observables also is observed.