ShantanuT01/DACTYL-Pretraining huggingface dataset:
Recent progress in the fabrication of materials has made it possible to create arbitrary non-periodic two-dimensional structures in the quantum plasmon regime. This paves the way for exploring the plasmonic properties of electron gases in complex geometries such as fractals. In this work, we study the plasmonic properties of Sierpinski carpets and gaskets, two prototypical fractals with different ramification, by fully calculating their dielectric functions. We show that the Sierpinski carpet has a dispersion comparable to a square lattice, but the Sierpinski gasket features highly localized plasmon modes with a flat dispersion. This strong plasmon confinement in finitely ramified fractals can provide a novel setting for manipulating light at the quantum scale.
The mass measurement of galaxy clusters is an important tool for the determination of cosmological parameters describing the matter and energy content of the Universe. However, the standard methods rely on various assumptions about the shape or the level of equilibrium of the cluster. We present a novel method of measuring cluster masses. It is complementary to most of the other methods, since it only uses kinematical information from outside the virialized cluster. Our method identifies objects, as galaxy sheets or filaments, in the cluster outer region, and infers the cluster mass by modeling how the massive cluster perturbs the motion of the structures from the Hubble flow. At the same time, this technique allows to constrain the three-dimensional orientation of the detected structures with a good accuracy. We use a cosmological numerical simulation to test the method. We then apply the method to the Coma cluster, where we find two galaxy sheets, and measure the mass of Coma to be Mvir=(9.2\pm2.4)10^{14} Msol, in good agreement with previous measurements obtained with the standard methods.
High-dimensional quantum states are promising resources for quantum communication and processing. In this context the frequency degree of freedom of light combines the advantages of robustness and easy handling with standard classical telecommunication components. In this work we propose a method to generate and control the symmetry of broadband biphoton frequency states, based on the interplay of cavity effects and relative temporal delay between the two photons of each pair. We demonstrate it using an integrated AlGaAs semiconductor platform producing quantum frequency combs, working at room temperature and compliant with electrical injection. These results open interesting perspectives for the development of massively parallel and reconfigurable systems for complex quantum operations.
A recently proposed "gedanken experiment" [G.Z. Machabeli and A.D. Rogava. Phys. Rev. A {\bf 50}, 98 (1994)], exhibiting surprising behavior, is reexamined. A description of this behavior in terms of the laboratory inertial frame is presented, avoiding uncertainties arising due to a definition of a centrifugal force in relativity. The surprising analogy with the radial geodesic motion in Schwarzschild geometry is discovered. The definition of the centrifugal force, suggested by J.C. Miller and M.A. Abramowicz, is discussed.
We develop criteria for hitting probabilities of anisotropic Gaussian random fields with associated canonical pseudo-metric given by a class of gauge functions. This yields lower and upper bounds in terms of general notions of capacity and Hausdorff measure, respectively, therefore extending the classical estimates with the Bessel-Riesz capacity and the $\gamma$-dimensional Hausdorff measure. We apply the criteria to a system of linear stochastic partial differential equations driven by space-time noises that are fractional in time and either white or colored in space.
We show that string/M theory compactifications to maximally symmetric space-times using manifolds whose scalar curvature is everywhere negative, must have significant warping, large stringy corrections, or both.
This paper has been merged with the preprint nucl-th/0210057. The combined version is accepted for publication is Phys. Rev. C
Simulation tasks are insightful tools to compare information-theoretic resources. Considering a generalization of usual Bell scenarios where external quantum inputs are provided to the parties, we show that any entangled quantum state exhibits correlations that cannot be simulated using only shared randomness and classical communication, even when the amount and rounds of classical communication involved are unrestricted. We indeed construct explicit Bell-like inequalities that are necessarily satisfied by such classical resources but nevertheless violated by correlations obtainable from entangled quantum states, when measured a single copy at a time.
We define polynomials of one variable t whose values at t=0 and 1 are the multiple zeta values and the multiple zeta-star values, respectively. We give an application to the two-one conjecture of Ohno-Zudilin, and also prove the cyclic sum formula for these polynomials.
When carbon is ignited off-center in a CO core of a super-AGB star, its burning in a convective shell tends to propagate to the center. Whether the C flame will actually be able to reach the center depends on the efficiency of extra mixing beneath the C convective shell. Whereas thermohaline mixing is too inefficient to interfere with the C-flame propagation, convective boundary mixing can prevent the C burning from reaching the center. As a result, a C-O-Ne white dwarf (WD) is formed, after the star has lost its envelope. Such a "hybrid" WD has a small CO core surrounded by a thick ONe zone. In our 1D stellar evolution computations the hybrid WD is allowed to accrete C-rich material, as if it were in a close binary system and accreted H-rich material from its companion with a sufficiently high rate at which the accreted H would be processed into He under stationary conditions, assuming that He could then be transformed into C. When the mass of the accreting WD approaches the Chandrasekhar limit, we find a series of convective Urca shell flashes associated with high abundances of 23Na and 25Mg. They are followed by off-center C ignition leading to convection that occupies almost the entire star. To model the Urca processes, we use the most recent well-resolved data for their reaction and neutrino-energy loss rates. Because of the emphasized uncertainty of the convective Urca process in our hybrid WD models of SN Ia progenitors, we consider a number of their potentially possible alternative instances for different mixing assumptions, all of which reach a phase of explosive C ignition, either off or in the center. Our hybrid SN Ia progenitor models have much lower C to O abundance ratios at the moment of the explosive C ignition than their pure CO counterparts, which may explain the observed diversity of the SNe Ia.
Chiral magnets give rise to the anti-symmetric Dzyaloshinskii-Moriya (DM) interaction, which induces topological nontrivial textures such as magnetic skyrmions. The topology is characterized by integer values of the topological charge. In this work, we performed the Monte-Carlo calculation of a two-dimensional model of the chiral magnet. A surprising upturn of the topological charge is identified at high fields and high temperatures. This upturn is closely related to thermal fluctuations at the atomic scale, and is explained by a simple physical picture based on triangulation of the lattice. This emergent topology is also explained by a field-theoretic analysis using $CP^{1}$ formalism.
We present a characterization of topological phases in photonic lattices. Our theory relies on a formal equivalence between the singular value decomposition of the non-Hermitian coupling matrix and the diagonalization of an effective Hamiltonian. By means of that mapping we unveil an application of topological band theory to the description of quantum amplification with non-reciprocal systems. We exemplify our ideas with an array of photonic cavities which can be mapped into a topological insulator Hamiltonian in the AIII symmetry class. We investigate stability properties and prove the existence of stable topologically non-trivial steady-state phases. Finally, we show numerically that the topological amplification process is robust against disorder in the lattice parameters.
I derive precise results for absorbing-state phase transitions using exact (numerically determined) quasistationary probability distributions for small systems. Analysis of the contact process on rings of 23 or fewer sites yields critical properties (control parameter, order-parameter ratios, and critical exponents z and beta/nu_perp) with an accuracy of better than 0.1%; for the exponent nu_perp the accuracy is about 0.5%. Good results are also obtained for the pair contact process.
We present the first comprehensive archival study of the X-ray properties of ultracompact dwarf (UCD) galaxies, with the goal of identifying weakly-accreting central black holes in UCDs. Our study spans 578 UCDs distributed across thirteen different host systems, including clusters, groups, fossil groups, and isolated galaxies. Of the 336 spectroscopically-confirmed UCDs with usable archival Chandra imaging observations, 21 are X-ray-detected. Imposing a completeness limit of $L_X>2\times10^{38}$ erg s$^{-1}$, the global X-ray detection fraction for the UCD population is $\sim3\%$. Of the 21 X-ray-detected UCDs, seven show evidence of long-term X-ray time variability on the order of months to years. X-ray-detected UCDs tend to be more compact than non-X-ray-detected UCDs, and we find tentative evidence that the X-ray detection fraction increases with surface luminosity density and global stellar velocity dispersion. The X-ray emission of UCDs is fully consistent with arising from a population of low-mass X-ray binaries (LMXBs). In fact, there are fewer X-ray sources than expected using a naive extrapolation from globular clusters. Invoking the fundamental plane of black hole activity for SUCD1 near the Sombrero galaxy, for which archival Jansky Very Large Array imaging at 5 GHz is publicly available, we set an upper limit on the mass of a hypothetical central black hole in that UCD to be $\lesssim10^5M_{\odot}$. While the majority of our sources are likely LMXBs, we cannot rule out central black holes in some UCDs based on X-rays alone, and so we address the utility of follow-up radio observations to find weakly-accreting central black holes.
With the aim of deriving symmetric hyperbolic free-evolution systems for GR that possess Hamiltonian structure and allow for the popular puncture gauge condition we analyze the hyperbolicity of Hamiltonian systems. We develop helpful tools which are applicable to either the first order in time, second order in space or the fully second order form of the equations of motion. For toy models we find that the Hamiltonian structure can simplify the proof of symmetric hyperbolicity. In GR we use a special structure of the principal part to prove symmetric hyperbolicity of a formulation that includes gauge conditions which are very similar to the puncture gauge.
We present a class of spherically symmetric spacetimes corresponding to bubbles separating two regions with constant values of the scalar curvature, or equivalently with two different cosmological constants, in quadratic F(R) theory. The bubbles are obtained by means of the junction formalism, and the matching hypersurface supports in general a thin shell and a gravitational double layer. In particular, we find that pure double layers are possible for appropriate values of the parameters of the model whenever the quadratic coefficient is negative. This is the first example of a pure double layer in a gravitational theory.
Astronomical observations, analytical solutions and numerical simulations have provided the building blocks to formulate the current theory of young stellar object jets. Although each approach has made great progress independently, it is only during the last decade that significant efforts are being made to bring the separate pieces together. Building on previous work that combined analytical solutions and numerical simulations, we apply a sophisticated cooling function to incorporate optically thin energy losses in the dynamics. On the one hand, this allows a self-consistent treatment of the jet evolution and on the other, it provides the necessary data to generate synthetic emission maps. Firstly, analytical disk and stellar outflow solutions are properly combined to initialize numerical two-component jet models inside the computational box. Secondly, magneto-hydrodynamical simulations are performed in 2.5D, following properly the ionization and recombination of a maximum of $29$ ions. Finally, the outputs are post-processed to produce artificial observational data. The first two-component jet simulations, based on analytical models, that include ionization and optically thin radiation losses demonstrate promising results for modeling specific young stellar object outflows. The generation of synthetic emission maps provides the link to observations, as well as the necessary feedback for the further improvement of the available models.
For a local singular plane curve germ $f(X,Y)=0$ we characterize all nonsingular $\lambda\in\bbC\{X,Y\}$ such that the {\L}ojasiewicz exponent of $\grad\,f$ is not attained on the polar curve $\bJ(\lambda,f)=0$. When $f$ is not Morse we prove that for the same $\lambda$'s the maximal polar quotient $q_0(f,\lambda)$ is strictly less than its generic value $q_0(f)$. Our main tool is the Eggers tree of singularity constructed as a decorated graph of relations between balls in the space of branches defined by using a logarithmic distance.
We consider the initial value problem associated to the neural field equation of Amari type with plasticity \[ u_t(x,t)=-u(x,t)+\int_{\Omega}w(x,y)[1+\gamma g( u(x,t) - u(y,t) )] f(u(y,t))\; dy, \;(x,t) \in \Omega \times (0, \infty), \] where $\Omega\subset\mathbb{R}^m$, $f$ and $g$ are bounded and continuously differentiable functions with bounded derivative, and $\gamma\ge0$ is the plasticity synaptic coefficient. We show that the problem is well posed in $C_b(\mathbb{R}^m)$ and $L^1(\Omega)$ with $\Omega$ compact. The proof follows from a classical fixed point argument when we consider the equation's flow. Strong convergence of solutions in the no plasticity limit ($\gamma\to0$) to solutions of Amari's equation is analysed. Finally, we prove existence of stationary solutions in a general way. As a particular case, we show that the Amari's model, after learning, leads to the stationary Schr\"odinger equation for a type of gain modulation.
For each del Pezzo surface $S$ with du Val singularities, we determine whether it admits a $(-K_S)$-polar cylinder or not. If it allows one, then we present an effective $\mathbb{Q}$-divisor $D$ that is $\mathbb{Q}$-linearly equivalent to $-K_S$ and such that the open set $S\setminus\mathrm{Supp}(D)$ is a cylinder. As a corollary, we classify all the del Pezzo surfaces with du Val singularities that admit nontrivial $\mathbb{G}_a$-actions on their affine cones defined by their anticanonical divisors.
In this paper we study the analyticity of the group action of the automorphism group $G$ of a formal module $\bar{F}$ of height 2 (defined over $\overline{\mathbb{F}}_q$) on the Lubin-Tate deformation space $X$ of $\bar{F}$. It is shown that a wide open congruence group of level zero attached to a non-split torus acts analytically on a particular disc in $X$ on which the period morphism is not injective. For certain other discs with larger radii (defined in terms of quasi-canonical liftings) we find wide open rigid analytic groups which act analytically on these discs.
We use the new ultra-deep, near-infrared imaging of the Hubble Ultra-Deep Field (HUDF) provided by our UDF12 HST WFC3/IR campaign to explore the rest-frame UV properties of galaxies at redshifts z > 6.5. We present the first unbiased measurement of the average UV power-law index, beta, for faint galaxies at z ~ 7, the first meaningful measurements of beta at z ~ 8, and tentative estimates for a new sample of galaxies at z ~ 9. Utilising galaxy selection in the new F140W imaging to minimize colour bias, and applying both colour and power-law estimators of beta, we find beta = -2.1 (+/-0.2) at z ~ 7 for galaxies with M_UV ~ -18. This means that the faintest galaxies uncovered at this epoch have, on average, UV colours no more extreme than those displayed by the bluest star-forming galaxies at low redshift. At z ~ 8 we find a similar value, beta = -1.9 (+/-0.3). At z ~ 9, we find beta = -1.8 (+/-0.6), essentially unchanged from z ~ 6 - 7 (albeit highly uncertain). Finally, we show that there is as yet no evidence for a significant intrinsic scatter in beta within our new, robust z ~ 7 galaxy sample. Our results are most easily explained by a population of steadily star-forming galaxies with either ~ solar metallicity and zero dust, or moderately sub-solar (~ 10-20%) metallicity with modest dust obscuration (A_V ~ 0.1-0.2). This latter interpretation is consistent with the predictions of a state-of-the-art galaxy-formation simulation, which also suggests that a significant population of very-low metallicity, dust-free galaxies with beta ~ -2.5 may not emerge until M_UV > -16, a regime likely to remain inaccessible until the James Webb Space Telescope.
We prove upper bounds for the number of rational points on non-singular cubic curves defined over the rationals. The bounds are uniform in the curve and involve the rank of the corresponding Jacobian. The method used in the proof is a combination of the "determinant method" with an m-descent on the curve.
We generalize to arbitrary dimension the construction of a covariant and supersymmetric constraint for the massless superPoincare algebra, which was given for the eleven-dimensional case in a previous work. We also contrast it with a similar construction appropriate to the massive case. Finally we show that the constraint uniquely fixes the representation of the algebra.
We prove that if $u_1,\,u_2$ are solutions of the Benjamin-Ono equation defined in $ (x,t)\in\R \times [0,T]$ which agree in an open set $\Omega\subset \R \times [0,T]$, then $u_1\equiv u_2$. We extend this uniqueness result to a general class of equations of Benjamin-Ono type in both the initial value problem and the initial periodic boundary value problem. This class of 1-dimensional non-local models includes the intermediate long wave equation. Finally, we present a slightly stronger version of our uniqueness results for the Benjamin-Ono equation.
We present a detailed study of charged-current (CC) neutrino-nucleus reactions in a fully relativis- tic framework and comparisons with recent experiments spanning an energy range from hundreds of MeV up to 100 GeV within the SuperScaling Approach, which is based on the analysis of electron- nucleus scattering data and has been recently improved with the inclusion of Relativistic Mean Field theory effects. We also evaluate and discuss the impact of two-particle two-hole meson-exchange currents (2p-2h MEC) on neutrino-nucleus interactions through the analysis of two-particle two-hole axial and vector contributions to weak response functions in a fully relativistic Fermi gas. The results show a fairly good agreement with experimental data over the whole range of neutrino energies.
A Locally Recoverable Code is a code such that the value of any single coordinate of a codeword can be recovered from the values of a small subset of other coordinates. When we have $\delta$ non overlapping subsets of cardinality $r_i$ that can be used to recover the missing coordinate we say that a linear code $\mathcal{C}$ with length $n$, dimension $k$, minimum distance $d$ has $(r_1,\ldots, r_\delta)$-locality and denote it by $[n, k, d; r_1, r_2,\dots, r_\delta].$ In this paper we provide a new upper bound for the minimum distance of these codes. Working with a finite number of subgroups of cardinality $r_i+1$ of the automorphism group of a function field $\mathcal{F}| \mathbb{F}_q$ of genus $g \geq 1$, we propose a construction of $[n, k, d; r_1, r_2,\dots, r_\delta]$-codes and apply the results to some well known families of function fields.
Using a full spectral scan of an active region from the Extreme-Ultraviolet Imaging Spectrometer (EIS) we have obtained Emission Measure EM$(T)$ distributions in two different moss regions within the same active region. We have compared these with theoretical transition region EMs derived for three limiting cases, namely \textit{static equilibrium}, \textit{strong condensation} and \textit{strong evaporation} from \cite{ebtel}. The EM distributions in both the moss regions are strikingly similar and show a monotonically increasing trend from $\log T[\mathrm{K}]=5.15 -6.3$. Using photospheric abundances we obtain a consistent EM distribution for all ions. Comparing the observed and theoretical EM distributions, we find that the observed EM distribution is best explained by the \textit{strong condensation} case (EM$_{con}$), suggesting that a downward enthalpy flux plays an important and possibly dominant role in powering the transition region moss emission. The downflows could be due to unresolved coronal plasma that is cooling and draining after having been impulsively heated. This supports the idea that the hot loops (with temperatures of 3{-}5 MK) seen in the core of active regions are heated by nanoflares.
We consider the generation of neutrino Majorana mass and transition magnetic moment by the lepton-number violating $\lambda$ and/or $\lambda'$ couplings in R-parity-violating supersymmetric models. We update (and improve) the existing upper limits on the relevant couplings using the most recent data on neutrino masses and mixings, indicating also the possible improvement by the GENIUS project. We study the implication of this update on the induced neutrino magnetic moment.
The solution of rough differential equation, driven by the It\^o signature of a continuous local martingale, exists uniquely a.s. when the vector field is Lip(\beta) for \beta > 1, and coincides a.s. with the It\^o signature of the solution of parallel stochastic differential equation. Moreover, the It\^o solution can be recovered pathwisely by concatenating discounted Stratonovich solutions.
Two bright X-ray transients were reported from the Chandra Deep Field South archival data, namely CDF-S XT1 and XT2. Whereas the nature of the former is not identified, the latter was suggested as an excellent candidate for a rapidly spinning magnetar born from a binary neutron star (BNS) merger. Here we propose a unified model to interpret both transients within the framework of the BNS merger magnetar model. According to our picture, CDF-S XT2 is observed from the "free zone" where the magnetar spindown powered X-ray emission escapes freely, whereas CDF-S XT1 originates from the "trapped zone" where the X-ray emission is initially blocked by the dynamical ejecta and becomes transparent after the ejecta is pushed to a distance where Thomson optical depth drops below unity. We fit the magnetar model to the light curves of both transients and derived consistent parameters for the two events, with magnetic field, initial spin period and X-ray emission efficiency being ($B_p=10^{16}\,G$, $P=1.2\,\rm ms$, $\eta = 0.001$) and ($B_p=10^{15.8}\,G$, $P=4.4\, \rm ms$, $\eta = 0.001$) for XT1 and XT2, respectively. The "isotropic equivalent" ejecta mass of XT1 is $M_{\rm ej} \sim 10^{-3}$ $M_{\odot}$, while it is not constrained for XT2. Our results suggest that more extreme magnetar parameters are required to have XT1 detected from the trapped zone. The model parameters for both events are generally consistent with those derived from SGRB X-ray plateau observations. The host galaxy properties of both transients are also consistent with those of SGRBs. The event rate densities of both XT1 and XT2 are consistent with that of BNS mergers.