ShantanuT01/DACTYL-Pretraining huggingface dataset:
Considering lattice Hamiltonians designed using conformal field theory to have fractional quantum Hall states as ground states, we study the dynamics of one or two particles on such lattices. Examining the eigenspectrum and dynamics of the single-particle sector, we demonstrate that these Hamiltonians cannot be regarded as describing interacting particles placed on a Chern band, so that the physics is fundamentally different from fractional Chern insulators. The single-particle spectrum is shown to consist of eigenstates localized in shells which have larger radius for larger eigenenergies. This leads to chiral dynamics along reasonably well-defined orbits, both in the single-particle and in the two-particle sectors.
We extend the Fock-Tani formalism to include the meson-baryon interaction. The Fock-Tani formalism is a first principle method which allows the use of field theoretic methods for treating systems of composite particles. An application of this general result can be the $K^{+}N$ system which is now reconized as much more suitable system for the investigation of the short range nature of the hadronic repulsion.
Weak supersolutions to the porous medium equation are defined by means of smooth test functions under an integral sign. We show that nonnegative weak supersolutions become lower semicontinuous after redefinition on a set of measure zero. This shows that weak supersolutions belong to a class of supersolutions defined by a comparison principle.
In this paper we formulate a conjecture on the relationship between the equivariant \epsilon-constants (associated to a local p-adic representation V and a finite extension of local fields L/K) and local Galois cohomology groups of a Galois stable \mathbb{Z}_{p}-lattice T of V. We prove the conjecture for L/K being an unramified extension of degree prime to p and T being a p-adic Tate module of a one-dimensional Lubin-Tate group defined over \mathbb{Z}_{p} by extending the ideas of \cite{Breu} from the case of the multiplicative group \mathbb{G}_{m} to arbitrary one-dimensional Lubin-Tate groups. For the connection to the different formulations of the \epsilon-conjecture in \cite{BB}, \cite{FK}, \cite{Breu}, \cite{BlB} and \cite{BF} see \cite{Iz}.
Some important VLSI adder circuits are implemented using quantum dots (qd) and Spin Polarized Scanning Tunneling Microscopy (SPSTM) in Single Spin Logic (SSL) paradigm. A simple comparison between these adder circuits shows that the mirror adder implementation in SSL does not carry any advantage over CMOS adder in terms of complexity and number of qds, opposite to the trend observed in their charge-based counterparts. On the contrary, the transmission gate adder, Static and Dynamic Manchester carry gate adders in SSL reduce the complexity and number of qds, in harmony with the trend shown in transistor adders.
The question "How did we get here and what will the future bring?" captures the human imagination and the attention of the National Academy of Science's Astronomy and Astrophysics Survey Commitee (AASC). Fulfillment of this "fundamental goal" requires astronomers to have sensitive, high angular and spectral resolution observations in the far-infrared/submillimeter (far-IR/sub-mm) spectral region. With half the luminosity of the universe and vital information about galaxy, star and planet formation, observations in this spectral region require capabilities similar to those currently available or planned at shorter wavelengths. In this paper we summarize the scientific motivation, some mission concepts and technology requirements for far-IR/sub-mm space interferometers that can be developed in the 2010-2020 timeframe.
For a large class of processes with an absorbing state, statistical properties of the surviving sample attain time-independent values in the quasi-stationary (QS) regime. We propose a practical simulation method for studying quasi-stationary properties, based on the equation of motion governing the QS distribution. The method is tested in applications to the contact process. At the critical point, our method is about an order of magnitude more efficient than conventional simulation.
Quasars (QSOs) are extremely luminous active galatic nuclei currently observed up to redshift $z=7.642$. As such, they have the potential to be the next rung of the cosmic distance ladder beyond SNe Ia, if they can reliably be used as cosmological probes. The main issue in adopting QSOs as standard candles (similarly to Gamma-Ray Bursts) is the large intrinsic scatter in the relations between their observed properties. This could be overcome by finding correlations among their observables that are intrinsic to the physics of QSOs and not artifacts of selection biases and/or redshift evolution. The reliability of these correlations should be verified through well-established statistical tests. The correlation between the ultraviolet (UV) and X-ray fluxes developed by Risaliti \& Lusso is one of the most promising relations. We apply a statistical method to correct this relation for redshift evolution and selection biases. \textbf{Remarkably, we recover the the same parameters of the slope and the normalization as Risaliti \& Lusso. Our results establish the reliability of this relation, which is intrinsic to the QSO properties and not merely an effect of selection biases or redshift evolution. Hence,} the possibility to standardize QSOs as cosmological candles, thereby extending the Hubble diagram up to $z=7.54$.
The optical integrated spectra of three LMC young stellar clusters (NGC 1984, NGC 1994 and NGC 2011) exhibit concave continua and prominent molecular bands which deviate significantly from the predictions of single stellar population (SSP) models. In order to understand the appearance of these spectra, we create a set of young stellar population (MILES) models, which we make available to the community. We use archival International Ultraviolet Explorer integrated UV spectra to independently constrain the cluster masses and extinction, and rule out strong stochastic effects in the optical spectra. In addition, we also analyze deep colour-magnitude diagrams of the clusters to provide independent age determinations based on isochrone fitting. We explore hypotheses including age-spreads in the clusters, a top-heavy initial mass function, different SSP models and the role of red supergiant stars (RSG). We find that the strong molecular features in the optical spectra can only be reproduced by modeling an increased fraction of about 20 per cent by luminosity of RSG above what is predicted by canonical stellar evolution models. Given the uncertainties in stellar evolution at Myr ages, we cannot presently rule-out the presence of Myr age-spreads in these clusters. Our work combines different wavelengths as well as different approaches (resolved data as well as integrated spectra for the same sample) in order to reveal the complete picture. We show that each approach provides important information but in combination can we better understand the cluster stellar populations.
We report the detection of high-amplitude X-ray flaring of the AGN HE 1136-2304, which is accompanied by a strong increase in the flux of the broad Balmer lines, changing its Seyfert type from almost type 2 in 1993 down to 1.5 in 2014. HE 1136-2304 was detected by the XMM-Newton slew survey at >10 times the flux it had in the ROSAT all-sky survey, and confirmed with Swift follow-up after increasing in X-ray flux by a factor of 30. Optical spectroscopy with SALT shows that the AGN has changed from a Seyfert 1.95 to a Seyfert 1.5 galaxy, with greatly increased broad line emission and an increase in blue continuum AGN flux by a factor of > 4. The X-ray spectra from XMM-Newton and NuSTAR reveal moderate intrinsic absorption and a high energy cutoff at 100 keV. We consider several different physical scenarios for a flare, such as changes in obscuring material, tidal disruption events, and an increase in the accretion rate. We find that the most likely cause of the increased flux is an increase in the accretion rate, although it could also be due to a change in obscuration.
The present effort explores the influence of a longitudinal applied electric field on the magnetocaloric properties of graphenes. The magnetic entropy change $\Delta S(T,\Delta B,E)$ has two contributions: $S_{cos}(T,B,E)$ with an oscillating character on $m$, inversely proportional to the magnetic field; and $S_{per}(T,B,E)$ with a periodic character also on $m$. In comparison to the case without electric field, the maximum value of the magnetic entropy change either increases or decreases due to an applied electric field, depending on the value of $m$; and, in addition, the temperature in which the maximum entropy change occurs decreases due to the electric field.
Proposed space-based gravitational-wave detectors such as BBO and DECIGO can detect ~10^6 neutron-star binaries and determine luminosity distance to the binaries with a high precision. Combining the luminosity distance and electromagnetically-derived redshift, one would be able to probe cosmological expansion out to high redshift. In this paper, we show that the Hubble parameter as a function of redshift can be directly measured with monopole and dipole components of the luminosity distance on the sky. As a result, the measurement accuracies of the Hubble parameter in each redshift bin up to z=1 are 3-14 %, 1.5-8 %, and 0.8-4% for the observation time 1 yr, 3 yr, and 10 yr, respectively.
We study correlations betwen X-ray spectral index, strength of Compton reflection, and X-ray and radio fluxes in accreting black holes (Seyferts and black-hole binaries). We critically evaluate the evidence for the correlation of the X-ray spectral index with the strength of Compton reflection and consider in detail statistical and systematic effects that can affect it. We study patterns of spectral variability (in particular, pivoting of a power law spectrum) corresponding to the X-ray index-flux correlation. We also consider implications of the form of observed X-ray spectra and their variability for interpretation of the correlation between the radio and X-ray fluxes. Finally, we discuss accretion geometries that can account for the correlations and their overall theoretical interpretations.
Adaptive randomly reinforced urn (ARRU) is a two-color urn model where the updating process is defined by a sequence of non-negative random vectors $\{(D_{1,n}, D_{2,n});n\geq1\}$ and randomly evolving thresholds which utilize accruing statistical information for the updates. Let $m_1=E[D_{1,n}]$ and $m_2=E[D_{2,n}]$. Motivated by applications, in this paper we undertake a detailed study of the dynamics of the ARRU model. First, for the case $m_1 \neq m_2$, we establish $L_1$ bounds on the increments of the urn proportion at fixed and increasing times under very weak assumptions on the random threshold sequence. As a consequence, we deduce weak consistency of the evolving urn proportions. Second, under slightly stronger conditions, we establish the strong consistency of the urn proportions for all finite values of $m_1$ and $m_2$. Specifically, we show that when $m_1=m_2$ the proportion converges to a non-degenerate random variable. Third, we establish the asymptotic distribution, after appropriate centering and scaling, of the proportion of sampled balls in the case $m_1=m_2$. In the process, we settle the issue of asymptotic distribution of the number of sampled balls for a randomly reinforced urn (RRU). To address the technical issues, we establish results on the harmonic moments of the total number of balls in the urn at different times under very weak conditions, which is of independent interest.
The ill-posedness of Calder\'on's inverse conductivity problem, responsible for the poor spatial resolution of Electrical Impedance Tomography (EIT), has been an impetus for the development of hybrid imaging techniques, which compensate for this lack of resolution by coupling with a second type of physical wave, typically modeled by a hyperbolic PDE. Here we show how, using EIT data alone, to efficiently detect interior jumps and other singularities of the conductivity. Analysis of the complex geometrical optics solutions of Astala and P\"aiv\"arinta [\emph{Ann. Math.}, {\bf 163} (2006)] in 2D makes it possible to exploit an underlying complex principal type structure of the problem. We show that the leading term in a Neumann series is an invertible nonlinear generalized Radon transform of the conductivity. The wave front set of all higher-order terms can be characterized, and, under a prior, some are smoother than the leading term. Numerics indicate that this approach effectively detects inclusions within inclusions via EIT.
We report the results of AstroSat observations of Cygnus X-2 during February 2016. The source's power density spectrum generated using LAXPC data revealed the presence of a prominent Quasi-periodic Oscillation (QPO) at $\sim42$ Hz with broadband continuum noise at lower frequencies at $\sim10$ Hz. The large effective area of LAXPC at $\gtrsim$30 keV allowed for an unprecedented study of the energy dependence of the QPO and the broad noise continuum. The fractional r.m.s increases with energy, and its shape is similar for both the QPO and the continuum noise, suggesting a common radiative origin. However, while the QPO exhibits hard time lags, with the high energy photons lagging the low ones by a few milliseconds, the continuum noise shows the opposite behavior. The photon spectrum from SXT and LAXPC in $0.7-30$ keV band comprises the soft component from a disc and a hard Comptonized component from a hot corona. While the energy dependence of the r.m.s shows that the QPO and the continuum noise variability are dominated by the Comptonized component, the change in sign of the time-lag suggests that the dynamic origin of the QPO may be in the disk while the noise continuum may originate from the corona.
Using \Planck\ data combined with the Meta Catalogue of X-ray detected Clusters of galaxies (MCXC), we address the study of peculiar motions by searching for evidence of the kinetic Sunyaev-Zeldovich effect (kSZ). By implementing various filters designed to extract the kSZ generated at the positions of the clusters, we obtain consistent constraints on the radial peculiar velocity average, root mean square (rms), and local bulk flow amplitude at different depths. For the whole cluster sample of average redshift 0.18, the measured average radial peculiar velocity with respect to the cosmic microwave background (CMB) radiation at that redshift, i.e., the kSZ monopole, amounts to $72 \pm 60$ km s$^{-1}$. This constitutes less than 1% of the relative Hubble velocity of the cluster sample with respect to our local CMB frame. While the linear $\Lambda$CDM prediction for the typical cluster radial velocity rms at $z=0.15$ is close to 230km s$^{-1}$, the upper limit imposed by \Planck\ data on the cluster subsample corresponds to 800 km s$^{-1}$ at 95% confidence level, i.e., about three times higher. \Planck\ data also set strong constraints on the local bulk flow in volumes centred on the Local Group. There is no detection of bulk flow as measured in any comoving sphere extending to the maximum redshift covered by the cluster sample. A blind search for bulk flows in this sample has an upper limit of 254 km s$^{-1}$ (95% confidence level) dominated by CMB confusion and instrumental noise, indicating that the Universe is largely homogeneous on Gpc scales. In this context, in conjunction with supernova observations, \Planck\ is able to rule out a large class of inhomogeneous void models as alternatives to dark energy or modified gravity. The \Planck\ constraints on peculiar velocities and bulk flows are thus consistent with the $\Lambda$CDM scenario.
We propose and analyze a new metric that has two conformal factors a(t) and b(t) that combine the expansion of the universe and its effects on the spatial and temporal part of the Schwarzschild metric in isotropic coordinates. We present the solutions, their descriptions and we comment on their shortcomings. In the spatially flat case of an expanding universe, we derive from the proposed metric the special solutions of the field equations for the dust approximation and the McVittie metric. We show that the presence of a black hole does not modify the a(t) proportional to t^{2/3} law for dust and H=constant for dark energy.
We have observed the IC1396W globule in a narrow band filter centred on the 1-0 S(1) line of molecular hydrogen and in the J, H, K' broad-band filters. Three molecular hydrogen outflows could be identified by means of H2 emission. The projected axes of the flows are parallel to each other. By means of the NIR images and IRAS/ISOPHOT data we could identify the driving sources of all outflows, the possible Class0 source IRAS21246+5743 and two red objects (Class1/2). NIR photometry reveals an embedded cluster of young stars in the globule, coinciding with FIR emission. Other young stars in the field are more or less clustered in several small groups, an indication that star formation takes place at different positions at the same time in such small globules.
Consider a measurable space with an atomless finite vector measure. This measure defines a mapping of the $\sigma$-field into an Euclidean space. According to the Lyapunov convexity theorem, the range of this mapping is a convex compactum. Similar ranges are also defined for measurable subsets of the space. Two subsets with the same vector measure may have different ranges. We investigate the question whether, among all the subsets having the same given vector measure, there always exists a set with the maximal range of the vector measure. The answer to this question is positive for two-dimensional vector measures and negative for higher dimensions. We use the existence of maximal ranges to strengthen the Dvoretzky-Wald-Wolfowitz purification theorem for the case of two measures.
This expository paper is based on the author's series of lectures delivered at the January 1999 Mini-course in Number Theory, held at Sogang University (Seoul). The aim is to give an elementary and self-contained introduction to the theory of Newton polygons (namely, the $p$-adic Riemann hypothesis) for L-functions of exponential sums over a finite field.   The main idea of our approach is to establish a suitable local to global principal which would allowus to reduce the harder ``global'' case to various easier well understood "local" cases for which Stickelberger's theorem applies. For this purpose, a systematic decomposition method was introduced in our earlier paper and several decomposition theorems were proved, including the facial decomposition theorem, the star decomposition theorem and the hyperplane decomposition theorem. These theorems easily recover previously known results on Newton polygons of exponential sums. They are also enough for a number of further applications such as Mazur's conjecture for a generic hypersurface and a weaker form of the more general Adolphson-Sperber conjecture for a generic exponential sum. Using our earlier method, we have recently found a more flexible collapsing decomposition theorem. This theorem gives a fairly satisfactory answer to the full form of the Adolphson-Sperber conjecture. In particular, as an application, we now know that the full form of the Adolphson-Sperber conjecture is true in every low dimension $n\leq 3$ but false in every high dimension $n\geq 4$. These results are explained in these notes.
We are concerned with the asymptotic behaviour of classical solutions of systems of the form u_t = Au_xx + f(u, u_x), x in R, t>0, u(x,t) a vector in RN, with u(x,0)= U(x), where A is a positive-definite diagonal matrix and f is a 'bistable' nonlinearity satisfying conditions which guarantee the existence of a comparison principle. Suppose that there is a travelling-front solution w with velocity c, that connects two stable equilibria of f. We show that if U is bounded, uniformly continuously differentiable and such that w(x) - U(x) is small when the modulus of x is large, then there exists y in R such that u(., t) converges to w(.+y-ct) in the C1 norm at an exponential rate as t tends to infinity. Our approach extends an idea developed by Roquejoffre, Terman and Volpert in the convectionless case, where f is independent of u_x.
We introduce Gaussian Matrix Product States (GMPS), a generalization of Matrix Product States (MPS) to lattices of harmonic oscillators. Our definition resembles the interpretation of MPS in terms of projected maximally entangled pairs, starting from which we derive several properties of GMPS, often in close analogy to the finite dimensional case: We show how to approximate arbitrary Gaussian states by MPS, we discuss how the entanglement in the bonds can be bounded, we demonstrate how the correlation functions can be computed from the GMPS representation, and that they decay exponentially in one dimension, and finally relate GMPS and ground states of local Hamiltonians.
We present a new perturbative expansion for pionless effective field theory with Coulomb interactions in which at leading order the spin-singlet nucleon-nucleon channels are taken in the unitarity limit. Presenting results up to next-to-leading order for the Phillips line and the neutron-deuteron doublet-channel phase shift, we find that a perturbative expansion in the inverse 1S0 scattering lengths converges rapidly. Using a new systematic treatment of the proton-proton sector that isolates the divergence due to one-photon exchange, we renormalize the corresponding contribution to the 3H-3He binding energy splitting and demonstrate that the Coulomb force in pionless EFT is a completely perturbative effect in the trinucleon bound-state regime. In our new expansion, the leading order is exactly isospin-symmetric. At next-to-leading order, we include isospin breaking via the Coulomb force and two-body scattering lengths, and find for the energy splitting (E_B(3He)-E_B(3H))^NLO = (-0.86 +/- 0.17) MeV.
In this paper we generalize the binary coding procedure of perfect matchings from catacondensed benzenoid graphs to catacondensed even ring systems (also called cers). Next, we study cers with isomorphic resonance graphs. For this purpose, we define resonantly equivalent cers. Finally, we investigate cers whose resonance graphs are isomorphic to the resonance graphs of catacondensed benzenoid graphs. As a consequence we show that for each phenylene there exists a catacondensed benzenoid graph such that their resonance graphs are isomorphic.
We introduce the notion of ortho-symplectic super triple system, and apply it to find solutions of super Yang-Baxter equation. Also, the para-statistics are formulated as a Lie-super triple system.
The relationship between $l$-dependence and undularity of the optical model potential (OMP) is studied for the case of the elastic scattering of 33 MeV \nuc{3}{He} on $^{58}$Ni. The relationship that emerges follows the general features of the same relationship found for the proton OMP presented in arXiv:1705.07003. The general background is also presented in that reference.