ShantanuT01/DACTYL-Pretraining huggingface dataset:
We investigated discrete time quantum walks with an arbitrary initial state $\mid\Psi_{0}(\theta,\phi,\varphi)\rangle=\cos\theta e^{i\phi}\mid0L\rangle+\sin\theta e^{i\varphi}\mid0R\rangle$ with a U(2) coin $U(\alpha,\beta,\gamma)$. We discover that the average position $\bar{x}=\max(\bar{x})\cos(\alpha+\gamma+\phi-\varphi)$, with coin operator $U(\alpha,\pi/4,\gamma)$ and initial state $\mid\Phi_{0}(\pi/4,\phi,\varphi)\rangle=(e^{i\phi}\mid0L\rangle+e^{i\varphi}\mid0R\rangle)\sqrt{2}/2$. If we set initial state and coin operator to $\mid\Phi_{0}\rangle(\theta,\pi/2,0)=i\cos\theta\mid0L\rangle+\sin\theta\mid0R\rangle)$ and coin operator $U(0,\pi/4,0)$, for $\alpha+\gamma+\phi-\varphi=\pi/2$, we discover that $\bar{x}=-\max(\bar{x})\cos(2\theta).$ Last we verify the result above, and obtain the summarize properties of quantum walks with an arbitrary state. We get that $\bar{x}(\theta,\phi,\varphi,\alpha,\beta,\gamma,t)=\cos2\theta*\bar{x}_{|0L\rangle}(\beta,t)+\sin2\theta*\cos(\alpha+\gamma+\phi-\varphi)*\bar{x}_{(\mid0L\rangle+\mid0R\rangle)\sqrt{2}/2}(\alpha=\gamma=0,\beta,t)$. If the average positions $\bar{x}$ with initial state $|0L\rangle$ and $\mid\Psi_{0}\rangle=(\mid0L\rangle+\mid0R\rangle)\sqrt{2}/2$ and coin operator $U(0,\beta,0)$ are known, we can get the average position result of quantum walks with an arbitrary initial state and a U(2) coin operator.
We comment on the paper by H. Yoshioka and A. Odintsov, to appear in PRL, see cond-mat/9805106.
In the framework of extended gravity theories, we discuss the meaning of a time dependent "cosmological constant" and give a set of conditions to recover asymptotic de Sitter behaviour for a class of cosmological models independently of initial data. To this purpose we introduce a time-dependent (effective) quantity which asymptotically becomes the true cosmological constant. We will deal with scalar-tensor, fourth and higher than fourth-order theories.
We simulated the million degree interstellar medium and its soft X-ray images in the disk and halo of spiral galaxies using the bipolar hypershell (BHS) model. In this model hourglass-shaped expanding shells of several kpc radii are produced by a sudden energy release in the central region. We then applied our model to a mini-sample of starburst galaxies seen under different inclinations suhc as the nearly edge-on galaxies NGC 253. Our results reproduce the X-ray characteristics observed in the 0.1--2.4 keV ROSAT energy band: The bipolar hypershell morphology, the spectral energy distribution of the diffuse disk and halo emission as well as absorption gaps in the diffuse X-ray emission caused by a shadowing of soft X-rays due to cold intervening gas in the disks of the galaxies. The required total energy for the starburst is estimated to be of the order of $10^{55}$ ergs, corresponding to the overall kinetic energy generated in $\sim 10^4$ type-II supernova explosions. The expansion velocity of the shells is estimated to be $\sim 200$ \kms, which is necessary to heat the gas to $\sim 0.2$ keV (2.3 million K), and the age to be of the order of $3 \times 10^7$ years. In the case of the very nearby galaxy NGC 253 all characteristics of the BHS model can be studied with high spatial resolution. Using the property that the shell morphology is sensitive to the ambient density distribution, we propose using soft X-ray data to probe the gas distributions in the disk, halo and intergalactic space. The application of our model to images at higher spatial and spectral resolution, as provided by Chandra and XMM, will help us to further disentangle the ISM density distributions and will lead to a better understanding of the disk halo interface.
Recently, several new correlations between the observed $\gamma$-ray and the X-ray properties of gamma-ray bursts (GRBs) were inferred from a comprehensive analysis of the X-ray light curves of more than 650 GRBs measured with the Swift X-ray telescope (Swift/XRT) during the years 2004-2010. Like previously well established correlations, they challenge GRB models. Here we show that in the cannonball (CB) model of GRBs, the newly discovered correlations and those that follow from them, have the same simple kinematic origin as those discovered earlier. They result from the strong dependence of the observed radiations on the bulk motion Lorentz and Doppler factors of the jet of highly relativistic plasmoids (CBs) that produces these radiations by interaction with the medium through which it propagates.
The HEGRA collaboration has achieved outstanding results during the operation of the six imaging atmospheric Cherenkov telescopes from 1996 to 2002. The experimental work pioneered the field of TeV gamma-ray astronomy with observations during partial moon time and mainly by applying the stereoscopic observation mode using a system of five Cherenkov telescopes.   Concerning Galactic objects the HEGRA observations have led to a precise measurement of the energy spectrum of the Crab nebula between 0.5 and 80 TeV, the detection of the first shell type supernova remnant in the Northern hemisphere (Cassiopeia A) and the investigation of the yet unidentified HEGRA TeV gamma-ray source TeV J2032+4130 in the Cygnus region. In addition, a large fraction of the Galactic plane has been studied during dedicated scans.   Following the most precise measurements of the energy spectra of the well known extragalactic objects Mkn 421 and Mkn 501, the blazars H 1426+428 and 1ES 1959+650 have just been established as sources of TeV photons in the last two years. Extensive multi-wavelength campaigns have been successfully performed and spectroscopy of these four objects gives important clues for the understanding of the nonthermal emission processes and also on the optical to infrared part of the spectrum of the extragalactic background light. Recently, strong evidence for the nearby giant radio galaxy M 87 being a TeV gamma-ray emitter has been obtained.   Some of these results are highlighted in this article.
In the Renormalised Perturbation Theory (RPT) the Anderson impurity model is interpreted in terms of renormalised parameters $\boldsymbol{\tilde{\mu}}= (\tilde{\epsilon}_d, \tilde{\Delta}, \tilde{U})$ which are in a one-to-one correspondence with the bare impurity level $\epsilon_d$, hybridisation $\Delta$ and on-site interaction $U$. Though the renormalised parameters suffice to describe the low-energy fixed point of the model, the parameters themselves usually have to be determined using the Numerical Renormalisation Group. In this paper we address this issue by applying the flow equation method to the particle-hole symmetric model to derive a system of differential equations for $ \textrm{d}\boldsymbol{\tilde{\mu}}/ \textrm{d} U$. To leading order in $\tilde{U}$ this assumes a particularly simple form, permitting its analytic solution in this approximation. We find that our results for the renormalised parameters are in good agreement with the NRG and use them to calculate the Wilson ratio, spin susceptibility and conductance of the impurity.
A delta-function method was proposed to quantitatively evaluate the electromagnetic impedance matching degree. Measured electromagnetic parameters of {\alpha}-Fe/Fe3B/Y2O3 nanocomposites are applied to calculate the matching degree by the method. Compared with reflection loss and quarter-wave principle theory, the method accurately reveals the intrinsic mechanism of microwave transmission and reflection properties. A possible honeycomb structure with promising high-performance microwave absorption according to the method is also proposed.
We study vison excitations in a quantum dimer model interpolating between the Rokhsar-Kivelson models on the square and triangular lattices. In the square-lattice case, the model is known to be critical and characterized by U(1) topological quantum numbers. Introducing diagonal dimers brings the model to a Z_2 resonating-valence-bond phase. We study variationally the emergence of vison excitations at low concentration of diagonal dimers, close to the critical point. We find that, in this regime, vison excitations are large in size and their structure resembles vortices in type-II superconductors.
In this paper we study a new ideal $\mathcal{WR}$. The main result is the following: an ideal is not weakly Ramsey if and only if it is above $\mathcal{WR}$ in the Kat\v{e}tov order. Weak Ramseyness was introduced by Laflamme in order to characterize winning strategies in a certain game. We apply result of Natkaniec and Szuca to conclude that $\mathcal{WR}$ is critical for ideal convergence of sequences of quasi-continuous functions. We study further combinatorial properties of $\mathcal{WR}$ and weak Ramseyness. Answering a question of Filip\'ow et al. we show that $\mathcal{WR}$ is not $2$-Ramsey, but every ideal on $\omega$ isomorphic to $\mathcal{WR}$ is Mon (every sequence of reals contains a monotone subsequence indexed by a $\mathcal{I}$-positive set).
Local scale invariance (LSI) has been recently proposed as a possible extension of the dynamical scaling in systems at the critical point and during phase ordering. LSI has been applied inter alia to provide predictions for the scaling properties of the response function of non-equilibrium critical systems in the aging regime following a quench from the high-temperature phase to the critical point. These predictions have been confirmed by Monte Carlo simulations and analytical results for some specific models, but they are in disagreement with field-theoretical predictions. By means of Monte Carlo simulations of the critical two- and three-dimensional Ising model with Glauber dynamics, we study the intermediate integrated response, finding deviations from the corresponding LSI predictions that are in qualitative agreement with the field-theoretical computations. This result casts some doubts on the general applicability of LSI to critical dynamics.
Maximally supersymmetric theories can be described by a single scalar superfield in light-cone superspace. When they are also (super)conformally invariant, they are uniquely specified by the form of the dynamical supersymmetry. We present an explicit derivation of the light-cone superspace form of the dynamical supersymmetry in the cases of ten- and four-dimensional super-Yang-Mills, and the three-dimensional Bagger-Lambert-Gustavsson theory, starting from the covariant formulation of these theories.
We analyse a first-order dynamical phase transition that takes place in the Fredrickson--Andersen (FA) model. We construct a two-dimensional spin system whose thermodynamic properties reproduce the dynamical large deviations of the FA model and we analyse this system numerically, comparing our results with finite-size scaling theory. This allows us to rationalise recent results for the FA model, including the exponential divergence of its susceptibility at phase coexistence. We also discuss a simple interfacial model that reproduces quantitatively the behaviour of the FA model at coexistence.
We derive the single-particle eigenenergies and eigenfunctions for massless Dirac fermions confined to the surface of a sphere in the presence of a magnetic monopole, i.e., we solve the Landau level problem for electrons in graphene on the Haldane sphere. With the single-particle eigenfunctions and eigenenergies we calculate the Haldane pseudopotentials for the Coulomb interaction in the second Landau level and calculate the effective pseudopotentials characterizing an effective Landau level mixing Hamiltonian entirely in the spherical geometry to be used in theoretical studies of the fractional quantum Hall effect in graphene. Our treatment is analogous to the formalism in the planar geometry and reduces to the planar results in the thermodynamic limit.
We study the pseudorapidity dependent hydrodynamic response in heavy-ion collisions. A differential hydrodynamic relation is obtained for elliptic flow. Using event-by-event simulations of 3+1D MUSIC, with initial conditions generated via a multi-phase transport (AMPT) model, the differential response relation is verified. Based on the response relation, we find that the two-point correlation of elliptic flow in pseudorapidity are separated into the fluid response and the two-point correlation of initial eccentricity.
Let $X$ be a projective, normal, minimal and Gorenstein $n$-dimensional complex variety of general type. Suppose $X$ is of maximal Albanese dimension. We prove that $K^n_X \ge 2 n! \chi(K_X)$
The present paper concerns the invariants of generically nef vector bundles on ruled surfaces. By Mehta - Ramanathan Restriction Theorem and by Miyaoka characterization of semistable vector bundles on a curve, the generic nefness can be considered as a weak form of semistability. We establish a Bogomolov type inequality for generically nef vector bundles with nef general fiber restriction on ruled surfaces with no negative section. This gives an affermative answer in this case to a problem posed by Th. Peternell.   Concerning ruled surfaces with a negative section, we prove a a similar result for generically nef vector bundles, with nef and balanced general fiber restriction and with a numerical condition on first Chern class, which is satisfied, for instance, if in its class there is a reduced divisor.   Finally, we use such results to bound the invariants of curve fibrations, which factorize through finite covers of ruled surfaces.
We give a detailed exposition of the "vectorized" notation for dealing with quantum operations. This notation is used to highlight the relationships between representations of completely-positive dynamics. Vectorization considerably simplifies the analysis of different methods of quantum process tomography, and enables us to derive compact representation of the investigated quantum operations in terms of the resulting data.
The redshift distribution of flat-spectrum radio sources with 5 GHz flux densities S>5 mJy is a key component in using current radio lens surveys to probe the cosmological model. We have constructed the first flat-spectrum radio sample in the flux density range 3-20 mJy. Our new sample has 33 sources; we have determined the redshifts of 14 of these (42% complete). The low mean redshift, <z>~0.75, of our faintest sample needs to be confirmed by further observations to improve the sample completeness. We also increased the redshift completeness of several surveys of brighter flat-spectrum sources. While the mean redshift, <z>~1.1 of flat-spectrum samples fainter than 1 Jy is nearly constant, the fraction of the sources identifiable as quasars steadily drops from ~80% to ~10% as the flux density of the sources decreases.
Intermediate-mass black holes (IMBHs) of mass $M_{\bullet} \approx 10^{2} - 10^{5}$ solar masses, $M_{\odot}$, are the long-sought missing link between stellar black holes, born of supernovae, and massive black holes, tied to galaxy evolution by the empirical $M_{\bullet}/\sigma_{\star}$ correlation. We show that low-mass black hole seeds that accrete stars from locally dense environments in galaxies following a universal $M_{\bullet}/\sigma_{\star}$ relation grow over the age of the Universe to be above ${\mathcal{M}}_{0}\approx3\times10^{5}M_{\odot}$ ($5\%$ lower limit), independent of the unknown seed masses and formation processes. The mass ${\mathcal{M}}_{0}$ depends weakly on the uncertain formation redshift, and sets a universal minimal mass scale for present-day black holes. This can explain why no IMBHs have yet been found, and it implies that present-day galaxies with ${\sigma_{\star}<{\mathcal{S}}_{0}\approx40\,\mathrm{km\,s}^{-1}}$ lack a central black hole, or formed it only recently. A dearth of IMBHs at low redshifts has observable implications for tidal disruptions and gravitational wave mergers.
Let ${\bf A}={\bf A}_{n,m,k}$ be a random $n\times m$ matrix over $\mathbf{GF}_2$ wher each column consists of $k$ randomly chosen ones. Let $M$ be an arbirary fixed binary matroid. We show that if $m/n$ and $k$ are sufficiently large then as $n\to\infty$ the binary matroid induced by {\bf A} contains $M$ as a minor.
Although there are many results on the global solvability and the precise description of the large time behaviors of solutions to the initial-boundary value problems of the one-dimensional viscous radiative and reactive gas in bounded domain with two typical types of boundary conditions, no result is available up to now for the corresponding problems in unbounded domain. This paper focuses on the Cauchy problem of such a system with prescribed large initial data and the main purpose is to construct its global smooth non-vacuum solutions around a non-vacuum constant equilibrium state and to study the time-asymptotically nonlinear stability of such an equilibrium state. The key point in the analysis is to deduce the uniform positive lower and upper bounds on the specific volume and the temperature.
Investigating thermal transport in van der Waals heterostructure is of scientific interest and practical importance for their applications in a broad range. In this work, thermal conductivity of one-dimensional heterostructure consisting of carbon and boron nitride nanotubes is systematically investigated via molecular dynamics simulations. Thermal conductivity is found to have strong dependences on temperature, length and diameter. In addition, the axial strain and intensity of van der Waals interaction are demonstrated to be able to modulate thermal conductivity up to about 43% and 37%, respectively. Moreover, the dependence of thermal conductivity on the chirality of componential nanotubes is studied. These results are explained based on lattice dynamics insights. This work not only provides feasible strategies to modulate thermal conductivity, but also enhances the understanding of the fundamental physics of phonon transport in one-dimensional heterostructure.
Based on a bijection between domino tilings of an Aztec diamond and non-intersecting lattice paths, a simple proof of the Aztec diamond theorem is given in terms of Hankel determinants of the large and small Schr\"oder numbers.
Paper has been withdrawn due to a critical error in the numerical evaluation of the capture fraction.
We review the observed properties of exoplanets found by the Doppler technique which has revealed 152 exoplanets to date. We focus on our ongoing 18-year survey of 1330 FGKM type stars at Lick, Keck, and the Anglo-Australian Telescopes carried out with a uniform Doppler precision of 3 m/s. The 104 planets detected in our survey have masses as low as 15 M_Earth orbiting between 0.03 and 5.5 AU. The mass distribution rises toward the lowest detectable masses as dN/dM is proportional to M^-1.1. Nearly all giant planets orbiting within 2 AU of all FGK stars within 30 pc have now been discovered. The distribution of semi-major axes rises from 0.3 -- 3.0 AU (in bins of Delta log a), but remains unknown for larger orbits. Extrapolation suggests that 12% of the FGK stars harbor exoplanets within 20 AU. The median orbital eccentricity is <e>=0.25 (excluding those tidally circularized), lower than previously measured . Planets orbiting beyond 3 AU continue to exhibit non-zero eccentricity, suggesting that the circular orbits of giant planets in our Solar System are unusual. The occurrence rate of ``hot Jupiters'' within 0.1 AU is 1.2$\pm$0.3 %. The probability of occurrence of planets varies as the square of the stellar metal abundance, $P \propto N^2_Fe, ranging from $<$3% for stars of subsolar metallicity to 25% for stars with [Fe/H] > +0.3. Nearly 14% of planet-bearing stars harbor multiple-planet systems, occasionally locked in resonances. Kepler and Corot should measure the occurrence of earth-sized planets. The Space Interferometry Mission (SIM) will detect planets with masses as low as 3 M_ Earth orbiting within 2 AU of nearby stars and will measure masses, orbits and multiplicity. These candidate rocky planets will motivate spectroscopic follow-up by the ``Terrestrial Planet Finder'' and Darwin.}
In this paper, evolution of the high energy area of universe, through the scenario of 5 dimensional (5D) universe, has been studied. For this purpose, we solve Einstein equations for 5D metric and 5D perfect fuid to derive Friedmann-like equations. Then we obtain the evolution of scale factor and energy density with respect to both space-like and time-like extra dimensions. We obtain the novel equations for the space-like extra dimension and show that the matter with zero pressure cannot exist in the bulk. Also, for dark energy fuid and vacuum fluid, we have both accelerated expansion and contraction in the bulk.
Motivated by the high-T_c cuprates, we consider a model of bosonic Cooper pairs moving on a square lattice via ring exchange. We show that this model offers a natural middle ground between a conventional antiferromagnetic Mott insulator and the fully deconfined fractionalized phase which underlies the spin-charge separation scenario for high-T_c superconductivity. We show that such ring models sustain a stable critical phase in two dimensions, the *Bose metal*. The Bose metal is a compressible state, with gapless but uncondensed boson and ``vortex'' excitations, power-law superconducting and charge-ordering correlations, and broad spectral functions. We characterize the Bose metal with the aid of an exact plaquette duality transformation, which motivates a universal low energy description of the Bose metal. This description is in terms of a pair of dual bosonic phase fields, and is a direct analog of the well-known one-dimensional bosonization approach. We verify the validity of the low energy description by numerical simulations of the ring model in its exact dual form. The relevance to the high-T_c superconductors and a variety of extensions to other systems are discussed, including the bosonization of a two dimensional fermionic ring model.
We present measurements of galaxy clustering from the Baryon Oscillation Spectroscopic Survey (BOSS), which is part of the Sloan Digital Sky Survey III (SDSS-III). These use the Data Release 9 (DR9) CMASS sample, which contains 264,283 massive galaxies covering 3275 square degrees with an effective redshift z=0.57 and redshift range 0.43 < z < 0.7. Assuming a concordance Lambda-CDM cosmological model, this sample covers an effective volume of 2.2 Gpc^3, and represents the largest sample of the Universe ever surveyed at this density, n = 3 x 10^-4 h^-3 Mpc^3. We measure the angle-averaged galaxy correlation function and power spectrum, including density-field reconstruction of the baryon acoustic oscillation (BAO) feature. The acoustic features are detected at a significance of 5\sigma in both the correlation function and power spectrum. Combining with the SDSS-II Luminous Red Galaxy Sample, the detection significance increases to 6.7\sigma. Fitting for the position of the acoustic features measures the distance to z=0.57 relative to the sound horizon DV /rs = 13.67 +/- 0.22 at z=0.57. Assuming a fiducial sound horizon of 153.19 Mpc, which matches cosmic microwave background constraints, this corresponds to a distance DV(z=0.57) = 2094 +/- 34 Mpc. At 1.7 per cent, this is the most precise distance constraint ever obtained from a galaxy survey. We place this result alongside previous BAO measurements in a cosmological distance ladder and find excellent agreement with the current supernova measurements. We use these distance measurements to constrain various cosmological models, finding continuing support for a flat Universe with a cosmological constant.
The main goal of a beta-beam facility is to determine the possible existence of CP violation in the lepton sector, the value of the third neutrino mixing angle and the mass hierarchy. Here we argue that a much broader physics case can be covered since the beta-beam concept can also be used to establish a low energy beta-beam facility. We discuss that the availability of neutrino beams in the 100 MeV energy range offers a unique opportunity to perform neutrino scattering experiments of interest for nuclear physics, for the study of fundamental interactions and of core-collapse supernova physics.