ShantanuT01/DACTYL-Pretraining huggingface dataset:
The paper is devoted to fundamental problems of the Wheeler - DeWitt quantum geometrodynamics, which was the first attempt to apply quantum principles to the Universe as a whole. Our purpose is to find out the origin of these problems and follow up their consequences. We start from Dirac generalized Hamiltonian dynamics as a cornerstone on which the Wheeler - DeWitt theory is based. We remind the main statements of the famous DeWitt's paper of 1967 and discuss the flaws of the theory: the well-known problem of time, the problem of Hilbert space and others. In the concluding part of the paper we consider new tendencies and approaches to quantum geometrodynamics appeared in the last decade.
Throughout this paper we study the existence of irreducible curves C on smooth projective surfaces S with singular points of prescribed topological types S_1,...,S_r. There are necessary conditions for the existence of the type \sum_{i=1}^r \mu(S_i) < aC^2+bC.K+c+1 for some fixed divisor K on S and suitable coefficients a, b and c, and the main sufficient condition that we find is of the same type, saying it is asymptotically optimal. Even for the case where S is the projective plane, ten years ago general results of this quality have not been known.   An important ingredient for the proof is a vanishing theorem for invertible sheaves on the blown up S of the form O_{S'}(\pi^*D-\sum_{i=1}^r m_iE_i), deduced from the Kawamata-Vieweg Vanishing Theorem. Its proof covers the first part of the paper, while the middle part is devoted to the existence theorems. In the last part we investigate our conditions on ruled surfaces, products of elliptic curves, surfaces in projective 3-space, and K3-surfaces.
Sources of high frequency gravitational waves are reviewed. Gravitational collapse, rotational instabilities and oscillations of the remnant compact objects are potentially important sources of gravitational waves. Significant and unique information for the various stages of the collapse, the evolution of protoneutron stars and the details of the equations of state of such objects can be drawn from careful study of the gravitational wave signal.
We develop a collection of numerical algorithms which connect ideas from polyhedral geometry and algebraic geometry. The first algorithm we develop functions as a numerical oracle for the Newton polytope of a hypersurface and is based on ideas of Hauenstein and Sottile. Additionally, we construct a numerical tropical membership algorithm which uses the former algorithm as a subroutine. Based on recent results of Esterov, we give an algorithm which recursively solves a sparse polynomial system when the support of that system is either lacunary or triangular. Prior to explaining these results, we give necessary background on polytopes, algebraic geometry, monodromy groups of branched covers, and numerical algebraic geometry.
The manipulation of quantum "resources" such as entanglement, coherence and magic states lies at the heart of quantum science and technology, empowering potential advantages over classical methods. In practice, a particularly important kind of manipulation is to "purify" the quantum resources, since they are inevitably contaminated by noise and thus often lose their power or become unreliable for direct usage. Here we prove fundamental limitations on how effectively generic noisy resources can be purified enforced by the laws of quantum mechanics, which universally apply to any reasonable kind of quantum resource. More explicitly, we derive nontrivial lower bounds on the error of converting any full-rank noisy state to any target pure resource state by any free protocol (including probabilistic ones)---it is impossible to achieve perfect resource purification, even probabilistically. Our theorems indicate strong limits on the efficiency of distillation, a widely used type of resource purification routine that underpins many key applications of quantum information science. In particular, this general result induces the first explicit lower bounds on the resource cost of magic state distillation, a leading scheme for realizing scalable fault-tolerant quantum computation. Implications for the standard error-correction-based methods are specifically discussed.
A (global) determinantal representation of hypersurface in P^n is a matrix, whose entries are linear forms in homogeneous coordinates and whose determinant defines the hypersurface.   We study the properties of such representations for singular (possibly reducible or non-reduced) hypersurfaces. In particular, we obtain the decomposability criteria for determinantal representations of globally reducible hypersurfaces.   Further, we classify the determinantal representations in terms of the corresponding kernel sheaves on $X$. Finally, we extend the results to the case of symmetric/self-adjoint representations, with implications to hyperbolic polynomials and generalized Lax conjecture.
A curve C in the projective plane is called non-negative if the self-intersection number of C after the minimal resolution of singularities of C is non-negative. Given a unicuspidal rational plane curve C with singular point P, we study the unique pencil Lambda_C on the projective plane satisfying C is in Lambda_C and P is its unique base point. We show that the general member of Lambda_C is a rational curve if and only if the curve C is non-negative. We also show that in such a case then Lambda_C has a dicritical of degree 1. Note that all currently known unicuspidal rational curves C in the projective plane are non-negative.
We present an ab initio relativistic k.p theory of the effect of magnetic exchange field on the band structure in the gap region of bulk crystals and thin films of three-dimensional layered topological insulators. For the field perpendicular to the layers (along $z$), we reveal novel unconventional scenarios of the response of the band-gap edges to the magnetization. The modification of the valence and conduction states is considered in terms of their $\Gamma$-point spin $s^z$ and total angular momentum $J^z$ on the atomic sites where the states are localized. The actual scenario depends on whether $s^z$ and $J^z$ have the same or opposite sign. In particular, the opposite sign for the valence state and the same sign for the conduction state give rise to an unconventional response in Bi$_2$Te$_3$ -- both in the bulk crystal and in ultra-thin films, which fundamentally distinguishes this topological insulator from Bi$_2$Se$_3$, where both states have the same sign. To gain a deeper insight into different scenarios in insulators with both inverted and non-inverted zero-field band structure, a minimal four-band third-order k.p model is constructed from first principles. Within this model, we analyze the field-induced band structure of the insulators and identify Weyl nodes that appear in a magnetic phase and behave differently depending on the scenario. We characterize the topology of the modified band structure by the Chern number $\mathcal{C}$ and find the unconventional response to be accompanied by a large Chern number $\mathcal{C}=\pm3$.
We investigated multilayer plates made by exfoliation from a high-quality MoS$_2$ crystal and reveal that they represent a new object - van der Waals homostructure consisting of a bulk core and a few detached monolayers on its surface. This architecture comprising elements with different electron band structure leads to specific luminescence, when the broad emission band from the core is cut by the absorption peaks of strong exciton resonances in the surface monolayers. The exfoliated flakes exhibit strong optical anisotropy. We have observed a conversion of normally incident light polarization to $15\%$ in transmission geometry. This background effect is due to fluctuations of the c axis relative to the normal, whereas the pronounced resonance contribution is explained by the polarization anisotropy of excitons localized in the stripes of dissected surface monolayers.
The SuperNova / Acceleration Probe (SNAP) is a space-based experiment to measure the expansion history of the Universe and study both its dark energy and the dark matter. The experiment is motivated by the startling discovery that the expansion of the Universe is accelerating. A 0.7 square-degree imager comprised of 36 large format fully-depleted n-type CCD's sharing a focal plane with 36 HgCdTe detectors forms the heart of SNAP, allowing discovery and lightcurve measurements simultaneously for many supernovae. The imager and a high-efficiency low-resolution integral field spectrograph are coupled to a 2-m three mirror anastigmat wide-field telescope, which will be placed in a high-earth orbit. The SNAP mission can obtain high-signal-to-noise calibrated light-curves and spectra for over 2000 Type Ia supernovae at redshifts between z=0.1 and 1.7. The resulting data set can not only determine the amount of dark energy with high precision, but test the nature of the dark energy by examining its equation of state. In particular, dark energy due to a cosmological constant can be differentiated from alternatives such as "quintessence", by measuring the dark energy's equation of state to an accuracy of +/-0.05, and by studying its time dependence.
The details of the stellar mass assembly of brightest cluster galaxies (BCGs) remain an unresolved problem in galaxy formation. We have developed a novel approach that allows us to construct a sample of clusters that form an evolutionary sequence, and have applied it to the Spitzer IRAC Shallow Cluster Survey (ISCS) to examine the evolution of BCGs in progenitors of present-day clusters with mass of (2.5-4.5)x10^{14}Msun. We follow the cluster mass growth history extracted from a high resolution cosmological simulation, and then use an empirical method that infers the cluster mass based on the ranking of cluster luminosity to select high-z clusters of appropriate mass from ISCS to be progenitors of the given set of z=0 clusters. We find that, between z=1.5 and 0.5, the BCGs have grown in stellar mass by a factor of 2.3, which is well-matched by the predictions from a state-of-the-art semi-analytic model. Below z=0.5 we see hints of differences in behavior between the model and observation.
The Leggett-Garg inequality attempts to classify experimental outcomes as arising from one of two possible classes of physical theories: those described by macrorealism (which obey our intuition about how the macroscopic classical world behaves), and those that are not (e.g., quantum theory). The development of cloud-based quantum computing devices enables us to explore the limits of macrorealism in new regimes. In particular, here we take advantage of the properties of the programmable nature of the IBM quantum experience to observe the violation of the Leggett-Garg inequality (in the form of a ``quantum witness") as a function of the number of constituent systems (qubits), while simultaneously maximizing the `disconnectivity', a potential measure of macroscopicity, between constituents. Our results show that two-qubit and four-qubit ``cat states" (which have large disconnectivity) are seen to violate the inequality, and hence can be classified as nonmacrorealistic. In contrast, a six-qubit cat state does not violate the ``quantum-witness" beyond a so-called clumsy invasive-measurement bound, and thus is compatible with ``clumsy macrorealism". As a comparison, we also consider un-entangled product states with n = 2, 3, 4, and 6 qubits, in which the disconnectivity is low.
We present the discovery of only the second radio-selected, z ~ 6 quasar. We identified SDSS J222843.54+011032.2 (z=5.95) by matching the optical detections of the deep Sloan Digital Sky Survey (SDSS) Stripe 82 with their radio counterparts in the Stripe82 VLA Survey. We also matched the Canadian-France-Hawaiian Telescope Legacy Survey Wide (CFHTLS Wide) with the Faint Images of the Radio Sky at Twenty-cm (FIRST) survey but have yet to find any z ~ 6 quasars in this survey area. The discovered quasar is optically-faint, z = 22.3 and M_{1450} ~ -24.5, but radio-bright, with a flux density of f$_{1.4GHz, peak}$ = 0.31mJy and a radio-loudness of R ~ 1100 (where R = f_{5GHz}/f_{2500}). The i-z color of the discovered quasar places it outside the color selection criteria for existing optical surveys. We conclude by discussing the need for deeper wide-area radio surveys in the context of high-redshift quasars.
We consider the Cauchy problem for second order differential operators with two independent variables $P=D_t^2-D_x(b(t)a(x))D_x$. Assume that $b(t)$ is a nonnegative $C^{n,alpha}$ function and $a(x)$ is a nonnegative Gevrey function of order $s>1$ we prove that the Cauchy problem for $P$ is well-posed in the Gevrey class of any order $s<s'<1+(n+alpha)/2$.
We construct a new mesoscopic model for granular media using Dynamical Density Functional Theory (DDFT). The model includes both a collision operator to incorporate inelasticity and the Helmholtz free energy functional to account for external potentials, interparticle interactions and volume exclusion. We use statistical data from event-driven microscopic simulations to determine the parameters not given analytically by the closure relations used to derive the DDFT. We numerically demonstrate the crucial effects of each term in the DDFT, and the importance of including an accurately parametrised pair correlation function.
We study the approximation of $\mathbb{E}f(X_T)$ by a Monte Carlo algorithm, where $X$ is the solution of a stochastic differential equation and $f$ is a given function. We introduce a new variance reduction method, which can be viewed as a statistical analogue of Romberg extrapolation method. Namely, we use two Euler schemes with steps $\delta$ and $\delta^{\beta},0<\beta<1$. This leads to an algorithm which, for a given level of the statistical error, has a complexity significantly lower than the complexity of the standard Monte Carlo method. We analyze the asymptotic error of this algorithm in the context of general (possibly degenerate) diffusions. In order to find the optimal $\beta$ (which turns out to be $\beta=1/2$), we establish a central limit type theorem, based on a result of Jacod and Protter for the asymptotic distribution of the error in the Euler scheme. We test our method on various examples. In particular, we adapt it to Asian options. In this setting, we have a CLT and, as a by-product, an explicit expansion of the discretization error.
We study the asymptotic behaviour of a real-valued diffusion whose non-regular drift is given as a sum of a dissipative term and a bounded measurable one. We prove that two trajectories of that diffusion converge a.s. to one another at an exponential explicit rate as soon as the dissipative coefficient is large enough. A similar result in $L_p$ is obtained.
A conjecture of Pukhlikov states that a smooth Fano variety of dimension at least four and index one is birationally rigid. We show that a general member of the linear system given by the ample generator of the Picard group of the moduli space of stable, rank two bundles with fixed determinant of odd degree on a curve of genus at least three, is not birationally rigid.
Dark soliton states of Bose-Einstein condensates in harmonic traps are studied both analytically and computationally by the direct solution of the Gross-Pitaevskii equation in three dimensions. The ground and self-consistent excited states are found numerically by relaxation in imaginary time. The energy of a stationary soliton in a harmonic trap is shown to be independent of density and geometry for large numbers of atoms. Large amplitude field modulation at a frequency resonant with the energy of a dark soliton is found to give rise to a state with multiple vortices. The Bogoliubov excitation spectrum of the soliton state contains complex frequencies, which disappear for sufficiently small numbers of atoms or large transverse confinement. The relationship between these complex modes and the snake instability is investigated numerically by propagation in real time.
Heterostructures and crystal interfaces play a major role in state-of-the-art semiconductor devices and play a central role in the field of oxide electronics. In oxides the link between the microscopic properties of the interfaces and bulk properties of the resulting heterostructures challenge our fundamental understanding. Insights on the early growth stage of interfaces and its influence on resulting physical properties are scarce -- typically the information is inferred from post growth characterization. Here, we report on real time measurements of the transport properties of SrTiO3-based heterostructures while the crystal heterostructure is forming. Surprisingly, we detect a conducting interface already at the initial growth stage, much earlier than the well-established critical thickness limit for observing conductivity ex-situ after sample growth. We investigate how the conductivity depends on various physical processes occurring during pulsed laser depositions, including light illumination, particle bombardment by the plasma plume, interactions with the atmosphere and oxygen migration from SrTiO3 to the thin films of varying compositions. Using this approach, we propose a new design tool to control the electrical properties of interfaces in real time during their formation.
We introduce a periodic two-dimensional $\mu$-$b$-equation and a periodic two-dimensional two-component $(\mu)$-Camassa-Holm equation which we study as geodesic flows on the diffeomorphism group of the torus and a semidirect product respectively. The paper explains the derivation of these equations within V.I. Arnold's (1966) general framework, some analogies to recently discussed related equations and gives a self-contained presentation of the geometric aspects. As an application, we obtain well-posedness results and some explicit curvature computations.
Structured illumination microscopy (SIM) is a very important super-resolution microscopy technique, which provides high speed super-resolution with about two-fold spatial resolution enhancement. Several attempts aimed at improving the performance of SIM reconstruction algorithm have been reported. However, most of these highlight only one specific aspect of the SIM reconstruction -- such as the determination of the illumination pattern phase shift accurately -- whereas other key elements -- such as determination of modulation factor, estimation of object power spectrum, Wiener filtering frequency components with inclusion of object power spectrum information, translocating and the merging of the overlapping frequency components -- are usually glossed over superficially. In addition, most of the work reported lie scattered throughout the literature and a comprehensive review of the theoretical background is found lacking. The purpose of the present work is two-fold: 1) to collect the essential theoretical details of SIM algorithm at one place, thereby making them readily accessible to readers for the first time; and 2) to provide an open source SIM reconstruction code (named OpenSIM), which enables users to interactively vary the code parameters and study it's effect on reconstructed SIM image.
We report the Fermi-LAT gamma-ray detection of the 2021 outburst of the symbiotic recurrent nova RS Ophiuchi. In this system, unlike classical novae from cataclysmic binaries, the ejecta from the white dwarf form shocks when interacting with the dense circumstellar wind environment of the red giant companion. We find the LAT spectra from 50 MeV to ~20-23 GeV, the highest-energy photons detected in some sub-intervals, are consistent with $\pi^{\rm 0}$-decay emission from shocks in the ejecta as proposed by Tatischeff & Hernanz (2007) for its previous 2006 outburst. The LAT light-curve displayed a fast rise to its peak >0.1 GeV flux of $\simeq$6x10^-6 ph cm^-2 s^-1 beginning on day 0.745 after its optically-constrained eruption epoch of 2021 August 8.50. The peak lasted for ~1 day, and exhibited a power-law decline up to the final LAT detection on day 45. We analyze the data on shorter timescales at early times and found evidence of an approximate doubling of emission over ~200 minutes at day 2.2, possibly indicating a localized shock-acceleration event. Comparing the data collected by the AAVSO, we measured a constant ratio of ~2.8x10^-3 between the gamma-ray and optical luminosities except for a ~5x smaller ratio within the first day of the eruption likely indicating attenuation of gamma rays by ejecta material and lower high-energy proton fluxes at the earliest stages of the shock development. The hard X-ray emission due to bremsstrahlung from shock-heated gas traced by the Swift-XRT 2-10 keV light-curve peaked at day ~6, later than at GeV and optical energies. Using X-ray derived temperatures to constrain the velocity profile, we find the hadronic model reproduces the observed >0.1 GeV light-curve.
Optical and near-infrared spectroscopy of the newly discovered peculiar L dwarf 2MASS J11263991-5003550 are presented. Folkes et al. identified this source as a high proper motion L9+/-1 dwarf based on its strong H2O absorption at 1.4 micron. We find that the optical spectrum of 2MASS J1126-5003 is in fact consistent with that of a normal L4.5 dwarf with notably enhanced FeH absorption at 9896 A. However, its near-infrared spectrum is unusually blue, with strong H2O and weak CO bands similar in character to several recently identified ``blue L dwarfs''. Using 2MASS J1126-5003 as a case study, and guided by trends in the condensate cloud models of Burrows et al. and Marley et al., we find that the observed spectral peculiarities of these sources can be adequately explained by the presence of thin and/or large-grained condensate clouds as compared to normal field L dwarfs. Atypical surface gravities or metallicities alone cannot reproduce the observed peculiarities, although they may be partly responsible for the unusual condensate properties. We also rule out unresolved multiplicity as a cause for the spectral peculiarities of 2MASS J1126-5003. Our analysis is supported by examination of Spitzer mid-infrared spectral data from Cushing et al. which show that bluer L dwarfs tend to have weaker 10 micron absorption, a feature tentatively associated with silicate oxide grains. With their unique spectral properties, blue L dwarfs like 2MASS J1126-5003 should prove useful in studying the formation and properties of condensates and condensate clouds in low temperature atmospheres.
We investigate analytically a connection between the t-J model and the strongly correlated Bardeen-Cooper-Schrieffer (BCS) Hamiltonian, with the effect of strong electron correlations accounted by the Gutzwiller projection. We show that in the immediate vicinity of half filling the projected 2D BCS Hamiltonian with strong pairing develops an antiferromagnetically (AF) ordered ground state. This result explicitly demonstrates that antiferromagnetism in this model appears as a natural consequence of the strong Coulomb repulsion in a low doped regime. At moderate doping the ground state of the Gutzwiller-projected BCS Hamiltonian becomes qualitatively similar to Anderson's resonating valence bond state which is known to fit nicely the properties of the t-J model in this regime. These two properties taken together indicate that the projected BCS Hamiltonian captures the essential low-energy physics of the t-J model in the whole underdoped region.
In this paper, we study the geometric invariant theory on algebraic spaces, and construct te moduli spaces of $\mathcal{H}$-semistable sheaves on projective Deligne-Mumford stacks over algebraic spaces $S$. We prove that this moduli space is projective over $S$ as an algebraic space.
In this paper, we study the perfect and the insulated conductivity problems with multiple inclusions imbedded in a bounded domain in $\mathbb{R}^n, n\ge 2$. For these two extreme cases of the conductivity problems, the gradients of their solutions may blow up as two inclusions approach each other. We establish the gradient estimates for the perfect conductivity problems and an upper bound of the gradients for the insulated conductivity problems in terms of the distances between any two closely spaced inclusions.