ShantanuT01/DACTYL-Pretraining huggingface dataset:
We investigate the single qubit transformations under several typical coherence-free operations, such as, incoherent operation (IO), strictly incoherent operation (SIO), physically incoherent operation (PIO), and coherence preserving operation (CPO). Quantitative connection has been built between IO and SIO in single qubit systems. Moreover, these coherence-free operations have a clear hierarchical relationship in single qubit systems: CPO $\subset$ PIO $\subset$ SIO=IO. A new and explicit proof for the necessary and sufficient condition of single qubit transformation via IO or SIO has been provided, which indicates that SIO with only two Kraus operators are enough to realize this transformation. The transformation regions of single qubits via CPO and PIO are also given. Our method provides a geometric illustration to analyze single qubit coherence transformations by introducing the Bloch sphere depiction of the transformation regions, and tells us how to construct the corresponding coherence-free operations.
We propose an experimentally feasible scheme to achieve quantum computation based solely on geometric manipulations of a quantum system. The desired geometric operations are obtained by driving the quantum system to undergo appropriate adiabatic cyclic evolutions. Our implementation of the all-geometric quantum computation is based on laser manipulation of a set of trapped ions. An all-geometric approach, apart from its fundamental interest, promises a possible way for robust quantum computation.
The quantum theory of the mazer in the non-resonant case (a detuning between the cavity mode and the atomic transition frequencies is present) is written. The generalization from the resonant case is far from being direct. Interesting effects of the mazer physics are pointed out. In particular, it is shown that the cavity may slow down or speed up the atoms according to the sign of the detuning and that the induced emission process may be completely blocked by use of a positive detuning. It is also shown that the detuning adds a potential step effect not present at resonance and that the use of positive detunings defines a well-controlled cooling mechanism. In the special case of a mesa cavity mode function, generalized expressions for the reflection and transmission coefficients have been obtained. The general properties of the induced emission probability are finally discussed in the hot, intermediate and cold atom regimes. Comparison with the resonant case is given.
Let $V$ be a valuation ring and $K$ be its field of fraction. We show that the canonical map $\Br(V) \to \Br(K)$ is injective.
We prove that any arithmetically Gorenstein curve on a smooth, general hypersurface $X\subset \bbP^{4}$ of degree at least 6, is a complete intersection. This gives a characterisation of complete intersection curves on general type hypersurfaces in $\bbP^4$. We also verify that certain 1-cycles on a general quintic hypersurface are non-trivial elements of the Griffiths group.
The electromagnetic probe is a very valuable tool to study the dynamics of few nucleons. It can be very helpful in shedding light on the not yet fully understood three-nucleon forces. We present an update on the theoretical studies of electromagnetic induced reactions, such as photo-disintegration and electron scattering off 4He. We will show that they potentially represent a tool to discriminate among three-nucleon forces. Then, we will discuss the charge radius and the nuclear electric polarizability of the 6He halo nucleus.
The progenitor systems of the class of "Ca-rich transients" is a key open issue in time domain astrophysics. These intriguing objects exhibit unusually strong calcium line emissions months after explosion, fall within an intermediate luminosity range, are often found at large projected distances from their host galaxies, and may play a vital role in enriching galaxies and the intergalactic medium. Here we present multi-wavelength observations of iPTF15eqv in NGC 3430, which exhibits a unique combination of properties that bridge those observed in Ca-rich transients and Type Ib/c supernovae. iPTF15eqv has among the highest [Ca II]/[O I] emission line ratios observed to date, yet is more luminous and decays more slowly than other Ca-rich transients. Optical and near-infrared photometry and spectroscopy reveal signatures consistent with the supernova explosion of a < 10 solar mass star that was stripped of its H-rich envelope via binary interaction. Distinct chemical abundances and ejecta kinematics suggest that the core collapse occurred through electron capture processes. Deep limits on possible radio emission made with the Jansky Very Large Array imply a clean environment ($n <$ 0.1 cm$^{-3}$) within a radius of $\sim 10^{17}$ cm. Chandra X-ray Observatory observations rule out alternative scenarios involving tidal disruption of a white dwarf by a black hole, for masses > 100 solar masses). Our results challenge the notion that spectroscopically classified Ca-rich transients only originate from white dwarf progenitor systems, complicate the view that they are all associated with large ejection velocities, and indicate that their chemical abundances may vary widely between events.
Potential energy surfaces calculated with self-consistent mean-field methods are a very powerful tool, since their solutions are, in theory, global minima of the non-constrained subspace. However, this minimization leads to an incertitude concerning the saddle points, that can sometimes be no more saddle points in bigger constrained subspaces (fake saddle points), or can be missing on a trajectory (it missing saddle points). These phenomena are the consequences of discontinuities of the self-consistent potential energy surfaces (SPES). These discontinuities may have important consequences, since they can for example hide the real height of an energy barrier, and avoid any use of a SPES for further dynamical calculations, barrier penetrability estimations, or trajectory predictions. Discontinuities are not related to the quality of the production of a SPES, since even a perfectly converged SPES with an ideally fine mesh can be discontinuous. In this paper we explain what are the discontinuities, their consequences, and their origins. We then propose a numerical method to detect and identify discontinuities on a given SPES, and finally we discuss what are the best ways to transform a discontinuous SPES into a continuous one.
Let $g \geq 2$. A real number is said to be g-normal if its base g expansion contains every finite sequence of digits with the expected limiting frequency. Let \phi denote Euler's totient function, let \sigma be the sum-of-divisors function, and let \lambda be Carmichael's lambda-function. We show that if f is any function formed by composing \phi, \sigma, or \lambda, then the number \[ 0. f(1) f(2) f(3) \dots \] obtained by concatenating the base g digits of successive f-values is g-normal. We also prove the same result if the inputs 1, 2, 3, \dots are replaced with the primes 2, 3, 5, \dots. The proof is an adaptation of a method introduced by Copeland and Erdos in 1946 to prove the 10-normality of 0.235711131719\ldots.
Using the $\scr L$-invariant constructed in our previous paper we prove a Mazur-Tate-Teitelbaum style formula for derivatives of p-adic L-functions of elliptic modular forms at near central points. In the second version of the paper the case of potentially crystalline reduction is also covered.
Nonperturbative approximation schemes are inevitable even in weakly coupled theories if the nonequilibrium behavior of quantum fields is investigated. The two-particle irreducible (2PI) effective action formalism provides an efficient framework for obtaining resummation schemes both in and out of equilibrium. We briefly review the these techniques and discuss recent findings for nonequilibrium field theories.
The shape of two-dimensional invasion percolation clusters are studied numerically for both non-trapping (NTIP) and trapping (TIP) invasion percolation processes. Two different anisotropy quantifiers, the anisotropy parameter and the asphericity are used for probing the degree of anisotropy of clusters. We observe that in spite of the difference in scaling properties of NTIP and TIP, there is no difference in the values of anisotropy quantifiers of these processes. Furthermore, we find that in completely random media, the invasion percolation clusters are on average slightly less isotropic than standard percolation clusters. Introducing isotropic long-range correlations into the media reduces the isotropy of the invasion percolation clusters. The effect is more pronounced for the case of persisting long-range correlations. The implication of boundary conditions on the shape of clusters is another subject of interest. Compared to the case of free boundary conditions, IP clusters of conventional rectangular geometry turn out to be more isotropic. Moreover, we see that in conventional rectangular geometry the NTIP clusters are more isotropic than TIP clusters.
Our boundary-value approach to quantum processes in the gravitational collapse to a black hole leads to quantum amplitudes (not just probabilities) for transitions between data posed on initial and final hypersurfaces $\Sigma_{I,F}$, separated by a Lorentzian proper-time interval $T$, measured at spatial infinity. Following Feynman's $+i\epsilon$ approach, we rotate: $T\to {\mid}T{\mid} \exp(-i\theta)$, for $0<\theta\leq\pi/2$. The {\it classical} complexified boundary-value problem is expected to be well-posed for $0<\theta\leq\pi/2$, with classical action $S_{\rm class}$. For a locally supersymmetric Lagrangian, containing supergravity, possibly coupled to supermatter, the resulting quantum amplitude will be proportional to $\exp(iS_{\rm class})$, apart from possible loop corrections which are negligible for boundary data with frequencies below the Planck scale. The Lorentzian quantum amplitude is recovered by taking the limit as $\theta\to 0_+$ of this amplitude. In the present paper, a connection is made between this boundary value approach and the original approach to quantum evaporation in gravitational collapse to a black hole, {\it via} Bogoliubov coefficients. This connection is developed through consideration of the radial equation obeyed by the (adiabatic) non-spherical classical perturbations. When one studies the resulting final probability distribution, based on our quantum amplitudes above, one finds that this distribution can also be interpreted in terms of the Wigner quasi-probability distribution for harmonic oscillators.
The motion of satellite constellations similar to GPS and Galileo is numerically simulated and, then, the region where bifurcation (double positioning) occurs is appropriately represented. In the cases of double positioning, the true location may be found using additional information (angles or times). The zone where the Jacobian, J, of the transformation from inertial to emission coordinates vanishes is also represented and interpreted. It is shown that the uncertainties in the satellite world lines produce positioning errors, which depend on the value of |J|. The smaller this quantity the greater the expected positioning errors. Among all the available 4-tuples of satellites, the most appropriate one -for a given location- should minimize positioning errors (large enough |J| values) avoiding bifurcation. Our study is particularly important to locate objects which are far away from Earth, e.g., satellites.
Non-relativistic quantum mechanics for a free particle is shown to emerge from classical mechanics through an invariance principle under transformations that preserve the Heisenberg position-momentum inequality. These transformations are induced by isotropic space dilations. This invariance imposes a change in the laws of classical mechanics that exactly corresponds to the transition to quantum mechanics. The Schroedinger equation appears jointly with a second nonlinear equation describing non-unitary processes. Unitary and non-unitary evolutions are exclusive and appear sequentially in time. The non-unitary equation admits solutions that seem to correspond to the collapse of the wave function.
In state-of-the-art quantum key distribution (QKD) systems, the main limiting factor in increasing the key generation rate is the timing resolution in detecting photons. Here, we present and experimentally demonstrate a strategy to overcome this limitation, also for high-loss and long-distance implementations. We exploit the intrinsic wavelength correlations of entangled photons using wavelength multiplexing to generate a quantum secure key from polarization entanglement. The presented approach can be integrated into both fiber- and satellite-based quantum-communication schemes, without any changes to most types of entanglement sources. This technique features a huge scaling potential allowing to increase the secure key rate by several orders of magnitude as compared to non-multiplexed schemes.
The preliminary data on hadron multiplicities measured in central Pb+Pb collisions at 158A GeV/c are analyzed. The ideal hadron gas model fails to give a reasonable explanation to the Pb+Pb data sets. We study the possible effects of pion enhancement due to different hard-core repulsion for pions and other hadrons and strangeness suppression because of incomplete chemical equilibrium. Each of these two modifications improves the results. The combined effect of these two mechanisms leads to an extremely good agreement with the data. An interpretation of the obtained results in terms of the possible quark-gluon plasma formation at the early stage of the collision is also discussed.
The recent phenomenal interest in convolutional neural networks (CNNs) must have made it inevitable for the super-resolution (SR) community to explore its potential. The response has been immense and in the last three years, since the advent of the pioneering work, there appeared too many works not to warrant a comprehensive survey. This paper surveys the SR literature in the context of deep learning. We focus on the three important aspects of multimedia - namely image, video and multi-dimensions, especially depth maps. In each case, first relevant benchmarks are introduced in the form of datasets and state of the art SR methods, excluding deep learning. Next is a detailed analysis of the individual works, each including a short description of the method and a critique of the results with special reference to the benchmarking done. This is followed by minimum overall benchmarking in the form of comparison on some common dataset, while relying on the results reported in various works.
In this work we extend the approach used in [Emanuel Gallo and Osvaldo M. Moreschi, Phys. Rev. D 83, 12 083007 (2011)] to the study of weak gravitational lensing in a plasma medium. First, we present expressions for the deflection angle and optical scalars in terms of the components of the energy-momentum tensor for spherically symmetric lenses surrounded by a cold non-magnetized plasma. Second, we show that the same expressions can be deduced using the Gauss-Bonnet theorem. Finally, we establish a correspondence between the spatial orbits of photons in a non-homogeneous plasma and the non-geodesic curves followed by test massive particles whose dynamics also depend on an external central field. As an application, we use the Gauss-Bonnet theorem to compute the deflection angle of the non-geodesic trajectories followed by relativistic test massive charged particles in a Reissner-Nordstr\"om spacetime.
The results of 4,747 intensified CCD observations of double stars, made with the 26-inch refractor of the U.S. Naval Observatory, are presented. Each observation of a system represents a combination of over two thousand short-exposure images. These observations are averaged into 2,667 mean relative positions and range in separation from 0.328" to 95.9", with a median separation of 8.673". Four orbits are improved. This is the 22nd in this series of papers and covers the period 4 January 2016 through 29 December 2016.
We present several coupled-cluster calculations of ground and excited states of 4He and 16O employing methods from quantum chemistry. A comparison of coupled cluster results with the results of exact diagonalization of the hamiltonian in the same model space and other truncated shell-model calculations shows that the quantum chemistry inspired coupled cluster approximations provide an excellent description of ground and excited states of nuclei, with much less computational effort than traditional large-scale shell-model approaches. Unless truncations are made, for nuclei like 16O, full-fledged shell-model calculations with four or more major shells are not possible. However, these and even larger systems can be studied with the coupled cluster methods due to the polynomial rather than factorial scaling inherent in standard shell-model studies. This makes the coupled cluster approaches, developed in quantum chemistry, viable methods for describing weakly bound systems of interest for future nuclear facilities.
The evolution of infinitesimal, localized perturbations is investigated in a one-dimensional diatomic gas of hard-point particles (HPG) and thereby connected to energy diffusion. As a result, a Levy walk description, which was so far invoked to explain anomalous heat conductivity in the context of non-interacting particles is here shown to extend to the general case of truly many-body systems. Our approach does not only provide a firm evidence that energy diffusion is anomalous in the HPG, but proves definitely superior to direct methods for estimating the divergence rate of heat conductivity which turns out to be $0.333\pm 0.004$, in perfect agreement with the dynamical renormalization--group prediction (1/3).
A scaling variable for electron scattering off nuclei in the Delta-region is shown to exist. A scaling law for a large variety of scattering data with different kinematics is found. This property turns out to be very sensitive to the reaction mechanism. We will show that this outcome follows from drastic medium induced modifications on the momentum and energy dependence of the Delta width.
We study the series $\psi_s(z):=\sum_{n=1}^{\infty} \sec(n\pi z)n^{-s}$, and prove that it converges under mild restrictions on $z$ and $s$. The function possesses a modular transformation property, which allows us to evaluate $\psi_{s}(z)$ explicitly at certain quadratic irrational values of $z$. This supports our conjecture that $\pi^{-k} \psi_{k}(\sqrt{j})\in\mathbb{Q}$ whenever $k$ and $j$ are positive integers with $k$ even. We conclude with some speculations on Bernoulli numbers.
We investigate the idea of a "general boundary" formulation of quantum field theory in the context of the Euclidean free scalar field. We propose a precise definition for an evolution kernel that propagates the field through arbitrary spacetime regions. We show that this kernel satisfies an evolution equation which governs its dependence on deformations of the boundary surface and generalizes the ordinary (Euclidean) Schroedinger equation. We also derive the classical counterpart of this equation, which is a Hamilton-Jacobi equation for general boundary surfaces.
We present deep HST near-IR and Spitzer mid-IR observations of a large sample of spectroscopically-confirmed galaxies at z >= 6. The sample consists of 51 Lyman-alpha emitters (LAEs) at z ~ 5.7, 6.5, and 7.0, and 16 Lyman-break galaxies (LBGs) at 5.9 < z < 6.5. The near-IR images were mostly obtained with WFC3 in the F125W and F160W bands, and the mid-IR images were obtained with IRAC in the 3.6um and 4.5um bands. Our galaxies also have deep optical imaging data from Subaru Suprime-Cam. We utilize the multi-band data and secure redshifts to derive their rest-frame UV properties. These galaxies have steep UV continuum slopes roughly between beta ~ -1.5 and -3.5, with an average value of beta ~ -2.3, slightly steeper than the slopes of LBGs in previous studies. The slope shows little dependence on UV continuum luminosity except for a few of the brightest galaxies. We find a statistically significant excess of galaxies with slopes around beta ~ -3, suggesting the existence of very young stellar populations with extremely low metallicity and dust content. Our galaxies have moderately strong rest-frame Lyman-alpha equivalent width (EW) in a range of ~10 to ~200 \AA. The star-formation rates are also moderate, from a few to a few tens solar masses per year. The LAEs and LBGs in this sample share many common properties, implying that LAEs represent a subset of LBGs with strong Lyman-alpha emission. Finally, the comparison of the UV luminosity functions between LAEs and LBGs suggests that there exists a substantial population of faint galaxies with weak Lyman-alpha emission (EW < 20 \AA) that could be the dominant contribution to the total ionizing flux at z >= 6.
We study a canonical basis for spaces of weakly holomorphic modular forms of weights 12, 16, 18, 20, 22, and 26 on the full modular group. We prove a relation between the Fourier coefficients of modular forms in this canonical basis and a generalized Ramanujan tau-function, and use this to prove that these Fourier coefficients are often highly divisible by 2.
Hydrocarbons are ubiquitous in the interstellar medium, but their formation is still not well understood, depending on the physical environment they are found in. M8 is host to one of the brightest HII regions and PDRs in our galaxy. Using the APEX, and the IRAM 30 m telescopes, we performed a line survey toward Herschel 36 (Her 36), which is the main ionizing stellar system in M8, and an imaging survey within 1.3 $\times$ 1.3 pc around Her 36 of various transitions of C$_{2}$H and c-C$_{3}$H$_{2}$. We used both LTE and non-LTE methods to determine the physical conditions of the emitting gas along with the column densities and abundances of the observed species, which we compared with (updated) gas phase photochemical PDR models. In order to examine the role of PAHs in the formation of small hydrocarbons and to investigate their association with M8, we compared archival GLIMPSE 8 $\mu$m and the SPIRE 250 $\mu$m continuum images with the C$_{2}$H emission maps. We observed a total of three rotational transitions of C$_{2}$H with their hyperfine structure components and four rotational transitions of c-C$_{3}$H$_{2}$ with ortho and para symmetries toward M8. Fragmentation of PAHs seems less likely to contribute to the formation of small hydrocarbons as the 8 $\mu$m emission does not follow the distribution of C$_{2}$H emission, which is more associated with the molecular cloud. From the quantitative analysis, we obtained abundances of $\sim$ 10$^{-8}$ and 10$^{-9}$ for C$_{2}$H and c-C$_{3}$H$_{2}$ respectively, and volume densities of the hydrocarbon emitting gas in the range $n(\rm H_2)$ $\sim$ 5 $\times$ 10$^{4}$--5 $\times$ 10$^{6}$ cm$^{-3}$. The observed column densities of C$_{2}$H and c-C$_3$H$_{2}$ are reproduced reasonably well by our PDR models. This supports the idea that in high-UV flux PDRs, gas phase chemistry is sufficient to explain hydrocarbon abundances.