ShantanuT01/DACTYL-Pretraining huggingface dataset:
Construction of genuinely entangled multipartite subspaces with certain characteristics has become a relevant task in various branches of quantum information. Here we show that such subspaces can be obtained from an arbitrary collection of bipartite entangled subspaces under joining of their adjacent subsystems. In addition, it is shown that direct sums of such constructions under certain conditions are genuinely entangled. These facts are then used in detecting entanglement of tensor products of mixed states and constructing subspaces that are distillable across every bipartite cut, where for the former application we include example with the analysis of genuine entanglement of a tripartite state obtained from two Werner states.
We introduce a minimal network model which generates a modular structure in a self-organized way. To this end, we modify the Barabasi-Albert model into the one evolving under the principle of division and independence as well as growth and preferential attachment (PA). A newly added vertex chooses one of the modules composed of existing vertices, and attaches edges to vertices belonging to that module following the PA rule. When the module size reaches a proper size, the module is divided into two, and a new module is created. The karate club network studied by Zachary is a prototypical example. We find that the model can reproduce successfully the behavior of the hierarchical clustering coefficient of a vertex with degree k, C(k), in good agreement with empirical measurements of real world networks.
CO observations in active galactic nuclei and star-bursts reveal high kinetic temperatures. Those environments are thought to be very turbulent due to dynamic phenomena such as outflows and high supernova rates. We investigate the effect of mechanical heating (MH) on atomic fine-structure and molecular lines, and their ratios. We use those ratios as a diagnostic to constrain the amount of MH in an object and also study its significance on estimating the H2 mass. Equilibrium PDRs models were used to compute the thermal and chemical balance for the clouds. The equilibria were solved for numerically using the optimized version of the Leiden PDR-XDR code. Large velocity gradient calculations were done as post-processing on the output of the PDR models using RADEX. High-J CO line ratios are very sensitive to MH. Emission becomes at least one order of magnitude brighter in clouds with n~10^5~cm^-3 and a star formation rate of 1 Solar Mass per year (corresponding to a MH rate of 2 * 10^-19 erg cm^-3 s^-1). Emission of low-J CO lines is not as sensitive to MH, but they do become brighter in response to MH. Generally, for all of the lines we considered, MH increases excitation temperatures and decreases the optical depth at the line centre. Hence line ratios are also affected, strongly in some cases. Ratios involving HCN are a good diagnostic for MH, such as HCN(1-0)/CO(1-0) and HCN(1-0)/HCO^+(1-0). Both ratios increase by a factor 3 or more for a MH equivalent to > 5 percent of the surface heating, as opposed to pure PDRs. The first major conclusion is that low-J to high-J intensity ratios will yield a good estimate of the MH rate (as opposed to only low-J ratios). The second one is that the MH rate should be taken into account when determining A_V or equivalently N_H, and consequently the cloud mass. Ignoring MH will also lead to large errors in density and radiation field estimates.
The aim of the present paper is to present a versatile scheme for the computation of optical properties of solids, with particular emphasis on realistic many-body calculations for correlated materials. Geared at the use with localized basis sets, we extend the commonly known lattice "Peierls substitution" approach to the case of multi-atomic unit cells. We show in how far this generalization can be deployed as an approximation to the full Fermi velocity matrix elements that enter the continuum description of the response of a solid to incident light. We further devise an upfolding scheme to incorporate optical transitions, that involve high energy orbitals that had been downfolded in the underlying many-body calculation of the electronic structure. As an application of the scheme, we present results on a material of longstanding interest, vanadium dioxide, VO2. Using dynamical mean-field data of both, the metallic and the insulating phase, we calculate the corresponding optical conductivities, elucidate optical transitions and find good agreement with experimental results.
The aim of this paper is to prove inequalities towards instances of the Bloch-Kato conjecture for Hilbert modular forms of parallel weight two, when the order of vanishing of the $L$-function at the central point is zero or one. We achieve this implementing an inductive Euler system argument which relies on explicit reciprocity laws for cohomology classes constructed using congruences of automorphic forms and special points on several Shimura curves.
This article focuses on finding the eigenvalues of the Laplacian matrix of the comaximal graph $\Gamma(\mathbb Z_n)$ of the ring $\mathbb Z_n$ for $n> 2$. We determine the eigenvalues of $\Gamma(\mathbb Z_n)$ for various $n$ and also provide a procedure to find the eigenvalues of $\Gamma(\mathbb Z_n)$ for any $n> 2$. We show that $\Gamma(\mathbb Z_n)$ is Laplacian Integral for $n=p^\alpha q^\beta$ where $p,q$ are primes and $\alpha, \beta$ are non-negative integers. The algebraic and vertex connectivity of $\Gamma(\mathbb Z_n)$ have been shown to be equal for all $n> 2$. An upper bound on the second largest eigenvalue of $\Gamma(\mathbb Z_n)$ has been obtained and a necessary and sufficient condition for its equality has also been determined. Finally we discuss the multiplicity of the spectral radius and the multiplicity of the algebraic connectivity of $\Gamma(\mathbb Z_n)$. Some problems have been discussed at the end of this article for further research.
Spatial symmetries occur in combination with temporal symmetries in a wide range of physical systems in nature, including time-periodic quantum systems typically described by the Floquet formalism. In this context, groups formed by three-dimensional point group symmetry operations in combination with time translation operations are discussed in this work. The derivation of these 'spatio-temporal' groups from conventional point groups and their irreducible representations is outlined, followed by a complete listing. The groups are presented in a template similar to space group operations, and are visualized using a modified version of conventional stereographic projections. Simple examples of physical processes that simultaneously exhibit symmetry in space and time are identified and used to illustrate the application of spatio-temporal groups.
We embed the Next-to Minimal Supersymmetric Standard Model into gauge mediation of supersymmetry breaking and study the phenomenology of scenarios where the gauge-mediation contributions to soft parameters are deflected by superpotential interactions of the gauge singlet with the messenger fields and the Higgs doublets. This kind of models provide a satisfactory solution to the mu-b_mu problem of gauge mediation, compatible with the adequate pattern of electroweak symmetry breaking and a realistic spectrum with supersymmetric partners at the TeV scale without requiring a significant fine tuning.
We present a measurement of the gravitational lensing of the Cosmic Microwave Background (CMB) temperature and polarization fields obtained by cross-correlating the reconstructed convergence signal from the first season of ACTPol data at 146 GHz with Cosmic Infrared Background (CIB) fluctuations measured using the Planck satellite. Using an overlap area of 206 square degrees, we detect gravitational lensing of the CMB polarization by large-scale structure at a statistical significance of 4.5 sigma. Combining both CMB temperature and polarization data gives a lensing detection at 9.1 sigma significance. A B-mode polarization lensing signal is present with a significance of 3.2 sigma. We also present the first measurement of CMB lensing--CIB correlation at small scales corresponding to l > 2000. Null tests and systematic checks show that our results are not significantly biased by astrophysical or instrumental systematic effects, including Galactic dust. Fitting our measurements to the best-fit lensing-CIB cross power spectrum measured in Planck data, scaled by an amplitude A, gives A=1.02 +0.12/-0.18 (stat.) +/-0.06(syst.), consistent with the Planck results.
The Fan Region is one of the dominant features in the polarized radio sky, long thought to be a local (distance < 500 pc) synchrotron feature. We present 1.3-1.8 GHz polarized radio continuum observations of the region from the Global Magneto-Ionic Medium Survey (GMIMS) and compare them to maps of Halpha and polarized radio continuum intensity from 0.408-353 GHz. The high-frequency (> 1 GHz) and low-frequency (< 600 MHz) emission have different morphologies, suggesting a different physical origin. Portions of the 1.5 GHz Fan Region emission are depolarized by about 30% by ionized gas structures in the Perseus Arm, indicating that this fraction of the emission originates >2 kpc away. We argue for the same conclusion based on the high polarization fraction at 1.5 GHz (about 40%). The Fan Region is offset with respect to the Galactic plane, covering -5{\deg} < b < +10{\deg}; we attribute this offset to the warp in the outer Galaxy. We discuss origins of the polarized emission, including the spiral Galactic magnetic field. This idea is a plausible contributing factor although no model to date readily reproduces all of the observations. We conclude that models of the Galactic magnetic field should account for the > 1 GHz emission from the Fan Region as a Galactic-scale, not purely local, feature.
An alternative process is presented for diffractive Higgs boson production in peripheral $pp$ collisions, where the particles interact through the Double Pomeron Exchange. The event rate is computed as a central-rapidity distribution for Tevatron and LHC energies leading to a result around 0.6 pb, higher than the predictions from previous approaches. Therefore, this result arises as an enhanced signal for the detection of the Higgs boson in hadron colliders. The predictions for the Higgs boson photoproduction are compared to the ones obtained from a similar approach proposed by the Durham group, enabling an analysis of the future developments of its application to $pp$ and $AA$ collisions.
The frustrated one-dimensional (1D) quantum magnet LiCuSbO$_4$ is one rare realization of the $J_1-J_2$ spin chain model with an easily accessible saturation field, formerly estimated to 12~T. Exotic multipolar nematic phases were theoretically predicted in such compounds just below the saturation field, but without unambiguous experimental observation so far. In this paper we present extensive experimental research of the compound in the wide temperature (30mK$-$300K) and field (0$-$13.3T) range by muon spin rotation ($\mu$SR), $^7$Li nuclear magnetic resonance (NMR) and magnetic susceptibility (SQUID). $\mu$SR experiments in zero magnetic field demonstrate the absence of long range 3D ordering down to 30mK. Together with former heat capacity data [S.E. Dutton \emph{et al}, Phys. Rev. Lett. 108, 187206 (2012)], magnetic susceptibility measurements suggest short range correlated vector chiral phase in the field range $0-4$T. In the intermediate field values (5$-$12T), the system enters in a 3D ordered spin density wave phase with 0.75$\mu_B$ per copper site at lowest temperatures (125mK), estimated by NMR. At still higher field, the magnetization is found to be saturated above 13T where the spin lattice $T_1^{-1}$ relaxation reveals a spin gap estimated to 3.2(2)K. We narrow down the possibility of observing a multipolar nematic phase to the range 12.5$-$13T.
It is shown that the known solutions for nonexpanding impulsive gravitational waves generated by null particles of arbitrary multipole structure can be obtained by boosting the Weyl solutions describing static sources with arbitrary multipole moments, at least in a Minkowski background. We also discuss the possibility of boosting static sources in (anti-) de Sitter backgrounds, for which exact solutions are not known, to obtain the known solutions for null multipole particles in these backgrounds.
We explore Seiberg-like dualities, or mutations, for ${\cal N}=4$ quiver quantum mechanics in the context of wall-crossing. In contrast to higher dimensions, the 1d Seiberg-duality must be performed with much care. With fixed Fayet-Iliopoulos constants, at most two nodes can be mutated, one left and the other right, mapping a chamber of a quiver into a chamber of a mutated quiver. We delineate this complex pattern for triangle quivers and show how the Witten indices are preserved under such finely chosen mutations. On the other hand, the quiver invariants, or wall-crossing-safe part of supersymmetric spectra, mutate more straightforwardly, whereby a quiver is mapped to a quiver. The mutation rule that preserves the quiver invariant is different from the usual one, however, which we explore and confirm numerically.
All the Lie point symmetries of the near extremal horizon geometry equation, in the case of 4-dimensional Einstein vacuum spacetime with cosmological constant, are the diffeomorphisms of the space of the null generators of the horizon. This result is also generalised to the Maxwell-Einstein spacetime.
We examine Hubeny's scenario according to which a near-extremal Reissner-Nordstr\"om black hole can absorb a particle and be driven toward an over-extremal state in which the charge exceeds the mass, signaling the destruction of the black hole. Our analysis incorporates the particle's electromagnetic self-force and the energy radiated to infinity in the form of electromagnetic waves. With these essential ingredients, our sampling of the parameter space reveals no instances of an overcharged final state, and we conjecture that the self-force acts as a cosmic censor, preventing the destruction of a near-extremal black hole by the absorption of a charged particle. We argue, on the basis of the third law of black-hole mechanics, that this conclusion is robust and should apply to attempts to overspin a Kerr black hole.
We consider the Blandford-Znajek (BZ) mechanism for extracting black hole spin energy to drive astrophysical jets. Analyses of the BZ mechanism generally take no account of any electric charge on the black hole. But, as noted by Wald and others, if the medium surrounding the black hole is an ionized plasma with mobile charges, then a spinning hole quickly acquires an electric charge. The effect of this charge is to nullify the electric field structures which drive the BZ mechanism. Since jets are now observed in a wide variety of classes of accreting objects, most of which do not contain a central black hole, it seems likely that the jet driving mechanism in all astrophysical objects uses energy directly from the accretion disc, rather than black hole spin.
Within the superfield approach, we discuss two-dimensional noncommutative super-QED. Its all-order finiteness is shown explicitly.
An ill-posed Cauchy problem for the wave equation is considered: the solution is to be determined by the Cauchy data on some part of the time-space boundary. By means of Fourier method we obtain a regularization algorithm for this problem, which is given by rather explicit formula.
We establish a Liouville-type theorem for a subcritical nonlinear problem, involving a fractional power of the sub-Laplacian in the Heisenberg group. To prove our result we will use the local realization of fractional CR covariant operators, which can be constructed as the Dirichlet-to-Neumann operator of a degenerate elliptic equation in the spirit of Caffarelli and Silvestre, as established in \cite{FGMT}. The main tools in our proof are the CR inversion and the moving plane method, applied to the solution of the lifted problem in the half-space $\mathbb H^n\times \mathbbR^+$.
We present here the summary of the "Electroweak and Searches in DIS and Hadron Colliders" working group activities at the DIS 2010 conference. The theory contributions will be presented first, followed by the experimental ones. The experimental results include measurements from the Tevatron (CDF and \DO) and HERA (H1 and ZEUS) experiments, and studies from the LHC (ATLAS and CMS). Results from the B-factories (BaBar and Belle) and from NA62 are also summarised.
Let F be a polystable sheaf on a smooth minimal projective surface of Kodaira dimension 0. Then the DG-Lie algebra RHom(F,F) of derived endomorphisms of F is formal. The proof is based on the study of equivariant $L_{\infty}$ minimal models of DG-Lie algebras equipped with a cyclic structure of degree 2 which is non-degenerate in cohomology, and does not rely (even for K3 surfaces) on previous results on the same subject.
The strong lensing events that are observed in compact clusters of galaxies can, both statistically and individually, return important clues about the structural properties of the most massive structures in the Universe. Substantial work is ongoing in order to understand the degree of similarity between the lensing cluster population and the population of clusters as a whole, with members of the former being likely more massive, compact, and substructured than members of the latter. In this work we exploit synthetic clusters extracted from the {\sc MareNostrum Universe} cosmological simulation in order to estimate the correlation between the strong lensing efficiency and other bulk properties of lensing clusters, such as the virial mass and the bolometric X-ray luminosity. We found that a positive correlation exist between all these quantities, with the substantial scatter being smaller for the luminosity-cross section relation. We additionally used the relation between the lensing efficiency and the virial mass in order to construct a synthetic optical depth that agrees well with the true one, while being extremely faster to be evaluated. We finally estimated what fraction of the total giant arc abundance is recovered when galaxy clusters are selected according to their dynamical activity or their X-ray luminosity. Our results show that there is a high probability for high-redshift strong lensing clusters to be substantially far away from dynamical equilibrium, and that $30-40\%$ of the total amount of giant arcs are lost if looking only at very X-ray luminous objects.
We address the problem of finding the optimal common resource for an arbitrary family of target states in quantum resource theories based on majorization, that is, theories whose conversion law between resources is determined by a majorization relationship, such as it happens with entanglement, coherence or purity. We provide a conclusive answer to this problem by appealing to the completeness property of the majorization lattice. We give a proof of this property that relies heavily on the more geometric construction provided by the Lorenz curves, which allows to explicitly obtain the corresponding infimum and supremum. Our framework includes the case of possibly non-denumerable sets of target states (i.e. targets sets described by continuous parameters). In addition, we show that a notion of approximate majorization, which has recently found application in quantum thermodynamics, is in close relation with the completeness of this lattice. Finally, we provide some examples of optimal common resources within the resource theory of quantum coherence.
Recently, Babson and Steingrimsson (see [BS]) introduced generalized permutations patterns that allow the requirement that two adjacent letters in a pattern must be adjacent in the permutation.   We study generating functions for the number of permutations on $n$ letters avoiding $1-3-2$ (or containing $1-3-2$ exactly once) and an arbitrary generalized pattern $\tau$ on $k$ letters, or containing $\tau$ exactly once. In several cases the generating function depends only on $k$ and is expressed via Chebyshev polynomials of the second kind, and generating function of Motzkin numbers.
In the first of a series of forthcoming publications, we present a panchromatic catalog of 102 visually-selected early-type galaxies (ETGs) from observations in the Early Release Science (ERS) program with the Wide Field Camera 3 (WFC3) on the Hubble Space Telescope (HST) of the Great Observatories Origins Deep Survey-South (GOODS-S) field. Our ETGs span a large redshift range, 0.35 < z < 1.5, with each redshift spectroscopically-confirmed by previous published surveys of the ERS field. We combine our measured WFC3 ERS and ACS GOODS-S photometry to gain continuous sensitivity from the rest-frame far-UV to near-IR emission for each ETG. The superior spatial resolution of the HST over this panchromatic baseline allows us to classify the ETGs by their small-scale internal structures, as well as their local environment. By fitting stellar population spectral templates to the broad-band photometry of the ETGs, we determine that the average masses of the ETGs are comparable to the characteristic stellar mass of massive galaxies, 11< log(M [Solar]) < 12.   By transforming the observed photometry into the GALEX FUV and NUV, Johnson V, and SDSS g' and r' bandpasses we identify a noteworthy diversity in the rest-frame UV-optical colors and find the mean rest-frame (FUV-V)=3.5 and (NUV-V)=3.3, with 1$\sigma$ standard deviations approximately equal to 1.0. The blue rest-frame UV-optical colors observed for most of the ETGs are evidence for star-formation during the preceding gigayear, but no systems exhibit UV-optical photometry consistent with major recent (<~50 Myr) starbursts. Future publications which address the diversity of stellar populations likely to be present in these ETGs, and the potential mechanisms by which recent star-formation episodes are activated, are discussed.
In a recent work, Allen, B\"{o}ttcher, H\`{a}n, Kohayakawa, and Person provided a first general analogue of the blow-up lemma applicable to sparse (pseudo)random graphs thus generalising the classic tool of Koml\'{o}s, S\'{a}rk\"{o}zy, and Szemer\'{e}di. Roughly speaking, they showed that with high probability in the random graph $G_{n,p}$ for $p \geq C(\log n/n)^{1/\Delta}$, sparse regular pairs behave similarly as complete bipartite graphs with respect to embedding a spanning graph $H$ with $\Delta(H) \leq \Delta$. However, this is typically only optimal when $\Delta \in \{2,3\}$ and $H$ either contains a triangle ($\Delta = 2$) or many copies of $K_4$ ($\Delta = 3$). We go beyond this barrier for the first time and present a sparse blow-up lemma for cycles $C_{2k-1}, C_{2k}$, for all $k \geq 2$, and densities $p \geq Cn^{-(k-1)/k}$, which is in a way best possible. As an application of our blow-up lemma we fully resolve a question of Nenadov and \v{S}kori\'{c} regarding resilience of cycle factors in sparse random graphs.
The electron transmission $T$ is evaluated through waveguides, in which the strength of the spin-orbit interaction(SOI) $\alpha$ is varied periodically, using the transfer-matrix technique. It is shown that $T$ exhibits a {\it spin-transistor} action, as a function of $\alpha$ or of the length of one of the two subunits of the unit cell, provided only one mode is allowed to propagate in the waveguide. A similar but not periodic behavior occurs as a function of the incident electron energy. A transparent formula for $T$ through one unit is obtained and helps explain its periodic behavior. The structure considered is a good candidate for the establishment of a realistic spin transistor.