ShantanuT01/DACTYL-Pretraining huggingface dataset:
We point out that in a large class of superstring--inspired $E(6)$ models, either an e+e- collider operating at a center--of--mass energy $\rs= 1.5$ TeV or higher must detect the pair production of charged or neutral exotic leptons, or an e+e- collider with $\rs \geq 300$ GeV must discover at least one light neutral Higgs boson with invisible branching ratio exceeding 50\%. If neither of these two signals is seen, the lightest neutral exotic lepton would overclose the universe, and the model could be completely excluded, independent of the values of the numerous free parameters. Future Higgs searches might lower the energy of the e+e- collider needed to test these models decisively. The only assumptions we have to make are that $R-$parity is exact, so that the lightest exotic lepton is stable if it is lighter than the lightest neutralino, and that no $SO(10)$ singlet scalar gets a vacuum expectation of order $10^{10}$ GeV or higher. If the second condition is violated, the model effectively reduces to an $SO(10)$ model as far as collider experiments are concerned.
We present an analysis of the cooling of a micro-mechanical resonator by means of measurements and back action. The measurements are performed via the coupling to a Cooper-pair box, and although the coupling does not lead to net cooling, the extraction of information and hence entropy from the system leads to a pure quantum state. Under suitable circumstances, the states become very close to coherent states, conditioned on the measurement record, and can hence be displaced to the oscillator ground state.
The Sznajd model of socio-physics, that only a group of people sharing the same opinion can convince their neighbors, is applied to a scale-free random network modeled by a deterministic graph. We also study a model for elections based on the Sznajd model and the exponent obtained for the distribution of votes during the transient agrees with those obtained for real elections in Brazil and India. Our results are compared to those obtained using a Barabasi-Albert scale-free network.
In this work, we investigate the question, whether the conventional analysis of the electromagnetic form factors of the nucleon, evaluated in the framework of the cloudy bag model (CBM) or other chirally invariant hybrid quark models utilizing the same philosophy, is gauge invariant. In order to address that point, we first formulate the CBM in a style that resembles the technique of loop integrals. Evaluating the self energy and the electromagnetic form factors of the nucleon in that manner and comparing with the standard analysis where nonrelativistic perturbation theory is used, allows us to show that our approach is appropriate and to point out, what approximations are made in the standard derivation of the model. {}From the form of those loop integrals, we then show that additional diagrams are needed to preserve electromagnetic gauge invariance and we assess the corresponding corrections.
A 2D problem of acoustic wave scattering by a segment bearing impedance boundary conditions is considered. In the current paper (the first part of a series of two) some preliminary steps are made, namely, the diffraction problem is reduced to two matrix Riemann-Hilbert problems with exponential growth of unknown functions (for the symmetrical part and for the antisymmetrical part). For this, the Wiener--Hopf problems are formulated, they are reduced to auxiliary functional problems by applying the embedding formula, and finally the Riemann-Hilbert problems are formulated by applying the Hurd's method.   In the second part the Riemann-Hilbert problems will be solved by a novel method of OE-equation.
We consider a non-local spin valve in a Van der Pauw cross geometry with four ferromagnetic electrodes. Two antiparallel ferromagnets are used as (charge) source and drain while the detector circuit involves measuring the voltage between two collinear ferromagnets with parallel or antiparallel magnetizations. We find a potentially large increase of the non-local spin voltage. The setup displays several additional interesting properties: (i) infinite GMR for the non-local resistance (if a symmetry requirement for the device is met); (ii) ON-OFF switch effect, when the injector electrodes are parallel instead of antiparallel; (iii) insensitivity to offset voltages. The device can additionally be used as a Direct Spin Hall Effect probe and as a reprogrammable magneto-logic gate implementing basic operations (NOR, NAND, inverter, AND, OR,...).
We consider families of Calabi-Yau n-folds containing singular fibres and study relations between the occurring singularity structure and the decomposition of the local Weil zeta-function. For 1-parameter families, this provides new insights into the combinatorial structure of the strong equivalence classes arising in the Candelas - de la Ossa - Rodrigues-Villegas approach for computing the zeta-function. This can also be extended to families with more parameters as is explored in several examples, where the singularity analysis provides correct predictions for the changes of degree in the decomposition of the zeta-function when passing to singular fibres. These observations provide first evidence in higher dimensions for Lauder's conjectured analogue of the Clemens-Schmid exact sequence.
We consider the following nonlinear singular elliptic equation $$-{div} (|x|^{-2a}\nabla u)=K(x)|x|^{-bp}|u|^{p-2}u+\la g(x) \quad{in} \RR^N,$$ where $g$ belongs to an appropriate weighted Sobolev space, and $p$ denotes the Caffarelli-Kohn-Nirenberg critical exponent associated to $a$, $b$, and $N$. Under some natural assumptions on the positive potential $K(x)$ we establish the existence of some $\la\_0>0$ such that the above problem has at least two distinct solutions provided that $\la\in(0,\la\_0)$. The proof relies on Ekeland's Variational Principle and on the Mountain Pass Theorem without the Palais-Smale condition, combined with a weighted variant of the Brezis-Lieb Lemma.
We present the results of C18O(J=1-0) mapping observations of a 20'x18' area in the Lynds 1204 molecular cloud associated with the Sharpless 2-140 (S140) H II region. The C18O cube (alpha-delta-vLSR) data shows that there are three clumps with sizes of \sim 1 pc in the region. Two of them have peculiar red shifted velocity components at their edges, which can be interpreted as the results of the interaction between the cloud and the Cepheus Bubble. From the C18O cube data, the clumpfind identified 123 C18O cores, which have mean radius, velocity width in FWHM, and LTE mass of 0.36\pm0.07 pc, 0.37\pm0.09 km s-1, and 41\pm29 Msun, respectively. All the cores in S140 are most likely to be gravitationally bound by considering the uncertainty in the C18O abundance. We derived a C18O core mass function (CMF), which shows a power-law-like behavior above a turnover at 30 Msun. The best-fit power-law index of -2.1\pm0.2 is quite consistent with those of the IMF and the C18O CMF in the OMC-1 region by Ikeda & Kitamura (2009). Kramer et al. (1998) estimated the power-law index of -1.65 in S140 from the C18O(J=2-1) data, which is inconsistent with this study. However, the C18O(J=2-1) data are spatially limited to the central part of the cloud and are likely to be biased toward high-mass cores, leading to the flatter CMF. Consequently, this study and our previous one strongly support that the power-law form of the IMF has been already determined at the density of \sim 10^{3-4} cm^{-3}, traced by the C18O(J=1-0) line.
We investigate dynamical symmetry enlargement in the half-filled SU(4) Hubbard chain using non-perturbative renormalization group and Quantum Monte Carlo techniques. A spectral gap is shown to open for arbitrary Coulombic repulsion $U$. At weak coupling, $U \lesssim 3t$, a SO(8) symmetry between charge and spin-orbital excitations is found to be dynamically enlarged at low energy. At strong coupling, $U \gtrsim 6t$, the charge degrees of freedom dynamically decouple and the resulting effective theory in the spin-orbital sector is that of the SO(6) antiferromagnetic Heisenberg model. Both regimes exhibit spin-Peierls order. However, although spin-orbital excitations are $incoherent$ in the SO(6) regime they are $coherent$ in the SO(8) one. The cross-over between these regimes is discussed.
We prove that there exist some stacks, representable over the stack of stable curves, having the following universal property with respect to N\'eron models of Jacobians. For every one-parameter family of stable curves, with regular total space, the N\'eron model of the Jacobian of its generic fibre is isomorphic to the base change of the above stacks via the moduli map of the given family. We also obtain a stack compactification of the universal Picard scheme and hence a geometrically meaningful completion of the N\'eron model of the Jacobian for every family as above.
The principle of common cause is discussed as a possible fundamental principle of physics. Some revisions of Reichenbach's formulation of the principle are given, which lead to a version given by Bell. Various similar forms are compared and some equivalence results proved. The further problems of causality in a quantal system, and indeterministic causal structure, are addressed, with a view to defining a causality principle applicable to quantum gravity.
Below the Kondo temperature $T_{\rm K}$ electron spin resonance (ESR) usually is not observable from the Kondo-ion itself because the characteristic spin fluctuation energy results in a huge width of the ESR line. The heavy fermion metal YbRh$_{2}$Si$_{2}$ seems to be an exceptional case where definite ESR spectra show characteristic properties of the Kondo-ion Yb$^{3+}$ well \textit{below} $T_{\rm K}$. We found that the spin dynamics of YbRh$_{2}$Si$_{2}$, as determined by its ESR relaxation, is spatially characterized by an anisotropy of the zero temperature residual relaxation only.
Recent analyses of the gamma-ray spectrum from the ultra-luminous infrared galaxy Arp 220 have revealed a discrepancy in the cosmic ray energy injection rates derived from the gamma-rays versus the radio emission. While the observed radio emission is consistent with the star formation rate inferred from infrared observations, a significantly higher cosmic ray population is necessary to accurately model the measured gamma-ray flux. To resolve this discrepancy between the radio and gamma-ray observations, we find that we must increase the cosmic ray energy injection rate and account for an infrared optical depth greater than unity. Raising the energy injection rate naturally raises the total gamma-ray flux but also raises the radio flux unless there is also an increase in the energy loss rate for cosmic ray leptons. A optically thick medium results in an increase in energy losses via inverse Compton for cosmic ray leptons and preserves agreement with submillimeter, millimeter, and infrared wavelength observations.
The evolution of the energy difference between the neutron states $1i_{13/2}$ and $1h_{9/2}$ in the $N=82$ isotones and that between the proton states $1h_{11/2}$ and $1g_{7/2}$ in the $Z = 50$ isotopes are investigated within the framework of the relativistic Hartree-Fock theory, using the density-dependent effective interactions PKA1 and PKO$i$ ($i = 1 $, $ 2 $, $ 3 $). By identifying the contributions of the tensor force, which is naturally induced via the Fock terms, we find that the tensor force plays crucial roles in the evolution of the shell structure. The strength of the tensor force is also explored. It is found that moderately increasing the coupling strength of pion-nucleon coupling, i.e., $f_{\pi}$, will significantly improve the description of the shell-structure evolution. In particular, reducing the density dependence of $f_{\pi}$ is shown to be more preferable, in comparison to enlarging $f_{\pi}$ with a factor. This is in consistence with the idea of "tensor renormalization persistency" and provides valuable guidance for the development of nuclear energy density functional in the relativistic framework.
We report the discovery of 40 bright quasars and active galactic nuclei (AGNs) at low Galactic latitude (b<20deg). The low Galactic latitude region has been considered a place to avoid when searching for extragalactic sources, because of the high Galactic extinction, as well as a large number of stars contaminating the sample selection. Bright quasars (R<~17) suffer more from such difficulties because they look like bright stars, which are numerous at low b, yet their surface number density is very low. In order to find quasars in this region of the sky less explored for extragalactic sources, we have started a survey of low Galactic latitude bright quasars as a part of the Seoul National University Quasar Survey in Optical (SNUQSO). Quasar candidates have been selected from radio and near-infrared (NIR) data. Out of 88 targets, we identify 29 bright quasars/AGNs around the antigalactic center, and 11 bright quasars/AGNs in the outskirts of the Galactic center, from two observing runs in 2006 at the Bohyunsan Optical Astronomical Observatory (BOAO) in Korea. Our finding demonstrates that quasars/AGNs can be discovered effectively, even at low Galactic latitude, using multiwavelength data.
An approach by Stephen is used to investigate the critical properties of randomly diluted resistor networks near the percolation threshold by means of renormalized field theory. We reformulate an existing field theory by Harris and Lubensky. By a decomposition of the principal Feynman diagrams we obtain a type of diagrams which again can be interpreted as resistor networks. This new interpretation provides for an alternative way of evaluating the Feynman diagrams for random resistor networks. We calculate the resistance crossover exponent $\phi$ up to second order in $\epsilon=6-d$, where $d$ is the spatial dimension. Our result $\phi=1+\epsilon /42 +4\epsilon^2 /3087$ verifies a previous calculation by Lubensky and Wang, which itself was based on the Potts--model formulation of the random resistor network.
We prove unique continuation properties of solutions to a large class of nonlinear, non-local dispersive equations. The goal is to show that if $u_1,\,u_2$ are two suitable solutions of the equation defined in $\mathbb R^n\times[0,T]$ such that for some non-empty open set $\Omega\subset \mathbb R^n\times[0,T]$, $u_1(x,t)=u_2(x,t)$ for $(x,t) \in \Omega$, then $u_1(x,t)=u_2(x,t)$ for any $(x,t)\in\mathbb R^n\times[0,T]$. The proof is based on static arguments. More precisely, the main ingredient in the proofs will be the unique continuation properties for fractional powers of the Laplacian established by Ghosh, Salo and Ulhmann in \cite{GhSaUh}, and some extensions obtained here.
We give a $q$-enumeration of circular Dyck paths, which is a superset of the classical Dyck paths enumerated by the Catalan numbers. These objects have recently been studied by Alexandersson and Panova. Furthermore, we show that this $q$-analogue exhibits the cyclic sieving phenomenon under a natural action of the cyclic group. The enumeration and cyclic sieving is generalized to M\"obius paths. We also discuss properties of a generalization of cyclic sieving, which we call subset cyclic sieving. Finally, we also introduce the notion of Lyndon-like cyclic sieving that concerns special recursive properties of combinatorial objects exhibiting the cyclic sieving phenomenon.
We studied the electronic structure of the heavy fermion compound Yb(Ru$_{1-x}$Rh$_{x}$)$_2$Ge$_2$ with $x=0$ and nominally $x=0.125$ using ARPES and LDA calculations. We find a valence band structure of Yb corresponding to a non-integer valence close to $3+$. The three observed crystal electric field levels with a splitting of 32 and 75 meV confirm the suggested configuration with a quasi-quartet ground state. The experimentally determined band structure of the conduction electrons with predominantly Ru $4d$ character is well reproduced by our calculations. YbRu$_2$Ge$_2$ undergoes a non-magnetic phase transition into a ferroquadrupolar ordered state below 10.2\,K and then to an antiferromagnetically ordered state below 6.5\,K. A small hole Fermi surface shows nesting features in our calculated band structure and its size determined by ARPES is close to the magnetic ordering wave vector found in neutron scattering. The transitions are suppressed when YbRu$_2$Ge$_2$ is doped with 12.5% Rh. The electron doping leads to a shift of the band structure and successive Lifshitz transitions.
A linear system is a pair $(P,\mathcal{L})$ where $\mathcal{L}$ is a family of subsets on a ground finite set $P$, such that $|l\cap l^\prime|\leq 1$, for every $l,l^\prime \in \mathcal{L}$. The elements of $P$ and $\mathcal{L}$ are called points and lines, respectively, and the linear system is called intersecting if any pair of lines intersect in exactly one point. A subset $T$ of points of $P$ is a transversal of $(P,\mathcal{L})$ if $T$ intersects any line, and the transversal number, $\tau(P,\mathcal{L})$, is the minimum order of a transversal. On the other hand, a 2-packing set of a linear system $(P,\mathcal{L})$ is a set $R$ of lines, such that any three of them have a common point, then the 2-packing number of $(P,\mathcal{L})$, $\nu_2(P,\mathcal{L})$, is the size of a maximum 2-packing set. It is known that the transversal number $\tau(P,\mathcal{L})$ is bounded above by a quadratic function of $\nu_2(P,\mathcal{L})$. An open problem is to haracterize the families of linear systems which satisfies $\tau(P,\mathcal{L})\leq \lambda\nu_2(P,\mathcal{L})$, for some $\lambda\geq1$. In this paper, we give an infinite family of linear systems $(P,\mathcal{L})$ which satisfies $\tau(P,\mathcal{L})=\nu_2(P,\mathcal{L})$ with smallest possible cardinality of $\mathcal{L}$, as well as some properties of $r$-uniform intersecting linear systems $(P,\mathcal{L})$, such that $\tau(P,\mathcal{L})=\nu_2(P,\mathcal{L})=r$. Moreover, we state a characterization of $4$-uniform intersecting linear systems $(P,\mathcal{L})$ with $\tau(P,\mathcal{L})=\nu_2(P,\mathcal{L})=4$.
In this work we use density functional theory (DFT) to investigate the influence of semi-local exchange and correlation effects on the electronic and optical properties of zinc oxide. We find that the inclusion of such effects using the Tran-Blaha modified Becke-Johnson potential yields an excellent description of the electronic structure of this material giving energy band gap which is systematically larger than the one obtained with standard local functionals such as the generalized gradient approximation. The discrepancy between the experimental and theoretical band gaps is then significantly reduced at a computational low cost. We also calculated the dielectric functions of ZnO and find a violet shift to the absorption edge which is in good agreement with experimental results.
The most general exclusion single species reaction-diffusion models with nearest-neighbor interactions one a one dimensional lattice are investigated, for which the evolution of full intervals are closed. Using a generating function method, the probability that n consecutive sites be full is investigated. The stationary values of these probabilities, as well as the spectrum of the time translation generator (Hamiltonian) of these are obtained. It is shown that depending on the reaction rates the model could exhibit a dynamical phase transition.
We report the experimental observation of commensurability oscillations (COs) in 1D graphene superlattices. The widely tunable periodic potential modulation in hBN encapsulated graphene is generated via the interplay of nanopatterned few layer graphene acting as a local bottom gate and a global Si back gate. The longitudinal magneto-resistance shows pronounced COs, when the sample is tuned into the unipolar transport regime. We observe up to six CO minima, providing evidence for a long mean free path despite the potential modulation. Comparison to existing theories shows that small angle scattering is dominant in hBN/graphene/hBN heterostructures. We observe robust COs persisting to temperature exceeding $T=150$ K. At high temperatures, we find deviations from the predicted $T$-dependence, which we ascribe to electron-electron scattering.
Perfect state transfer (PST) is discussed in the context of passive quantum networks with logical bus topology, where many logical nodes communicate using the same shared media, without any external control. The conditions under which, a number of point-to-point PST links may serve as building blocks for the design of such multi-node networks are investigated. The implications of our results are discussed in the context of various Hamiltonians that act on the entire network, and are capable of providing PST between the logical nodes of a prescribed set in a deterministic manner.
In a recent note W. Kohnen asks whether the values of Dedekind sums are dense in the field of $p$-adic numbers. The present paper answers this question. Dedekind sums do not approximate units of $\mathbb Z_2$ or $\mathbb Z_3$, so they are not dense in $\mathbb Q_2$ or $\mathbb Q_3$. But they are dense in $\mathbb Q_p$ if $p\ge 5$.
Hydrogen molecules have two nuclear spin isomers: ortho-H2 and para-H2. The ortho-to-para ratio (OPR) is known to affect chemical evolution as well as gas dynamics in space. Therefore, understanding the mechanism of OPR variation in astrophysical environments is important. In this work, the nuclear spin conversion (NSC) processes of H2 molecules on diamond-like carbon and graphite surfaces are investigated experimentally by employing temperature-programmed desorption and resonance-enhanced multiphoton ionization methods. For the diamond-like carbon surface, the NSC time constants were determined at temperatures of 10-18 K and from 3900 plusminus 800 s at 10 K to 750 plusminus 40 s at 18 K. Similar NSC time constants and temperature dependence were observed for a graphite surface, indicating that bonding motifs (sp3 or sp2 hybridization) have little effect on the NSC rates.
We systematically analyze all possible supersymmetry multiplets that include the supersymmetry current and the energy-momentum tensor in various dimensions, focusing on N=1 in four dimensions. The most general such multiplet is the S-multiplet, which includes 16 bosonic and 16 fermionic operators. In special situations it can be decomposed, leading to smaller multiplets with 12+12 or even 8+8 operators. Physically, these multiplets give rise to different brane charges in the supersymmetry algebra. The S-multiplet is needed when the algebra contains both string and domain wall charges. In lower dimensions (or in four-dimensional N=2 theories) the algebra can include space-filling brane charges, which are associated with partial supersymmetry breaking. This phenomenon is physically distinct from ordinary spontaneous supersymmetry breaking. Our analysis leads to new results about the dynamics of supersymmetric field theories. These include constraints on the existence of certain charged branes and the absence of magnetic charges in U(1) gauge theories with a Fayet-Iliopoulos term.
Digital face manipulation has become a popular and fascinating way to touch images with the prevalence of smartphones and social networks. With a wide variety of user preferences, facial expressions, and accessories, a general and flexible model is necessary to accommodate different types of facial editing. In this paper, we propose a model to achieve this goal based on an end-to-end convolutional neural network that supports fast inference, edit-effect control, and quick partial-model update. In addition, this model learns from unpaired image sets with different attributes. Experimental results show that our framework can handle a wide range of expressions, accessories, and makeup effects. It produces high-resolution and high-quality results in fast speed.