ShantanuT01/DACTYL-Pretraining huggingface dataset:
Characterizing multiloop topologies is an important step towards developing novel methods at high perturbative orders in quantum field theory. In this article, we exploit the Loop-Tree Duality (LTD) formalism to analyse multiloop topologies that appear for the first time at five loops. Explicitly, we open the loops into connected trees and group them according to their topological properties. Then, we identify a kernel generator, the so-called N$^7$MLT universal topology, that allow us to describe any scattering amplitude of up to five loops. Furthermore, we provide factorization and recursion relations that enable us to write these multiloop topologies in terms of simpler subtopologies, including several subsets of Feynman diagrams with an arbitrary number of loops. Our approach takes advantage of many symmetries present in the graphical description of the original fundamental five-loop topologies. The results obtained in this article might shed light into a more efficient determination of higher-order corrections to the running couplings, which are crucial in the current and future precision physics program.
In the present paper, we investigate wormholes in 4D-Einstein-Gauss-Bonnet gravity without the requirement of exotic matters. We have taken the radial dependent red-shift function $\phi=\ln \left( {\frac {r_{{0}}}{r}}+1 \right)$ and shape function $b(r)={\frac{r_{0}\ln(r+1)}{\ln({r_0}+1)}}$ as well as anisotropic matter sources through equation of state (EoS) $p_r(r) = \omega \rho(r)$. We examine the energy conditions, flaring out condition, throat condition and anisotropic parameter. The volume integral quantifier is also analyzed to validate the existence and stability of the WH solution. We find, for -ve branch wormhole solutions satisfy the null energy conditions (NEC) throughout the entire space time and +ve branch reduces exactly to Morris-Thorne of GR.
We set observational constraints on the second clock effect, predicted by Weyl unified field theory, by investigating recent data on the dilated lifetime of muons accelerated by a magnetic field. These data were obtained in an experiment carried out in CERN aiming at measuring the anomalous magnetic moment of the muon. In our analysis we employ the definition of invariant proper time proposed by V. Perlick, which seems to be the appropriate notion to be worked out in the context of Weyl space-time.
The dependence on the single-particle states of the pairing matrix elements of the Gogny force and of the bare low-momentum nucleon-nucleon potential $v_{low-k}$ is studied in the semiclassical approximation for the case of a typical finite, superfluid nucleus ($^{120}$Sn). It is found that the matrix elements of $v_{low-k}$ follow closely those of $v_{Gogny}$ on a wide range of energy values around the Fermi energy $e_F$, those associated with $v_{low-k}$ being less attractive. This result explains the fact that around $e_F$ the pairing gap $\Delta_{Gogny}$ associated with the Gogny interaction (and with a density of single-particle levels corresponding to an effective $k$-mass $m_k\approx 0.7 m$) is a factor of about 2 larger than $\Delta_{low-k}$,being in agreement with $\Delta_{exp}$= 1.4 MeV. The exchange of low-lying collective surface vibrations among pairs of nucleons moving in time-reversal states gives rise to an induced pairing interaction $v_{ind}$ peaked at $e_F$. The interaction $(v_{low-k}+ v_{ind})Z_{\omega}$ arising from the renormalization of the bare nucleon-nucleon potential and of the single-particle motion ($\omega-$mass and quasiparticle strength $Z_{\omega}$) due to the particle-vibration coupling leads to a value of the pairing gap at the Fermi energy $\Delta_{ren}$ which accounts for the experimental value.
We discuss why the SU(3)^3 supersymmetric model with the most general superpotential can naturally break to the standard model if gauge singlets and a discrete symmetry are included. This mechanism does away with the need for fine-tuning in the form of the assumed absence of certain terms in the superpotential. It also automatically guarantees that any abelian discrete phase symmetry of the GUT will survive the symmetry breaking. Such a discrete symmetry, also known as the matter parity, is needed to suppress both proton decay and the flavor changing neutral current (FCNC), and may help solve the hierarchy problem.
Inverted HgTe/CdTe quantum wells have been used as a platform for the realization of 2D topological insulators, bulk insulator materials with spin-helical metallic edges states protected by time-reversal symmetry. This work investigates the spectrum and the charge transport in HgTe/CdTe quantum well junctions both in the topological regime and in the absence of time-reversal symmetry. We model the system using the BHZ effective Hamiltonian and compute the transport properties using recursive Green's functions with a finite differences' method. Specifically, we have studied the material's spatially-resolved conductance in a set-up with a gated central region, forming monopolar (n-n$^{\prime}$-n) and heteropolar (n-p-n, n-TI-n) double junctions, which have been recently realized in experiments. We find regimes in which the edge states carry spin-polarized currents in the central region even in the presence of a small magnetic field, which breaks TRS. More interestingly, the conductance displays spin-dependent, Fabry-Per\'ot-like oscillations as a function of the central gate voltage producing tunable, fully spin-polarized currents through the device.
It is common practice in molecular dynamics and Monte Carlo computer simulations to run multiple, separately-initialized simulations in order to improve the sampling of independent microstates. Here we examine the utility of an extreme case of this strategy, in which we run a large ensemble of $M$ independent simulations (a "swarm"), each of which is relaxed to equilibrium. We show that if $M$ is of order $10^3$, we can monitor the swarm's relaxation to equilibrium, and confirm its attainment, within $\sim 10\bar\tau$, where $\bar\tau$ is the equilibrium relaxation time. As soon as a swarm of this size attains equilibrium, the ensemble of $M$ final microstates from each run is sufficient for the evaluation of most equilibrium properties without further sampling. This approach dramatically reduces the wall-clock time required, compared to a single long simulation, by a factor of several hundred, at the cost of an increase in the total computational effort by a small factor. It is also well-suited to modern computing systems having thousands of processors, and is a viable strategy for simulation studies that need to produce high-precision results in a minimum of wall-clock time. We present results obtained by applying this approach to several test cases.
We present a sandpile model, in which the instability of a site is determined also by the variables in a neighbourhood. This is a modification of the Abelian Sandpile Model, in which abelianity is preserved: it shares several mathematical properties of the original abelian model, while producing a more realistic dynamics. We show how our model presents interesting hydrodynamic features.
We give a low temperature formula for the stationary occupations in Markovian systems away from detailed balance. Two applications are discussed, one to determine the direction of the ratchet current and one on population inversion. Both can take advantage of low temperature to improve the gain and typical nonequilibrium features. The new formula brings to the foreground the importance of kinetic aspects in terms of reactivities for deciding the levels with highest occupation and thus gives a detailed quantitative meaning to Landauer's blowtorch theorem at low temperature.
The pi-mesonic decay of the hypertriton is calculated based on a hypertriton wavefunction and 3N scattering states, which are rigorous solutions of 3-body Faddeev equations using realistic NN and hyperon-nucleon interactions. The total pi-mesonic decay rate is found to be 92% of the free Lambda decay rate, which is close to the experimental data. Together with the nonmesonic decay the total life time of 3Lambda H is predicted to be 2.78 x 10^-10 sec which is 6 % larger than for the free Lambda particle. The differential decay rate is evaluated as a function of the pion momentum. The decay into the N+d+pi channel is stronger than in the 3N+pi channel in contrast to the situation for the nonmesonic decay. The ratio for the decay rate into 3He + pi^- to the decay rate into all channels including pi^- is found to be 0.40, which is close to the experimental value. We visualise the decay into the dominant channel p+d+pi^- in a Dalitz plot. Finally we compare the polarisation of the outgoing proton in free unpolarised Lambda-decay to the polarisation of 3He in unpolarised 3_Lambda H-decay and we compare the closely related asymmetry of pi^- emitted parallel and antiparallel with respect to the spin-direction for a polarised Lambda to the corresponding asymmetry for a polarised 3_Lambda H.
We present the first measurement of the mass of a supermassive black hole (SMBH) in the nearby double-barred spiral galaxy NGC 3504 as part of the Measuring Black Holes Below the Milky Way ($M_{\star}$) mass galaxies (MBHBM$_{\star}$) Project. Our analysis is based on Atacama Large Millimeter/submillimeter Array (ALMA) Cycle-5 observations of the ${\rm ^{12}CO(2-1)}$ emission line. NGC 3504 has a circumnuclear gas disk (CND), which has a relatively high-velocity dispersion of 30 \kms. Our dynamical models of the CND yield a \Mbh~of $M_{\rm BH}=1.02^{+0.18}_{-0.15}\times10^7$\Msun and a mass-to-light ratio in $H$-band of \ml$_{\rm H}=0.66^{+1.44}_{-0.65}$ (\Msun/\Lsun). This black hole (BH) mass is consistent with BH--galaxy scaling relations. We also detect a central deficiency in the ${\rm ^{12}CO(2-1)}$ integrated intensity map with a diameter of 2.7 pc at the putative position of the SMBH. However, this hole is filled by a dense gas tracer ${\rm CS(5-4)}$ that peaks at the galaxy center found in one of the three low-velocity-resolution continuum spectral correlators. The ${\rm CS(5-4)}$ line has the same kinematics with the ${\rm ^{12}CO(2-1)}$ line within the CND, suggesting that it is also an alternative transition for measuring the central \Mbh~in NGC 3504 probably more accurately than the current commonly used of ${\rm ^{12}CO(2-1)}$ due to its centralization.
The last IceCube catalog of High Energy Starting Events (HESE) obtained with a livetime of 1347 days comprises 54 neutrino events equally-distributed between the three families with energies between 25 TeV and few PeVs. Considering the homogeneous flavors distribution (1:1:1) and the spectral features of these neutrinos the IceCube collaboration claims the astrophysical origin of these events with more than $5\sigma$. The spatial distribution of cited events does not show a clear correlation with known astrophysical accelerators leaving opened both the Galactic and the extra-Galactic origin interpretations. Here, we compute the neutrino diffuse emission of our Galaxy on the basis of a recently proposed phenomenological model characterized by radially-dependent cosmic-ray (CR) transport properties. We show that the astrophysical spectrum measured by IceCube experiment can be well explained adding to the diffuse Galactic neutrino flux (obtained with this new model) a extra-Galactic component derived from the astrophysical muonic neutrinos reconstructed in the Northern hemisphere. A good agreement between the expected astrophysical neutrino flux and the IceCube data is found for the full sky as well as for the Galactic plane region.
We study the asymptotic behavior of large data radial solutions to the focusing Schr\"odinger equation $i u_t + \Delta u = -|u|^2 u$ in $\R^3$, assuming globally bounded $H^1(\R^3)$ norm (i.e. no blowup in the energy space). We show that as $t \to \pm \infty$, these solutions split into the sum of three terms: a radiation term that evolves according to the linear Schr\"odinger equation, a smooth function localized near the origin, and an error that goes to zero in the $\dot H^1(\R^3)$ norm. Furthermore, the smooth function near the origin is either zero (in which case one has scattering to a free solution), or has mass and energy bounded strictly away from zero, and obeys an asymptotic Pohozaev identity. These results are consistent with the conjecture of soliton resolution.
We present transport measurements on a bilayer graphene sheet with homogeneous back gate and split top gate. The electronic transport data indicates the capability to direct electron flow through graphene nanostructures purely defined by electrostatic gating. By comparing the transconductance data recorded for different top gate geometries - continuous barrier and split-gate - the observed transport features for the split-gate can be attributed to interference effects inside the narrow opening.
In the context of $f\left(R, T\right) = R + 2 \beta T$ gravity, where $R$ is the Ricci scalar and $T$ is the trace of the energy-momentum tensor, the equilibrium structure of charged anisotropic white dwarfs (WDs) is studied. The stellar equations for the general case are derived and numerical solutions are found for the Chandrasekhar equation of state (EoS) and a charge density distribution proportional to the energy density $\rho_{\text{ch}} = \alpha \rho$. By adjusting different parameters, the properties of the solutions under various conditions are compared. Most importantly, by going beyond the trivial WD in GR in various ways, the solutions may exhibit super-Chandrasekhar behavior. This article is a study of a WD structure, and the results obtained may have a contrasting effect on astronomical observations such as superluminous type Ia supernovae.
We compute the characteristic parameters of magnetic dipole radiation of a neutron star undergoing torsional seismic vibrations under the action of Lorentz restoring force about axis of a dipolar magnetic field experiencing decay. After brief outline of general theoretical background of the model of vibration powered neutron star, we present numerical estimates of basic vibration and radiation characteristics, such as the oscillation frequency, lifetime, luminosity of radiation, and investigate their time dependence upon magnetic field decay. The presented analysis suggests that gradual decrease in frequencies of pulsating high-energy emission detected from a handful of currently monitored AXP/SGR-like X-ray sources can be explained as being produced by vibration powered magneto-dipole radiation of quaking magnetars.   \keywords{neutron stars, torsion Alfv\'en vibrations, vibration powered radiation, magnetic field decay, magnetars}
Our goal is to determine the stellar and wind properties of seven O stars in the cluster NGC2244 and three O stars in the OB association MonOB2. These properties give us insight into the mass loss rates of O stars, allow us to check the validity of rotational mixing in massive stars, and to better understand the effects of the ionizing flux and wind mechanical energy release on the surrounding interstellar medium and its influence on triggered star formation. We collect optical and UV spectra of the target stars which are analyzed by means of atmosphere models computed with the code CMFGEN. The spectra of binary stars are disentangled and the components are studied separately. All stars have an evolutionary age less than 5 million years, with the most massive stars being among the youngest. Nitrogen surface abundances show no clear relation with projected rotational velocities. Binaries and single stars show the same range of enrichment. This is attributed to the youth and/or wide separation of the binary systems in which the components have not (yet) experienced strong interaction. A clear trend of larger enrichment in higher luminosity objects is observed, consistent with what evolutionary models with rotation predict for a population of O stars at a given age. We confirm the weakness of winds in late O dwarfs. In general, mass loss rates derived from UV lines are lower than mass loss rates obtained from Ha. The UV mass loss rates are even lower than the single line driving limit in the latest type dwarfs. These issues are discussed in the context of the structure of massive stars winds. The evolutionary and spectroscopic masses are in agreement above 25 Msun but the uncertainties are large. Below this threshold, the few late-type O stars studied here indicate that the mass discrepancy still seems to hold.
Following on from two recent papers, here we examine the relationship between Newtonian gravitation and general relativity in more depth. This allows us to define a scalar potential which is just the proper time of the vector potential when the latter is interpreted as the geodesic velocity field. The results are closely related to spacetimes that admit Painlev\'{e}--Gullstrand synchronization.
We present Monte Carlo simulation results of the two-dimensional Zwanzig fluid, which consists of hard line segments which may orient either horizontally or vertically. At a certain critical fugacity, we observe a phase transition with a two-dimensional Ising critical point. Above the transition point, the system is in an ordered state, with the majority of particles being either horizontally or vertically aligned. In contrast to previous work, we identify the transition as being of the liquid-gas type, as opposed to isotropic-to-nematic. This interpretation naturally accounts for the observed Ising critical behavior. Furthermore, when the Zwanzig fluid is extended to more allowed particle orientations, we argue that in some cases the symmetry of a q-state Potts model with q>2 arises. This observation is used to interpret a number of previous results.
Assuming that vector and scalar diquarks exist in the Quark-Gluon Plasma near the critical temporature $T_c$, baryons can be produced through the processes of quarks and diquarks forming $({1/2})^+$ baryon states. Ratios of different baryons can be estimated through this method, if such kind of QGP with diquarks can exists.
Assuming GRH, we prove an explicit upper bound for the number of zeros of a Dedekind zeta function having imaginary part in $[T-a,T+a]$. We also prove a bound for the multiplicity of the zeros.
The concept of the one -- dimensional quantum mechanics in the relativistic configurational space (RQM) is reviewed briefly. The Relativistic Schroedinger equation (RSE) arising here is the finite-difference equation with the step equal to the Compton wave length of the particle. The different generalizations of the Dirac -- Infeld -- Hall factorizarion method for this case are constructed. This method enables us to find out all possible finite-difference generalizations of the most important nonrelativistic integrable case -- the harmonic oscillator. As it was shown (\cite{kmn},\cite{mir6}) in RQM the harmonic oscillator = $q$ -- oscillator. It is also shown that the relativistic and nonrelativistic QM's are different representations of the same theory. Thetransformation connecting these two representations is found in explicit form. It could be considered as the generalization of the Kontorovich -- Lebedev transformation.
I show that a flow structure where wide jets hit a slower expanding shell might be very efficient in channelling the kinetic energy of the jets to radiation, therefore accounting for, at a least a fraction of, intermediate luminosity optical transients (ILOTs) where the total radiation energy is much larger than what recombination energy of the outflow can supply. This type of flow might occur in the frame of the high-accretion-powered ILOT (HAPI) model, where there is a high mass accretion rate as a result of stellar merger or mass transfer in a binary system. I derive the condition on the jets half-opening angle for the jets not to penetrate through the slow shell, as well as the ratio of the photon diffusion time to expansion time. This ratio cannot be too large if a large fraction of the thermal energy is channelled to radiation. I apply the jet-powered radiation model to the Great Eruption of Eta Carinae, to V838~Mon, and to V4332~Sgr, and find a plausible set of parameters for these ILOTs. I expect the jet-powered radiation model to be more efficient in converting kinetic energy to radiation than ILOT models that are based on equatorial mass concentration. In many cases, thought, I expect both jets and equatorial mass concentration to occur in the same system.
We have conducted an automated search for galaxy clusters within a contiguous 16 square degree I-band survey in the north Galactic hemisphere. A matched filter detection algorithm identifies 444 cluster candidates in the range 0.2 <= z <= 1.2. The full catalog is presented along with the results from a follow-up spectroscopic survey. The estimated redshift distribution of the cluster candidates is consistent with a constant comoving density over the range 0.2 <= z_est <= 0.8. A decline in the cluster space density by more than a factor of 3 over this redshift range is rejected at >99.9% confidence level. We find that the space density of Lambda_CL >= 40 clusters in our survey lies in the range (1.6 - 1.8) x 10^{-5} h_{75}^{3} Mpc^{-3}, ~1.5 times higher than the local distribution of comparably rich Abell RC >= 0 clusters. The Lambda_CL distribution is consistent with a power-law. The discrepancy between the space density of Abell clusters and the clusters in this survey declines quickly as Lambda_CL increases, suggesting that the difference at lower richness is due to significant incompleteness in the Abell catalog. A percolation analysis reveals that 10 - 20% of the spectroscopically confirmed distant clusters are linked into superclusters at overdensities between 10 < {\delta\rho \over \rho} < 50, similar to what is seen in the local cluster distribution. This suggests that there has been little evolution of the cluster-cluster correlation length for z <= 0.5.
The Adler-Bardeen theorem has been proved only as a statement valid at all orders in perturbation theory, without any control on the convergence of the series. In this paper we prove a nonperturbative version of the Adler-Bardeen theorem in $d=2$ by using recently developed technical tools in the theory of Grassmann integration.
High angular resolution images of IRC+10216 are presented in several near infrared wavelengths spanning more than 8 years. These maps have been reconstructed from interferometric observations obtained at both Keck and the VLT, and also from stellar occultations by the rings of Saturn observed with the Cassini spacecraft. The dynamic inner regions of the circumstellar environment are monitored over eight epochs ranging between January 2000 and July 2008. The system is shown to experience substantial evolution within this period including the fading of many previously reported persistent features, some of which had been identified as the stellar photosphere. These changes are discussed in context of existing models for the nature of the underlying star and the circumstellar environment. With access to these new images, we are able to report that none of the previously identified bright spots in fact contain the star, which is buried in its own dust and not directly visible in the near infrared.
We propose closed-form expressions of the distributions of magnetic quantum number $M$ and total angular momentum $J$ for three and four fermions in single-$j$ orbits. The latter formulas consist of polynomials with coefficients satisfying congruence properties. Such results, derived using doubly-recursive relations over $j$ and the number of fermions, enable us to deduce explicit expressions for the total number of levels in the case of three-, four- and five-fermion systems. We present applications of these formulas, such as sum rules for six-$j$ and nine-$j$ symbols, obtained from the connection with fractional-parentage coefficients, an alternative proof of the Ginocchio-Haxton relation or cancellation properties of the number of levels with a given angular momentum.