ShantanuT01/DACTYL-Pretraining huggingface dataset:
We present a study of electric transport at high temperature in a model of strongly interacting spinless fermions without disorder. We use exact diagonalization to study the statistics of the energy eigenvalues, eigenstates, and the matrix elements of the current. These suggest that our nonrandom Hamiltonian behaves like a member of a certain ensemble of Gaussian random matrices. We calculate the conductivity $\sigma(\omega)$ and examine its behavior, both in finite size samples and as extrapolated to the thermodynamic limit. We find that $\sigma(\omega)$ has a prominent non-divergent singularity at $\omega=0$ reflecting a power-law long-time tail in the current autocorrelation function that arises from nonlinear couplings between the long-wavelength diffusive modes of the energy and particle number.
The purpose of this paper is to investigate the connection between context-free grammars and normal ordering problem, and then to explore various extensions of the Stirling grammar. We present grammatical characterizations of several well known combinatorial sequences, including the generalized Stirling numbers of the second kind related to the normal ordering problem and the $r$-Dowling polynomials. Also, possible avenues for future research are described.
The breakdown of the adiabatic Born-Oppenheimer approximation is striking dynamical phenomenon, however, it occurs only in a handful of layered materials. Here, I show that adiabaticity breaks down in doped single-layer transition metal dichalcogenides in a quite intriguing manner. Namely, significant nonadiabatic coupling, which acts on frequencies of the Raman-active modes, is prompted by a Lifshitz transition due to depopulation and population of multiple valence and conduction valleys, respectively. The outset of the latter event is shown to be dictated by the interplay of highly non-local electron-electron interaction and spin-orbit coupling. In addition, intense electron-hole pair scatterings due to electron-phonon coupling are inducing phonon linewidth modifications as a function of doping. Comprehending these intricate dynamical effects turns out to be a key for mastering characterization of electron doping in two-dimensional nano-devices by means of Raman spectroscopy.
The theory of quaternionic modular forms has been studied for decades as an example of the modular forms of many variables. The purpose of this study is to provide some congruence relations satisfied by such quaternionic modular forms.
The status of "ab initio" microscopic calculations of the 2H(p,gamma)3He and 3He(p,e+nu_e)4He reactions is reviewed. The methods used to generate accurate nuclear ground- and scattering-state wave functions, and to construct realistic electro-weak transition operators are described. The uncertainties in the theoretical predictions, particularly those relevant to the p-3He weak capture, are discussed. For the dp radiative capture, the theoretical results are compared with the TUNL data in the energy range 0--100 keV.
The exclusive photoproduction of $e^+e^-$ pairs from nucleons close to the vector meson production threshold ($1.4<\sqrt s <1.8$ GeV) results from two main processes: the emission of Bethe-Heitler pairs and the photoproduction of $\rho^0$- and $\omega$-mesons decaying into $e^+e^-$ pairs. The Bethe-Heitler amplitudes are purely electromagnetic and reflect mostly the nucleon magnetic structure. The $\gamma N\to e^+e^- N$ amplitudes arising from vector meson production and decay are derived from $\gamma N\to \rho^0 N$ and $\gamma N \to \omega N$ amplitudes supplemented by the Vector Meson Dominance assumption. The vector meson photoproduction amplitudes are calculated using a relativistic and unitary coupled-channel approach to meson-nucleon scattering. They depend sensitively on the coupling of vector fields to baryon resonances. The $\gamma N \to e^+e^- N$ differential cross sections display interference patterns. The interference of Bethe-Heitler pair production with vector meson $e^+e^-$ decay is quite small in the domain of validity of our model for all angles of the emitted $e^+e^-$ pair. The interference of $\rho^0$- and $\omega$-mesons in the $e^+e^-$ channel can be large. It is constructive for the $\gamma p \to e^+e^- p$ reaction and destructive for the $\gamma n \to e^+e^- n$ reaction. We discuss the shape and magnitude of the $e^+e^-$ pair spectra produced in the $\gamma p \to e^+e^- p$ and $\gamma n \to e^+e^- n$ reactions as functions of the pair emission angle and of the total center of mass energy $\sqrt s$.
We establish some well-posedness and comparison results for BSDEs driven by one- and multi-dimensional martingales. On the one hand, our approach is largely motivated by results and methods developed in Carbone et al. (2008) and El Karoui and Huang (1997). On the other hand, our results are also motivated by the recent developments in arbitrage pricing theory under funding costs and collateralization. A new version of the comparison theorem for BSDEs driven by a multi-dimensional martingale is established and applied to the pricing and hedging BSDEs studied in Bielecki and Rutkowski (2014) and Nie and Rutkowski (2014). This allows us to obtain the existence and uniqueness results for unilateral prices and to demonstrate the existence of no-arbitrage bounds for a collateralized contract when both agents have non-negative initial endowments.
The properties of relativistic radio jets are thought to be closely connected with the properties of accretion disks in active galactic nuclei. We explore this issue using a sample of 35 blazars with very-long baseline observations, for which we can estimate the kinetic powers of their relativistic jets, the bolometric luminosity of their accretion disks, and the masses of their black holes. Contrary to previous claims, we find that the jet kinetic power is significantly correlated with the disk luminosity. This supports the notion that the disk is somehow coupled to the jet, even on parsec scales. Moreover, we show that the correlation improves by including the black hole mass as a second parameter. The dominance of the jet, parameterized as the ratio of the jet kinetic power to the disk luminosity, is largely controlled by and is inversely correlated with the Eddington ratio of the accretion disk. This empirical relation should serve as a useful guide for theoretical models for jet formation.
Stationary features are occasionally observed in AGN jets. A notable example is the HST-1 knot in M87. Such features are commonly interpreted as re-confinement shocks in hydrodynamic jets or focusing nozzles in Poynting jets. In this paper we compute the structure and Lorentz factor of a highly magnetized jet confined by external pressure having a profile that flattens abruptly at some radius. We find the development of strong oscillations upon transition from the steeper to the flatter pressure profile medium. Analytic formula is derived for the location of the nodes of these oscillations. We apply the model to the M87 jet and show that if the jet remains magnetically dominated up to sub-kpc scales, then focusing is expected. The location of the HST-1 knot can be reconciled with recent measurements of the pressure profile around the Bondi radius if the jet luminosity satisfies $L_j\simeq10^{43}$ erg/s. However, we find that magnetic domination at the collimation break implies a Lorentz factor in excess of $10^2$, atypical to FRI sources. A much lower value of the asymptotic Lorentz factor would require substantial loading close to the black hole. In that case HST-1 may be associated with a collimation nozzle of a hydrodynamic flow.
The article revisits a result of Antonio Lei, David Loeffler, and Sarah Livia Zerbes concerning the structure of the image by the Iwasawa regulator map of the Iwasawa module associated with a semi-stable $p$-adic representation on an unramified finite extension of $Q_p$ and give a direct proof based on the results of "Repr\'esentations $p$-adiques et normes universelles: I. le cas cristallin" in the crystalline case and of "Th\'eorie d'Iwasawa des repr\'esentations $p$-adiques semi-stables" in the semi-stable case.
We present a backward approach for the interpretation of the evolution of the near-infrared and the far-infrared luminosity functions across the redshift range 0<z<3. In our method, late-type galaxies are treated by means of a parametric phenomenological method based on PEP/HerMES data up to z~4, whereas spheroids are described by means of a physically motivated backward model. The spectral evolution of spheroids is modelled by means of a single-mass model, associated to a present-day elliptical with K-band luminosity comparable to the break of the local early-type luminosity function. The formation of proto-spheroids is assumed to occurr across the redshift range 1< z < 5. The key parameter is represented by the redshift z_0.5 at which half proto-spheroids are already formed. A statistical study indicates for this parameter values between z_0.5=1.5 and z_0.5=3. We assume as fiducial value z_0.5~2, and show that this assumption allows us to describe accourately the redshift distributions and the source counts. By assuming z_0.5 ~ 2 at the far-IR flux limit of the PEP-COSMOS survey, the PEP-selected sources observed at z>2 can be explained as progenitors of local spheroids caught during their formation. We also test the effects of mass downsizing by dividing the spheroids into three populations of different present-day stellar masses. The results obtained in this case confirm the validity of our approach, i.e. that the bulk of proto-spheroids can be modelled by means of a single model which describes the evolution of galaxies at the break of the present-day early type K-band LF.
Many real-world networks have properties of small-world networks, with clustered local neighborhoods and low average-shortest path (ASP). They may also show a scale-free degree distribution, which can be generated by growth and preferential attachment to highly connected nodes, or hubs. However, many real-world networks consist of multiple, inter-connected clusters not normally seen in systems grown by preferential attachment, and there also exist real-world networks with a scale-free degree distribution that do not contain highly connected hubs. We describe spatial growth mechanisms, not using preferential attachment, that address both aspects.
We find that the spin-charge motion in a strongly confined two-dimensional hole gas (2DHG) supports a propagating mode of cubic dispersion apart from the diffusive mode due to momentum scattering. Propagating modes seem to be a generic property of systems with spin-orbit coupling. Through a rigorous Keldysh approach, we obtain the transport equations for the 2DHG, we analyze the behavior of the hole spin relaxation time, the diffusion coefficients, and the spin-charge coupled motion.
We study the random \'etale algebra generated by a random polynomial with i.i.d. coefficients distributed according to Haar measure normalized on $\mathbb{Z}_p$. We determine the probability that this random algebra is an unramified field, explicitly. In addition, we prove a private case of a conjecture made by Bhargava, Cremona, Fisher, and Gajovi\'c. More precisely, we show that this probability is a rational function of $p$ that is invariant under replacing $p$ by $1/p$.
A low-energy background field solution describing D-membrane configurations is constructed which is distinguished by the appearance of a Hermitian metric on the internal space. This metric is composed of a number of independent harmonic functions on the transverse space. Thus this construction generalizes the usual harmonic superposition rule. The BPS bound of these solutions is shown to be saturated indicating that they are supersymmetric. By means of T-duality, we construct more solutions of the IIA and IIB theories.
We compute the $\alpha_s^2 n_f$ perturbative QCD contribution to semileptonic B decay, including the finite mass of the charm quark. This result provides an estimate of the size of the two-loop correction, which is found to be about 50\% of the one-loop correction. We use these results to set the scale for the one-loop correction using the scheme of Brodsky, Lepage and Mackenzie and find a BLM scale of $\mu_{\rm BLM} = 0.13\, m_b$, when the inclusive semileptonic rate is expressed in terms of the $b$ and $c$ quark pole masses and the \msbar strong coupling. The two loop correction lies roughly midway between that obtained at $m_c=0$ and that obtained in the Shifman-Voloshin limit $m_b, m_c\gg m_b-m_c\gg\Lambda_{\rm QCD}$ while the corresponding BLM scale is somewhat closer to that obtained in the former case.
We study maximally supersymmetric Anti-de Sitter backgrounds in consistent N=2 truncations of type IIB supergravity compactified on the Sasaki-Einstein manifold $T^{1,1}$. In particular, we focus on truncations that contain fields coming from the nontrivial second and third cohomology forms on $T^{1,1}$. These give rise to N=2 supergravity coupled to two vector- and two hypermultiplets (Betti-vector truncation) or one vector- and three hypermultiplets (Betti-hyper truncation), respectively. We find that both truncations admit AdS$_5$ backgrounds with the gauge group always being broken but containing at least an $U(1)_R$ factor. Moreover, in both cases we show that the moduli space of AdS vacua is nontrivial and of maximal dimension. Finally, we explicitly compute the metrics on these moduli spaces.
The 30 Doradus (30 Dor) nebula in the Large Magellanic Cloud (LMC) is the brightest HII region in the Local Group and a prototype starburst similar to those found in high redshift galaxies. It is thus a stepping stone to understand the complex formation processes of stars in starburst regions across the Universe. Here, we have studied the formation history of massive stars in 30 Dor using masses and ages derived for 452 mainly OB stars from the spectroscopic VLT-FLAMES Tarantula Survey (VFTS). We find that stars of all ages and masses are scattered throughout 30 Dor. This is remarkable because it implies that massive stars either moved large distances or formed independently over the whole field of view in relative isolation. We find that both channels contribute to the 30 Dor massive star population. Massive star formation rapidly accelerated about 8 Myr ago, first forming stars in the field before giving birth to the stellar populations in NGC 2060 and NGC 2070. The R136 star cluster in NGC 2070 formed last and, since then, about 1 Myr ago, star formation seems to be diminished with some continuing in the surroundings of R136. Massive stars within a projected distance of 8 pc of R136 are not coeval but show an age range of up to 6 Myr. Our mass distributions are well populated up to $200\,\mathrm{M}_\odot$. The inferred IMF is shallower than a Salpeter-like IMF and appears to be the same across 30 Dor. By comparing our sample of stars to stellar models in the Hertzsprung-Russell diagram, we find evidence for missing physics in the models above $\log L/\mathrm{L}_\odot=6$ that is likely connected to enhanced wind mass loss for stars approaching the Eddington limit. [abridged]
The linearly polarized spectrum of the solar limb radiation produced by scattering processes is of great diagnostic potential for exploring the magnetism of the solar atmosphere. This spectrum shows an impressive richness of spectral details and enigmatic Q/I signals, whose physical origin must be clearly understood before they can be exploited for diagnostic purposes. The most enduring enigma is represented by the polarization signals observed in the D1 resonance lines of Na I (5896 A) and Ba II (4934 A), which were expected to be intrinsically unpolarizable. The totality of sodium and 18% of barium have hyperfine structure (HFS), and it has been argued that the only way to produce a scattering polarization signal in such lines is through the presence of a substantial amount of atomic polarization in their lower HFS levels. The strong sensitivity of these long-lived levels to depolarizing mechanisms led to the paradoxical conclusion that the observed D1-line polarization is incompatible with the presence in the lower solar chromosphere of inclined magnetic fields sensibly stronger than 0.01 G. Here we show that by properly taking into account the fact that the solar D1-line radiation has a non-negligible spectral structure over the short frequency interval spanned by the HFS transitions, it is possible to produce scattering polarization signals in the D1 lines of Na I and Ba II without the need of ground-level polarization. The resulting linear polarization is not so easily destroyed by elastic collisions and/or magnetic fields.
We establish the central limit theorem for the number of real roots of the Weyl polynomial $P_n(x)=xi_0 + xi_1 x+ ... + xi_n (n!)^{(-1/2)} x^n$, where $xi_i$ are iid Gaussian random variables. The main ingredients in the proof are new estimates for the correlation functions of the real roots of $P_n$ and a comparison argument exploiting local laws and repulsion properties of these real roots.
Recent molecular line observations with ALMA and NOEMA in several Brightest Cluster Galaxies (BCG) have revealed the large-scale filamentary structure at the center of cool core clusters. These filaments extend over 20-100kpc, they are tightly correlated with ionized gas (H$\alpha$, [NII]) emission, and have characteristic shapes: either radial and straight, or also showing a U-turn, like a horse-shoe structure.   The kinematics is quite regular and laminar, and the derived infall time is much longer than the free-fall time. The filaments extend up to the radius where the cooling time becomes larger than the infall time. Filaments can be perturbed by the sloshing of the BCG in its cluster, and spectacular cooling wakes have been observed. Filaments tend to occur at the border of cavities driven in the X-ray gas by the AGN radio jets. Observations of cool core clusters support the thermal instability scenario, which accounts for the multiphase medium in the upper atmospheres of BCG, where the right balance between heating and cooling is reached, and a chaotic cold gas accretion occurs. Molecular filaments are also seen associated to ram-pressure stripped spiral galaxies in rich galaxy clusters, and in jet-induced star formation, suggesting a very efficient molecular cloud formation even in hostile cluster environments.
We consider novel nonperturbative effects of type I theories compactified on singular ALE spaces obtained by adding NS branes. Such effects include a description of small $E_8$ instantons at singularities.
The Cataclysmic Variable Section of the American Association of Variable Star Observers (AAVSO) has initiated an observing campaign to study a subset of dwarf novae (DNe), known as Z Cam type (UGZ). We call this program the Z CamPaign. Since there is no strong agreement between the various published catalogues as to which few dozen DNe are actually Z Cam type systems, our primary goal is to accumulate enough data to construct detailed light curves, covering the entire range of variability, to determine unequivocally the 30 Z CamPaign subjects' membership in the UGZ class of DNe. We discuss the organization, science goals, and some early results of the Z CamPaign in detail.
We discuss baryon and lepton violation in the context of a simple 5-dimensional grand unified model, based on the orbifold S^1/(Z_2 x Z_2'). While gauge and Higgs degrees of freedom live in the bulk, matter is located on the boundaries of the space-time. We show that proton decay is naturally suppressed or even forbidden by suitable implementations of the parity symmetries in the matter sector. The corresponding mechanism does not affect the SU(5) description of fermion masses also including neutrinos.
Embedding 3D morphable basis functions into deep neural networks opens great potential for models with better representation power. However, to faithfully learn those models from an image collection, it requires strong regularization to overcome ambiguities involved in the learning process. This critically prevents us from learning high fidelity face models which are needed to represent face images in high level of details. To address this problem, this paper presents a novel approach to learn additional proxies as means to side-step strong regularizations, as well as, leverages to promote detailed shape/albedo. To ease the learning, we also propose to use a dual-pathway network, a carefully-designed architecture that brings a balance between global and local-based models. By improving the nonlinear 3D morphable model in both learning objective and network architecture, we present a model which is superior in capturing higher level of details than the linear or its precedent nonlinear counterparts. As a result, our model achieves state-of-the-art performance on 3D face reconstruction by solely optimizing latent representations.
In this communication I analyze the problem of complete exceptionality of wave propagation in a class of spin 2 field theories. I show that, under the imposition of the good weak-field limit, only two Lagrangians are completely exceptional. These are the linear Fierz Lagrangian, and a Born-Infeld-like Lagrangian. As a byproduct, I reobtain the result that in a nonlinear theory, spin 2 particles follow an effective metric that depends on the nonlinearities of the Lagrangian.
We present a comprehensive study of event-by-event multiplicity fluctuations in nucleon-nucleon and nucleus-nucleus interactions from AGS/FAIR to RHIC energies within the UrQMD transport approach. The scaled variances of negative, positive, and all charged hadrons are analysed. The scaled variance in central Pb+Pb collisions increases with energy and behaves similar to inelastic p+p interactions. We find a non-trivial dependence of multiplicity fluctuations on the rapidity and transverse momentum interval used for the analysis and on the centrality selection procedure. Quantitative predictions for the NA49 experiment are given, taking into account the acceptance of the detector and the selection procedure of central events.
Understanding how galaxies cease to form stars represents an outstanding challenge for galaxy evolution theories. This process of "star formation quenching" has been related to various causes, including Active Galactic Nuclei (AGN) activity, the influence of large-scale dynamics, and the environment in which galaxies live. In this paper, we present the first results from a follow-up of CALIFA survey galaxies with observations of molecular gas obtained with the APEX telescope. Together with EDGE survey CARMA observations, we collect $^{12}$CO observations that cover approximately one effective radius in 472 CALIFA galaxies. We observe that the deficit of galaxy star formation with respect to the star formation main sequence (SFMS) increases with the absence of molecular gas and with a reduced efficiency of conversion of molecular gas into stars, in line with results of other integrated studies. However, by dividing the sample into galaxies dominated by star formation and galaxies quenched in their centres (as indicated by the average value of the H$\alpha$ equivalent width), we find that this deficit increases sharply once a certain level of gas consumption is reached, indicating that different mechanisms drive separation from the SFMS in star-forming and quenched galaxies. Our results indicate that differences in the amount of molecular gas at a fixed stellar mass are the primary driver for the dispersion in the SFMS, and the most likely explanation for the start of star-formation quenching. However, once a galaxy is quenched, changes in star formation efficiency drive how much a retired galaxy separates in star formation rate from star-forming ones of similar masses. In other words, once a paucity of molecular gas has significantly reduced star formation, changes in the star formation efficiency are what drives a galaxy deeper into the red cloud, retiring it.