ShantanuT01/DACTYL-Pretraining huggingface dataset:
We compute the matrix elements for pion emission from the nucleon induced by twist-two light-cone operators in the kinematics where the pion is close to threshold. It is shown that the results of heavy baryon ChPT are in agreement with the results from the soft-pion theorem approach. Therefore the amplitude of soft-pion emission is directly related to the generalized parton distributions in the nucleon.
Motivated by the works of Cheskidov, Lopes Filho, Nussenzveig Lopes and Shvydkoy in [8, Commun. Math. Phys. 348: 129-143, 2016] and Chen and Yu in [5, J. Math. Pures Appl. 131: 1-16, 2019], we address how the $L^p$ control of vorticity could influence the energy conservation for the incompressible homogeneous and nonhomogeneous Euler equations in this paper. For the homogeneous flow in the periodic domain or whole space, we provide a self-contained proof for the criterion $\omega=\text{curl}u\in L^{3}(0,T;L^{\frac{3n}{n+2}}(\Omega))\,(n=2,3)$, which generalizes the corresponding result in [8] and can be viewed as in Onsager critical spatio-temporal spaces. Regarding the nonhomogeneous flow, it is shown that the energy is conserved as long as the vorticity lies in the same space as before and $\nabla\sqrt{\rho}$ belongs to $L^{\infty}(0,T;L^{n}(\mathbb{T}^{n}))\,(n=2,3)$, which gives an affirmative answer to a problem proposed by Chen and Yu in [5].
We develop combinatorial methods for computing the rotation distance between binary trees, i.e., equivalently, the flip distance between triangulations of a polygon. As an application, we prove that, for each n, there exist size n trees at distance 2n - O(sqrt(n)).
We present the analysis of Halpha3, an Halpha imaging survey of 409 galaxies selected from the HI Arecibo ALFALFA Survey in the Local Supercluster, including the Virgo cluster. We explore the relations between the stellar mass, the HI mass and the current, massive SFR of nearby galaxies in the Virgo cluster and we compare them with those of isolated galaxies in the Local Supercluster, disentangling the role of the environment in shaping the star formation properties of galaxies at the present cosmological epoch. We investigate the relationships between atomic neutral gas and newly formed stars in different environments, across many morphological types, and over a wide range of stellar masses adopting an updated calibration of the HI deficiency parameter. Studying the mean properties of late-type galaxies in the Local Supercluster, we find that galaxies in increasing local galaxy density conditions (or decreasing projected angular separation from M87) show a significant decrease in the HI content and in the mean specific star formation rate, along with a progressive reddening of their stellar populations. The gradual quenching of the star formation occurs outside-in, consistently with the predictions of the ram pressure model. Once considered as a whole, the Virgo cluster is effective in removing neutral hydrogen from galaxies, and this perturbation is strong enough to appreciably reduce the SFR of its entire galaxy population. An estimate of the present infall rate of 300-400 galaxies per Gyr in the Virgo cluster is obtained from the number of existing HI-rich late-type systems, assuming 200-300 Myr as the time scale for HI ablation. If the infall process has been acting at constant rate this would imply that the Virgo cluster has formed approximately 2 Gyr ago, consistently with the idea that Virgo is in a young state of dynamical evolution.
We reveal the rich magnon topology in honeycomb bilayer ferromagnets (HBF) induced by the combined effect of interlayer exchange, Dzyaloshinskii-Moriya interaction (DMI), and electrostatic doping (ED). In particular, we present a systematic study of the Hamiltonian non-adiabatic evolution in the HBF parametric space, spanned by the symmetry-breaking terms (DMI and ED) and interlayer exchange. We determine the band closure manifolds which are found to divide the parametric space into six distinct regions, matched with five distinct topological phases and one topologically trivial phase. The characteristic Chern numbers and thermal Hall conductivities are calculated for the topological phases. Edge spectra, dictated by the bulk-edge correspondence, are also analyzed in the nanoribbon version of the model. Both bulk and edge spectra are found to be nonreciprocal as a consequence of ED and edge magnons are observed to counter propagate on opposite edges. The predicted results offer new insights on the manipulation of magnonic Chern numbers and magnon topological transport via experimentally tunable parameters.
For a hypersurface in a projective space, we consider the set of pairs of a point and a line in the projective space such that the line intersects the hypersurface at the point with a fixed multiplicity. We prove that this set of pairs forms a smooth variety for a general hypersurface.
We present evidence for the existence of an IRAC excess in the spectral energy distribution (SED) of 5 galaxies at 0.6<z<0.9 and 1 galaxy at z=1.7. These 6 galaxies, located in the Great Observatories Origins Deep Survey field (GOODS-N), are star forming since they present strong 6.2, 7.7, and 11.3 um polycyclic aromatic hydrocarbon (PAH) lines in their Spitzer IRS mid-infrared spectra. We use a library of templates computed with PEGASE.2 to fit their multiwavelength photometry and derive their stellar continuum. Subtraction of the stellar continuum enables us to detect in 5 galaxies a significant excess in the IRAC band pass where the 3.3 um PAH is expected. We then assess if the physical origin of the IRAC excess is due to an obscured active galactic nucleus (AGN) or warm dust emission. For one galaxy evidence of an obscured AGN is found, while the remaining four do not exhibit any significant AGN activity. Possible contamination by warm dust continuum of unknown origin as found in the Galactic diffuse emission is discussed. The properties of such a continuum would have to be different from the local Universe to explain the measured IRAC excess, but we cannot definitively rule out this possibility until its origin is understood. Assuming that the IRAC excess is dominated by the 3.3 um PAH feature, we find good agreement with the observed 11.3 um PAH line flux arising from the same C-H bending and stretching modes, consistent with model expectations. Finally, the IRAC excess appears to be correlated with the star-formation rate in the galaxies. Hence it could provide a powerful diagnostic for measuring dusty star formation in z>3 galaxies once the mid-infrared spectroscopic capabilities of the James Webb Space Telescope become available.
Self-energy corrections due to fermion-magnon interaction are studied in the antiferromagnetic state of the $t-t'-t''$ Hubbard model within the rainbow (noncrossing) approximation in the full $U$ range from weak to strong coupling. The role of classical (mean-field) features of fermion and magnon dispersion, associated with finite $U,t',t''$, are examined on quantum corrections to quasiparticle energy, weight, one-particle density of states etc. A finite-$U$ induced classical dispersion term, absent in the $t-J$ model, is found to play an important role in suppressing the quasiparticle weight for states near ${\bf k}=(0,0)$, as seen in cuprates. For intermediate $U$, the renormalized AF band gap is found to be nearly half of the classical value, and the weak coupling limit is quite non-trivial due to strongly suppressed magnon amplitude. For finite $t'$, the renormalized AF band gap is shown to vanish at a critical interaction strength $U_c$, yielding a spin fluctuation driven first-order AF insulator - PM metal transition. Quasiparticle dispersion evaluated with the same set of Hubbard model cuprate parameters, as obtained from a recent magnon spectrum fit, provides excellent agreement with ARPES data for $\rm Sr_2 Cu O_2 Cl_2 $.
In this paper, we study the ergodicity of invariant sublinear expectation of sublinear Markovian semigroup. For this, we first develop an ergodic theory of an expectation-preserving map on a sublinear expectation space. Ergodicity is defined as any invariant set either has $0$ capacity itself or its complement has $0$ capacity. We prove, under a general sublinear expectation space setting, the equivalent relation between ergodicity and the corresponding transformation operator having simple eigenvalue $1$, and also with Birkhoff type strong law of large numbers if the sublinear expectation is regular. For sublinear Markov process, we prove that its ergodicity is equivalent to the Markovian semigroup having eigenvalue $1$ and it is simple in the space of bounded measurable functions. As an example we show that $G$-Brownian motion $\{B_t\}_{t\geq 0}$ on the unit circle has an invariant expectation and is ergodic if and only if ${\mathbb E}(-(B_1)^2)<0$. Moreover, it is also proved in this case that the invariant expectation is regular and the canonical stationary process has no mean-uncertainty under the invariant expectation.
This paper studies optimal Public Private Partnerships contract between a public entity and a consortium, in continuous-time and with a continuous payment, with the possibility for the public to stop the contract. The public ("she") pays a continuous rent to the consortium ("he"), while the latter gives a best response characterized by his effort. This effect impacts the drift of the social welfare, until a terminal date decided by the public when she stops the contract and gives compensation to the consortium. Usually, the public can not observe the effort done by the consortium, leading to a principal agent's problem with moral hazard. We solve this optimal stochastic control with optimal stopping problem in this context of moral hazard. The public value function is characterized by the solution of an associated Hamilton Jacobi Bellman Variational Inequality. The public value function and the optimal effort and rent processes are computed numerically by using the Howard algorithm. In particular, the impact of the social welfare's volatility on the optimal contract is studied.
We investigate the early onset of pionic color transparency ($\pi$CT) observed at Jefferson Laboratory (JLAB) in semi--exclusive pion electroproduction reaction $A(e,e'\pi^+)$ off nuclei. In the present description the primary $\gamma^*p \to \pi^+ n$ interaction is described very well both for the longitudinal and the transverse polarizations. For the final state interactions a coupled--channel treatment of the interactions of transmitted hadrons allows to go beyond the Glauber approximation. We show that a proper distinction between the soft hadronic and hard partonic components of the electroproduction amplitude is essential for a quantitative description of the measured nuclear transparency. The data are well reproduced if one assumes that point--like configurations are produced in the regime of hard deep--inelastic scattering (DIS) off partons and dominate the transverse channel.
We establish the fluctuation theorem in the presence of information exchange between a nonequilibrium system and other degrees of freedom such as an observer and a feedback controller, where the amount of information exchange is added to the entropy production. The resulting generalized second law sets the fundamental limit of energy dissipation and energy cost during the information exchange. Our results apply not only to feedback-controlled processes but also to a much broader class of information exchanges, and provides a unified framework of nonequilibrium thermodynamics of measurement and feedback control.
We investigate the detectability of leading-order relativistic effects in the bispectrum of future 21cm intensity mapping surveys. The relativistic signal arises from Doppler and other line-of-sight effects in redshift space. In the power spectrum of a single tracer, these effects are suppressed by a factor $\cH^2/k^2$. By contrast, in the bispectrum the relativistic signal couples to short-scale modes, leading to an imaginary contribution that scales as $\cH/k$, thus increasing the possibility of detection. Previous work has shown that this relativistic signal is detectable in a Stage IV H$\alpha$ galaxy survey. {We show that the signal is also detectable by next-generation 21cm intensity maps, but typically with a lower signal-to-noise, due to foreground and telescope beam effects.
Strong broad emission lines are the most important signatures of active galactic nuclei. These lines allowed to discover the cosmological nature of quasars, and at present these lines allow for convenient method of weighting the black holes residing in their nuclei. However, a question remains why such strong lines form there in the first place. Specifically, in the case of Low Ionization Lines, there must be a mechanism which leads to an efficient rise of the material from the surface of the accretion disk surrounding a black hole but at the same time should not give a strong signature of the systematic outflow, as the Balmer lines are not significantly shifted with respect to the Narrow Line Region. We determine the effective temperature of the accretion disk underlying the H$\beta$ line at the basis of the time delay measured from reverberation and the simple Shakura-Sunyaev theory of accretion disks. We obtain that this temperature is universal, and equal $995 \pm 74$ K, independently from the black hole mass and accretion rate of the source. This result suggests to us that the dust formation in the disk atmosphere is responsible for the strong rise of the material. However, as the material gains height above the disk it becomes irradiated, the dust evaporates, the radiation pressure force suddently drops and the material fall back again at the disk. Therefore, a failed wind forms. In the simple version of the model the disk irradiation is neglected, but in the present paper we also discuss this irradiation and we use the observed variation of the Broad Line Region in NGC 5548 to constrain the character of this non-local non-stationary phenomenon. The current instruments cannot resolve the Broad Line Region but future instrumentation may allow to test the model directly.
Many complex phenomena occurring in physics,chemistry, biology, finance, etc. can be reduced, by some projection process, to a 1-d stochastic Differential Equation (SDE) for the variable of interest. Typically, this SDE is both non-linear and non-markovian, so a Fokker Planck equation (FPE), for the probability density function (PDF), is generally not obtainable. However, a FPE is desirable because it is the main tool to obtain relevant analytical statistical information such as stationary PDF and First Passage Time. This problem has been addressed by many authors in the past, but due to an incorrect use of the interaction picture (the standard tool to obtain a reduced FPE) previous theoretical results were incorrect, as confirmed by direct numerical simulation of the SDE. We will show, in general, how to address the problem and we will derived the correct best FPE from a perturbation approach. The method followed and the results obtained have a general validity beyond the simple case of exponentially correlated Gaussian driving used here as an example; they can be applied even to non Gaussian drivings with a generic time correlation.
We perform inelastic neutron scattering measurements on the molecular nanomagnet Mn_12-acetate to measure the excitation spectrum up to 45meV (500K). We isolate magnetic excitations in two groups at 5-6.5meV (60-75K) and 8-10.5meV (95-120K), with higher levels appearing only at 27meV (310K) and 31meV (360K). From a detailed characterization of the transition peaks we show that all of the low-energy modes appear to be separate S = 9 excitations above the S = 10 ground state, with the peak at 27meV (310K) corresponding to the first S = 11 excitation. We consider a general model for the four exchange interaction parameters of the molecule. The static susceptibility is computed by high-temperature series expansion and the energy spectrum, matrix elements and ground-state spin configuration by exact diagonalization. The theoretical results are matched with experimental observation by inclusion of cluster anisotropy parameters, revealing strong constraints on possible parameter sets. We conclude that only a model with dominant exchange couplings J_1 ~ J_2 ~ 5.5meV (65K) and small couplings J_3 ~ J_4 ~ 0.6meV (7K) is consistent with the experimental data.
A scheme to generate shared tripartite entangled states, with two-trapped atoms in a cavity held by Alice (qubits A1 and A2) entangled to a single trapped atom in a remote lab owned by Bob (B), is proposed. The entanglement is generated through interaction of trapped atoms with two mode squeezed light shared by the two cavities. The proposed scheme is an extension of the proposal of ref. [W. Son, M. S. Kim, J. Lee, and D. Ahn, J. Mod. Opt. 49, 1739 (2002)], where the possibility of entangling two remote qubits using a bipartite continuous variable state was examined. While the global negativity detects the free entanglement of the three atom mixed state, the bound entanglement is detected by the negativity calculated from pure state decomposition of the state operator. The partial negativities calculated by selective partial transposition of the three atom mixed state detect the pairwise entanglement of qubit pairs A1B, A2B, and A1A2. The entanglement of three atoms is found to be W-like, no GHZ like quantum correlations being generated.
This note formulates a conjecture generalizing both the abc conjecture of Masser-Oesterl\'e and the author's diophantine conjecture for algebraic points of bounded degree. It also shows that the new conjecture is implied by the earlier conjecture.   As with most of the author's conjectures, this new conjecture stems from analogies with Nevanlinna theory; in this case it corresponds to a Second Main Theorem in Nevanlinna theory with truncated counting functions. The original abc conjecture of Masser and Oesterl\'e corresponds to the Second Main Theorem with truncated counting functions on P^1 for the divisor [0]+[1]+[\infty].
This paper seeks a quantitative comparison between the curves in the KPZ line ensemble [CH16] and a standard Brownian bridge under the $t^{1/3}$ vertical and $t^{2/3}$ horizontal scaling. The estimate we obtained is parallel to the one established in [Ham1], where the Airy line ensemble was studied. Our main tool is the soft Brownian Gibbs property enjoyed by the KPZ line ensemble. In view of the Gibbs property, the KPZ line ensemble differs from the Airy line ensemble mainly due to the intersecting nature of its curves, which results in the main technical difficulty in this paper. We develop a resampling framework, the soft jump ensemble, to tackle this difficulty. Our method is highly inspired by the jump ensemble technique developed in [Ham1].
The positron excess measured by PAMELA and AMS can only be explained if there is one or several sources injecting them. Moreover, at the highest energies, it requires the presence of nearby ($\sim$hundreds of parsecs) and middle age (maximum of $\sim$hundreds of kyr) source. Pulsars, as factories of electrons and positrons, are one of the proposed candidates to explain the origin of this excess. To calculate the contribution of these sources to the electron and positron flux at the Earth, we developed EDGE (Electron Diffusion and Gamma rays to the Earth), a code to treat diffusion of electrons and compute their diffusion from a central source with a flexible injection spectrum. We can derive the source's gamma-ray spectrum, spatial extension, the all-electron density in space and the electron and positron flux reaching the Earth. We present in this contribution the fundamentals of the code and study how different parameters affect the gamma-ray spectrum of a source and the electron flux measured at the Earth.
Blazhko stars from the extended $BVI_{\mathrm C}$ time series of RRab stars in the globular cluster, M3, are analysed. This is the largest sample of Blazhko stars with full details of their Blazhko properties in a homogeneous stellar system. Blazhko periods and light-curve solutions are determined/estimated for 83 fundamental-mode variables. The lack of phase modulation in Oosterhoff-type~II stars and the diminishing relative strength of the modulation in long-period Oosterhoff-type~I stars are the regular tendencies found between the pulsation and modulation properties of Blazko stars. Similarly to previous results, no modulation of the longest-period stars is detected. The onset of the modulation in a previously regular RRab star, and the similar distribution of modulated and non-modulated stars imply that the modulation is a temporal property of RRL stars, which may occur at any time in any RRab star except the coolest ones. Comparing the modulation periods in M3 and in other samples of Blazhko stars, the mean log$(P_{\mathrm {mod}})$ value is found to depend on the metallicity of the system. The separation of the temperature- and radius-change induced variations supports our previous finding that the photometric radius variation does not show any modulation. The pulsation-averaged mean brightness and temperature of Blazhko stars are found to be larger in the large-amplitude phase of the modulation than in the small-amplitude phase. The larger the amplitude of the modulation, the larger changes of the mean parameters are detected.
We prove that every log crepant birational morphism between log terminal surfaces is decomposed into log-flopping type divisorial contraction morphisms and log blow-downs. Repeating these two kinds of contractions we reach a minimal log minimal surface from any log minimal surface.
Whereas massless Dirac fermions in monolayer graphene exhibit Klein tunneling when passing through a potential barrier upon normal incidence, such a barrier totally reflects massive Dirac fermions in bilayer graphene due to difference in chirality. We show that, in the presence of magnetic barriers, such massive Dirac fermions can have transmission through even at normal incidence. The general consequence of this behaviour for multilayer graphene consisting of massless and massive modes are mentioned. We also briefly discuss the effect of a bias voltage on such magnetotransport.
We unify all existing results on the change of the speed of low--energy photons due to modifications of the vacuum, finding that it is given by a universal constant times the quotient of the difference of energy densities between the usual and modified vacua over the mass of the electron to the fourth power. Whether photons move faster or slower than $c$ depends only on the lower or higher energy density of the modified vacuum, respectively. Physically, a higher energy density is characterized by the presence of additional particles (real or virtual) in the vacuum whereas a lower one stems from the absence of some virtual modes. We then carry out a systematic study of the speed of propagation of massless particles for several field theories up to two loops on a thermal vacuum. Only low--energy massless particles corresponding to a massive theory show genuine modifications of their speed while remaining massless. All other modifications are mass-related, or running mass-related. We also develop a formalism for the Casimir vacuum which parallels the thermal one and check that photons travel faster than $c$ between plates.
We prove that the viscous Burgers equation has a globally defined smooth solution in all dimensions provided the initial condition and the forcing term are smooth and bounded together with their derivatives. Such solutions may have infinite energy. The proof does not rely on energy estimates, but on a combination of the maximum principle and quantitative Schauder estimates. We obtain precise bounds on the sup norm of the solution and its derivatives, making it plain that there is no exponential increase in time. In particular, these bounds are time-independent if the forcing term is zero. To get a classical solution, it suffices to assume that the initial condition and the forcing term have bounded derivatives up to order two.