ShantanuT01/DACTYL-Pretraining huggingface dataset:
We compute from first principles the infrared dispersion of the nonlinear susceptibility $\chi^{(2)}$ in zincblende semiconductors. At terahertz frequencies the nonlinear susceptibility depends not only on the purely electronic response $\chi^{(2)}_{\infty}$, but also on three other parameters $C_1$, $C_2$ and $C_3$ describing the contributions from ionic motion. They relate to the TO Raman polarizability, the second-order displacement-induced dielectric polarization, and the third-order lattice potential. Contrary to previous theory, we find that mechanical anharmonicity ($C_3$) dominates over electrical anharmonicity ($C_2$), which is consistent with recent experiments on GaAs. We predict that the sharp minimum in the intensity of second-harmonic generation recently observed for GaAs between $\omega_{\rm TO}/2$ and $\omega_{\rm TO}$ does not occur for several other III-V compounds.
The synchronization of charge oscillations after photoexcitation that has been realized through the emergence of an electronic breathing mode on dimer lattices is studied here from the viewpoint of the competition between interactions and randomness. We employ an extended Hubbard model at three-quarter filling on a simple dimer lattice and add random numbers to all transfer integrals between nearest-neighbor sites. Photoinduced dynamics are calculated using the time-dependent Schr\"odinger equation by the exact diagonalization method. Although the randomness tends to unsynchronize charge oscillations on different bonds during and after photoexcitation, sufficiently strong on-site repulsion $U$ overcomes this effect and synchronizes these charge oscillations some time after strong photoexcitation. The degree of synchronization is evaluated using an order parameter that is derived from the time profiles of the current densities on all bonds. As to the nearest-neighbor interaction $V$, if $V$ is weakly attractive, it increases the order parameter by facilitating the charge oscillations. The relevance of these findings to previously reported experimental and theoretical results for the organic conductor $\kappa$-(bis[ethylenedithio]tetrathiafulvalene)$_2$Cu[N(CN)$_2$]Br is discussed.
We give a procedure to determine equations for the modular curves $X_0(N)$ which are bielliptic and equations for the 30 values of $N$ such that $X_0(N)$ is bielliptic and nonhyperelliptic are presented.
The discussion is limited to first-class parametrized systems, where the definition of time evolution and observables is not trivial, and to finite dimensional systems in order that technicalities do not obscure the conceptual framework. The existence of reasonable true, or physical, degrees of freedom is rigorously defined and called {\em local reducibility}. A proof is given that any locally reducible system admits a complete set of perennials. For locally reducible systems, the most general construction of time evolution in the Schroedinger and Heisenberg form that uses only geometry of the phase space is described. The time shifts are not required to be 1symmetries. A relation between perennials and observables of the Schroedinger or Heisenberg type results: such observables can be identified with certain classes of perennials and the structure of the classes depends on the time evolution. The time evolution between two non-global transversal surfaces is studied. The problem is posed and solved within the framework of the ordinary quantum mechanics. The resulting non-unitarity is different from that known in the field theory (Hawking effect): state norms need not be preserved so that the system can be lost during the evolution of this kind.
We investigate the giant gravitons in the maximally supersymmetric IIB pp-wave from several viewpoints: (i) the dynamics of D3-branes, (ii) the world-sheet description and (iii) the correlation functions in the dual N=4 Yang-Mills theory. In particular, we derive the BPS equation of a D3-brane with magnetic flux, which is equivalent to multiple D-strings, and discuss the behavior of solutions in the presence of RR-flux. We find solutions which represent the excitations of the giant gravitons in that system.
In this paper, we study a Backward Stochastic Differential Equation with Jumps (BSDEJs in short) where the jumps have infinite activity. Following a forward approach based on Exponential Quadratic semimartingale, we prove the existence of solution of Quadratic BSDEJs with unbounded terminal condition and quadratic growth in z.
Ultrahigh energy cosmic rays are the most energetic of any subatomic particles ever observed in nature. The quest for their mysterious origin is currently a major scientific challenge. Here we explore the possibility that these particles originate from nearby starburst galaxies, a scenario that matches the recent observation by the Telescope Array experiment of a cosmic-ray hotspot above 57~EeV not far from the direction of the starburst galaxy M82. Specifically, we study the stochastic propagation in space of ultrahigh energy cosmic rays through the state-of-the-art simulation framework CRPropa~3, taking into account all relevant particle interactions as well as deflections by the intervening magnetic fields. To ensure a comprehensive understanding of this model, we consider the energy spectrum, the cosmogenic neutrinos and gamma rays, and the distribution of arrival directions. The starburst galaxy scenario reproduces well observations from both the Telescope Array and Pierre Auger Observatories, making it very attractive for explaining the origin of cosmic rays at the highest energies.
We study the existence of positive supersolutions of nonlocal equations $(-\Delta)^s u+ |\nabla u|^q=\lambda f(u)$ in exterior domains where the datum $f$ can be comparade with $u^{p}$ near the origin. We prove that the existence or bounded supersolutions its depend of the values of $p$, $q$ and $s$.
Recent studies based on the integrated light of distant galaxies suggest that the initial mass function (IMF) might not be universal. Variations of the IMF with galaxy type and/or formation time may have important consequences for our understanding of galaxy evolution. We have developed a new stellar population synthesis (SPS) code specifically designed to reconstruct the IMF. We implement a novel approach combining regularization with hierarchical Bayesian inference. Within this approach we use a parametrized IMF prior to regulate a direct inference of the IMF. This direct inference gives more freedom to the IMF and allows the model to deviate from parametrized models when demanded by the data. We use Markov Chain Monte Carlo sampling techniques to reconstruct the best parameters for the IMF prior, the age, and the metallicity of a single stellar population. We present our code and apply our model to a number of mock single stellar populations with different ages, metallicities, and IMFs. When systematic uncertainties are not significant, we are able to reconstruct the input parameters that were used to create the mock populations. Our results show that if systematic uncertainties do play a role, this may introduce a bias on the results. Therefore, it is important to objectively compare different ingredients of SPS models. Through its Bayesian framework, our model is well-suited for this.
We study the third order in time linear dissipative wave equation known as the Standard Linear Viscoelastic Model, that appears also as the linearization of the so-called Moore-Gibson-Thompson equation in Nonlinear Acoustics. We complete the description in a paper by R. Marchand et al. (2012) of the spectrum of the generator of the corresponding group of operators and show that, apart from some exceptional values of the parameters, this generator can be made to be a normal operator with a new scalar product, with a complete set of orthogonal eigenfunctions. Using this property we also obtain sharper decay estimates for the solutions as time tends to infinity, both when the operator is normal or not.
Suppose that a coin with bias theta is tossed at renewal times of a renewal process, and a fair coin is tossed at all other times. Let mu_\theta be the distribution of the observed sequence of coin tosses, and let u_n denote the chance of a renewal at time n. Harris and Keane showed that if sum_{n=1}^infty u_n^2=\infty, then mu_theta and \mu_0 are singular, while if sum_{n=1}^{infty} u_n^2<infty and theta is small enough, then mu_theta is absolutely continuous with respect to mu_0. They conjectured that absolute continuity should not depend on theta, but only on the square-summability of {u_n}. We show that in fact the power law governing the decay of {u_n} is crucial, and for some renewal sequences {u_n}, there is a {phase transition at a critical parameter theta_c in (0,1): for |theta|<theta_c the measures mu_theta$ and mu_0 are mutually absolutely continuous, but for |theta|>theta_c, they are singular. We also prove that when u_n=O(n^{-1}), the measures mu_theta for theta in [-1,1] are all mutually absolutely continuous.
A multi-channel algebraic scattering theory, to find solutions of coupled-channel scattering problems with interactions determined by collective models, has been structured to ensure that the Pauli principle is not violated. Positive (scattering) and negative (sub-threshold) solutions can be found to predict both the compound nucleus sub-threshold spectrum and all resonances due to coupled channel effects that occur on a smooth energy varying background.
The connection between the dipolar modulation asymmetry and the quadrupole-octopole alignment in the CMB is studied in this work. First, a generalization of the dipolar modulation model is proposed by considering that the amplitude may depend on the scale. As derived from a Bayesian inference analysis, this model fits the CMB data better than the scale-independent one. As an extension of the standard model, the scale-dependent dipolar modulation shows comparable evidence to the standard isotropic model in the large scales ($\ell_\mathrm{max} \leq 64$). The posterior distribution of the parameters of the scale-dependent model suggests that the amplitude of the dipolar modulation is large at the lowest multipoles. This large asymmetry induces a detectable correlation between the quadrupole and the octopole. The significance of the quadrupole-octopole alignment is analyzed under the assumption that the Universe has a scale-dependent dipolar modulation. The three alignment estimators considered in this paper show an increment of $80\%$ in the p-value, showing a clear correlation between these two CMB anomalies. Within this new scenario, only one of the alignment estimators is still below the $1\%$ probability level.
This is a brief review on the scenario of baryogenesis through leptogenesis. Leptogenesis is an appealing scenario that may relate the observed baryon asymmetry in the Universe to the low-energy neutrino data. In this review talk, particular emphasis is put on recent developments on the field, such as the flavourdynamics of leptogenesis and resonant leptogenesis near the electroweak phase transition. It is illustrated how these recent developments enable the modelling of phenomenologically predictive scenarios that can directly be tested at the LHC and indirectly in low-energy experiments of lepton-number and lepton-flavour violation.
We prove asymptotic formulas for cyclicity of reductions of elliptic curves over the rationals in a family of curves having specified torsion. These results agree with established conditional results and with average results taken over larger families. As a key tool, we prove an analogue of a result of Vl\u{a}du\c{t} that estimates the number of elliptic curves over a finite field with a specified torsion point and cyclic group structure.
In this Letter, we demonstrate that it is possible to form a two-dimensional (2D) silicene-like Si$_5$Ge compound by replacing the Si atoms occupying on-top sites in the planar-like structure of epitaxial silicene on ZrB$_2$(0001) by deposited Ge atoms. For coverages below 1/6 ML, the Ge deposition gives rise to a Si$_{6-x}$Ge$_{x}$ alloy (with $x$ between 0 and 1) in which the on-top sites are randomly occupied by Si or Ge atoms. The progressive increase of the valence band maximum with $x$ observed experimentally originates from a selective charge transfer from Ge atoms to Si atoms. These achievements provide evidence for the possibility of engineering the bandgap in 2D SiGe alloys in a way that is similar for their bulk counterpart.
We count the number of pairs in the single $j-$shell model of $^{44}$Ti for various interactions. For a state of total angular momentum $I$, the wave function can be written as $\Psi=\sum_{J_P J_N} D(J_P J_N) [(j^2)_{J_P}(j^2)_{J_N}]_I$, where $D(J_P J_N)$ is the probability amplitude that the protons couple to $J_P$ and the neutrons to $J_N$. For I=0 there are three states with ($I=0, T=0$) and one with ($I=0, T=2$). The latter is the double analog of $^{44}$Ca. In that case (T=2), the magnitude of $D(JJ)$ is the same as that of a corresponding two particle fractional parentage coefficient. In counting the number of pairs with an even angular momentum $J_A$ we find a new relationship obtained by diagonalizing a unitary nine-j symbol. We are also able to get results for the 'no-interaction' case for T=0 states, for which it is found that there are less ($J=1, T=0$) pairs than on the average. Relative to this 'no-interaction case' we find for the most realistic interaction used that there is an enhancement of pairs with angular momentum $J_A=0,2,1$ and 7, and a depletion for the others. Also considered are interactions in which only the ($J=0, T=1$) pair state is at lower energy, only the ($J=1, T=0$) pair state is lowered and where both are equally lowered.
The long wavelength modes lost to bright foregrounds in the interferometric 21-cm surveys can partially be recovered using a forward modeling approach that exploits the non-linear coupling between small and large scales induced by gravitational evolution. In this work, we build upon this approach by considering how adding external galaxy distribution data can help to fill in these modes. We consider supplementing the 21-cm data at two different redshifts with a spectroscopic sample (good radial resolution but low number density) loosely modeled on DESI-ELG at $z=1$ and a photometric sample (high number density but poor radial resolution) similar to LSST sample at $z=1$ and $z=4$ respectively. We find that both the galaxy samples are able to reconstruct the largest modes better than only using 21-cm data, with the spectroscopic sample performing significantly better than the photometric sample despite much lower number density. We demonstrate the synergies between surveys by showing that the primordial initial density field is reconstructed better with the combination of surveys than using either of them individually. Methodologically, we also explore the importance of smoothing the density field when using bias models to forward model these tracers for reconstruction.
In this paper, we investigate the problem of simultaneously generations of $r$-jets of $\omega_X\otimes L^{\otimes m}$ when $L$ is ample and base point free. It turns out that in this case, the bound of $m$ is optimistic, i.e. $m\geq f(r)=n+r+1$, which is linear in $r$. Our results work over arbitrary characteristics. We also treat the same problem when $X$ is singular where $\omega_X$ is replaced by the pushforward of canonical sheaves or the cohomology sheaves of dualizing complexes.
We have used the zCOSMOS-bright 10k sample to identify 3244 Spitzer/MIPS 24-micron-selected galaxies with 0.06< S(24um)< 0.50 mJy and I(AB)<22.5, over 1.5 deg^2 of the COSMOS field, and studied different spectral properties, depending on redshift. At 0.2<z<0.3, we found that different reddening laws of common use in the literature explain the dust extinction properties of around 80% of our infrared (IR) sources, within the error bars. For up to 16% of objects, instead, the Halpha/Hbeta ratios are too high for their IR/UV attenuations, which is probably a consequence of inhomogenous dust distributions. In only a few of our galaxies at 0.2<z<0.3 the IR emission could be mainly produced by dust heated by old rather than young stars. Besides, the line ratios of ~22% of our galaxies suggest that they might be star-formation/nuclear-activity composite systems. At 0.5<z<0.7, we estimated galaxy metallicities for 301 galaxies: at least 12% of them are securely below the upper-branch mass-metallicity trend, which is consistent with the local relation. Finally, we performed a combined analysis of the Hdelta equivalent-width versus Dn(4000) diagram for 1722 faint and bright 24um galaxies at 0.6<z<1.0, spanning two decades in mid-IR luminosity. We found that, while secondary bursts of star formation are necessary to explain the position of the most luminous IR galaxies in that diagram, quiescent, exponentially-declining star formation histories can well reproduce the spectral properties of ~40% of the less luminous sources. Our results suggest a transition in the possible modes of star formation at total IR luminosities L(TIR)=(3 +/-2)x10^11 Lsun.
We discuss in this short note how basic facts about divisors on moduli spaces of pointed curves give a solution to the Brill-Noether problem of nonexistence of linear series with prescribed ramification at unassigned points.
A new model of localized highly frustrated ferromagnetism is presented: kagome spin ice. By use of analytical and Monte Carlo calculations its massive groundstate entropy is evaluated. Monte Carlo calculations are also used to explore the phases in the presence of further-neighbor interactions and applied fields. The importance of thermal spin fluctuations and their ability to stabilize a variety of magnetic structures is clearly manifested. Remarkably, some of these phases are only partially ordered and present both disordered and ordered sublattices.
We show how to obtain constraints on $\beta=f/b$, the ratio of the matter growth rate and the bias that quantifies the linear redshift-space distortions, that are independent of the cosmological model, using multiple tracers of large-scale structure. For a single tracer the uncertainties on $\beta$ are constrained by the uncertainties in the amplitude and shape of the power spectrum, which is limited by cosmic variance. However, for two or more tracers this limit does not apply, since taking the ratio of power spectra cosmic variance cancels out, and in the linear (Kaiser) approximation one measures directly the quantity $(1+ \beta_1 \mu^2)^2/(1+ \beta_2 \mu^2)^2$, where $\mu$ is the angle of a given mode with the line of sight. We provide analytic formulae for the Fisher matrix for one and two tracers, and quantify the signal-to-noise ratio needed to make effective use of the multiple-tracer technique. We also forecast the errors on $\beta$ for a survey like Euclid.
The quasiclassical theory of massless chiral fermions is considered. The effective action is derived using time-dependent variational principle which provides a clear interpretation of relevant canonical variables. As a result their transformation properties under the action of Lorentz group are derived from first principles.
We test the hypothesis of non-radiative neutrinos decay using the latest IceCube data. Namely, we calculate the track-to-shower ratio expected in IceCube for the normal and inverted neutrino mass hierarchy taking into account the uncertainties in neutrino oscillation parameters. We show that the subset of data with energy above 60 TeV actually excludes the possibility of a neutrinos decay at the 1 sigma level of significance for both neutrino mass hierarchies.
We present new imaging observations of the remnant of Supernova (SN) 1987A at 44 GHz, performed in 2011 with the Australia Telescope Compact Array (ATCA). The $0\farcs35\times0\farcs23$ resolution of the diffraction-limited image is the highest achieved to date in high-dynamic range. We also present a new ATCA image at 18 GHz derived from 2011 observations, which is super-resolved to $0\farcs25$. The flux density is 40$\pm$2 mJy at 44 GHz and 81$\pm$6 mJy at 18 GHz. At both frequencies, the remnant exhibits a ring-like emission with two prominent lobes, and an east-west brightness asymmetry that peaks on the eastern lobe. A central feature of fainter emission appears at 44 GHz. A comparison with previous ATCA observations at 18 and 36 GHz highlights higher expansion velocities of the remnant eastern side. The 18-44 GHz spectral index is $\alpha=-0.80$ ($S_{\nu}\propto\nu^{\alpha}$). The spectral index map suggests slightly steeper values at the brightest sites on the eastern lobe, whereas flatter values are associated with the inner regions. The remnant morphology at 44 GHz generally matches the structure seen with contemporaneous X-ray and H$\alpha$ observations. Unlike the H$\alpha$ emission, both the radio and X-ray emission peaks on the eastern lobe. The regions of flatter spectral index align and partially overlap with the optically-visible ejecta. Simple free-free absorption models suggest that emission from a pulsar wind nebula or a compact source inside the remnant may now be detectable at high frequencies, or at low frequencies if there are holes in the ionised component of the ejecta.
We studied the outflow behaviour from accretion discs around black holes taking into account the vertical equilibrium accretion flow model. The outflow rate is found to depend crucially on flow composition. Our approach is to study the outflow behaviour as function of inflow around black holes with an equation of state which allows flow to be thermally relativistic close to black holes and non relativistic far away from black holes. We studied shock ejection model. A pure electron positron pair flow never undergoes shock transition while presence of some baryons (common in outflows and jets) makes it possible to have standing shock waves in the flow. It can be concluded that the presence of protons is necessary for the flow to show the outflow behaviour. The outflow rate is maximum when the flow contains the proton number density which is 27% of the electron number density. We conclude that a pure electron-positron jet is unlikely to form.
Let $q>r\ge1$ be coprime integers. Let $R(n,q,r)$ be the $n$th record gap between primes in the arithmetic progression $r$, $r+q$, $r+2q,\ldots,$ and denote by $N_{q,r}(x)$ the number of such records observed below $x$. For $x\to\infty$, we heuristically argue that if the limit of $N_{q,r}(x)/\log x$ exists, then the limit is 2. We also conjecture that $R(n,q,r)=O_q(n^2)$. Numerical evidence supports the conjectural (a.s.) upper bound $$R(n,q,r)<\varphi(q)n^2+(n+2)q\log^2 q.$$ The median (over $r$) of $R(n,q,r)$ grows like a quadratic function of $n$; so do the mean and quartile points of $R(n,q,r)$. For fixed values of $q\gtrsim200$ and $n\approx10$, the distribution of $R(n,q,r)$ is skewed to the right and close to both Gumbel and lognormal distributions; however, the skewness appears to slowly decrease as $n$ increases. The existence of a limiting distribution of $R(n,q,r)$ is an open question.
We consider the algebraization problem for principal bundles with reductive structure group, defined on the complement of a closed subset Z in a proper formal scheme. We show that, when Z is of codimension at least 3, an algebraization always exists. For codimension 2 we show that an algebraization exists precisely when a certain additional condition is satisfied.
Let $G$ be a graph. We say that a hypergraph $H$ is a Berge-$G$ if there is a bijection $\phi: E(G)\to E(H)$ such that $e\subseteq \phi(e)$ for all $e\in E(G)$. For any $r$-uniform hypergraph $H$ and a real number $p\geq 1$, the $p$-spectral radius $\lambda^{(p)}(H)$ of $H$ is defined as \[ \lambda^{(p)}(H):=\max_{{\bf x}\in\mathbb{R}^n,\,\|{\bf x}\|_p=1} r\sum_{\{i_1,i_2,\ldots,i_r\}\in E(H)} x_{i_1}x_{i_2}\cdots x_{i_r}. \] In this paper, we study the $p$-spectral radius of Berge-$G$ hypergraphs. We determine the $3$-uniform hypergraphs with maximum $p$-spectral radius for $p\geq 1$ among Berge-$G$ hypergraphs when $G$ is a path, a cycle or a star.