ShantanuT01/DACTYL-Pretraining huggingface dataset:
This paper contributes to the study of relative martingales. Specifically, for a closed random set $H$, they are processes null on $H$ which decompose as $M=m+v$, where $m$ is a c\`adl\`ag uniformly integrable martingale and, $v$ is a continuous process with integrable variations such that $v_{0}=0$ and $dv$ is carried by $H$. First, we extend this notion to stochastic processes not necessarily null on $H$, where $m$ is considered local martingale instead of a uniformly integrable martingale. Thus, we provide a general framework for the new larger class of relative martingales by presenting some structural properties. Second, as applications, we construct solutions for skew Brownian motion equations using continuous stochastic processes of the above mentioned new class. In addition, we investigate stochastic differential equations driven by a relative martingale.
WTe2 has attracted a great deal of attention because it exhibits extremely large and nonsaturating magnetoresistance. The underlying origin of such a giant magnetoresistance is still under debate. Utilizing laser-based angle-resolved photoemission spectroscopy with high energy and momentum resolutions, we reveal the complete electronic structure of WTe2. This makes it possible to determine accurately the electron and hole concentrations and their temperature dependence. We find that, with increasing the temperature, the overall electron concentration increases while the total hole concentration decreases. It indicates that the electron-hole compensation, if it exists, can only occur in a narrow temperature range, and in most of the temperature range there is an electron-hole imbalance. Our results are not consistent with the perfect electron-hole compensation picture that is commonly considered to be the cause of the unusual magnetoresistance in WTe2. We identified a flat band near the Brillouin zone center that is close to the Fermi level and exhibits a pronounced temperature dependence. Such a flat band can play an important role in dictating the transport properties of WTe2. Our results provide new insight on understanding the origin of the unusual magnetoresistance in WTe2.
We introduce a statistic on overpartitions called the $\overline{k}$-rank. When there are no overlined parts, this coincides with the $k$-rank of a partition introduced by Garvan. Moreover, it reduces to the D-rank of an overpartition when $k=2$. The generating function for the $\overline{k}$-rank of overpartitions is given. We also establish a relation between the generating function of self-3-conjugate overpartitions and the tenth order mock theta functions $X(q)$ and $\chi(q)$.
Allowed weak interaction rates for sd-shell nuclei in stellar environment are calculated using a generalized form of proton-neutron quasiparticle RPA model with separable Gamow-Teller forces. Twelve different weak rates are calculated for each nucleus as a function of temperature and density. This project consists of calculation of weak rates for a total of 709 nuclei with masses ranging from A = 18 to 100. This paper contains calculated weak rates for sd-shell nuclei. The calculated capture and decay rates take into consideration the latest experimental energy levels and ft value compilations. The results are also compared with earlier works. Particle emission processes from excited states, previously ignored, are taken into account, and are found to significantly affect some beta decay rates.
We derive conservative, multidimensional, energy-dependent moment equations for neutrino transport in core-collapse supernovae and related astrophysical systems, with particular attention to the consistency of conservative four-momentum and lepton number transport equations. After taking angular moments of conservative formulations of the general relativistic Boltzmann equation, we specialize to a conformally flat spacetime, which also serves as the basis for four further limits. Two of these---the multidimensional special relativistic case, and a conformally flat formulation of the spherically symmetric general relativistic case---are given in appendices for the sake of comparison with extant literature. The third limit is a weak-field, `pseudo-Newtonian' approach \citep{kim_etal_2009,kim_etal_2012} in which the source of the gravitational potential includes the trace of the stress-energy tensor (rather than just the mass density), and all orders in fluid velocity $v$ are retained. Our primary interest here is in the fourth limit: `$\mathcal{O}(v)$' moment equations for use in conjunction with Newtonian self-gravitating hydrodynamics. We show that the concept of `$\mathcal{O}(v)$' transport requires care when dealing with both conservative four-momentum and conservative lepton number transport, and present two self-consistent options: `$\mathcal{O}(v)$-plus' transport, in which an $\mathcal{O}(v^2)$ energy equation combines with an $\mathcal{O}(v)$ momentum equation to give an $\mathcal{O}(v^2)$ number equation; and `$\mathcal{O}(v)$-minus' transport, in which an $\mathcal{O}(v)$ energy equation combines with an $\mathcal{O}(1)$ momentum equation to give an $\mathcal{O}(v)$ number equation.
We discuss phenomenological consequences of renormalizable Z` models with continuously distributed mass. We point out that one of possible LHC signatures for such nodel is the existence of broad resonance in Drell-Yan reaction $pp \to Z^{`} \to l^+l^-$.
The two-photon quantum Rabi model with quadratic coupling is studied using extended squeezed states and we derive $G$-functions for Bargmann index $q=1/4$ and $3/4$. The simple singularity structure of the $G$-function allows to draw conclusions about the distribution of eigenvalues along the real axis. The previously found picture of the spectral collapse at critical coupling $g_{\mathrm{c}}$ has to be modified regarding the low lying states, especially the ground state: We obtain a finite gap between ground state and the continuum of excited states at the collapse point. For large qubit splitting, also other low lying states may be separated from the continuum at $g_{\mathrm{c}}$. We have carried out a perturbative analysis allowing for explicit and simple formulae of the eigenstates. Interestingly, a vanishing of the gap between ground state and excited continuum at $g_{\mathrm{c}}$ is obtained in each finite order of approximation. This demonstrates cleary the non-pertubative nature of the excitation gap. We corroborate these findings with a variational calculation for the ground state.
Quantum dynamics is linear. How do we know? From theory or experiment? The history of this question is reviewed. Nonlinear generalizations of quantum mechanics have been proposed. They predict small but clear nonlinear effects, which very accurate experiments have not seen. Is there a reason in principle why nonlinearity is not found? Is it impossible? Does quantum dynamics have to be linear? Attempts to prove this have not been decisive, because either their assumptions are not compelling or their arguments are not conclusive. The question has been left unsettled. There is a simple answer, based on a simple assumption. It was found in two steps separated by 44 years. They are steps back to simpler and more compelling assumptions. A proof of the assumptions of the Wigner-Bargmann proof has been known since 1962. It assumes that the maps of density matrices in time are linear. For this step, it is also assumed that density matrices are mapped one-to-one onto density matrices. An alternative is to assume that pure states are mapped one-to-one onto pure states and that entropy does not decrease. In a step taken in 2006, it is proved that the maps of density matrices in time are linear. It is assumed, as in the earlier step, that at each time the physical quantities and states are described by the usual linear structures of quantum mechanics, so the question is only about how things change in time. Beyond that, the proof assumes only that the dynamics does not depend on anything outside the system, but must allow the system to be described as part of a larger system.
Seyfert 1.8/1.9 are sources showing weak broad H-alpha components in their optical spectra. We aim at testing whether Seyfert 1.8/1.9 have similar properties at UV and X-ray wavelengths to Seyfert 2. We use the 15 Seyfert 1.8/1.9 in the Veron Cetty and Veron catalogue with public data available from the Chandra and/or XMM-Newton archives at different dates, with timescales between observations ranging from days to years. Our results are homogeneously compared with a previous work using the same methodology applied to a sample of Seyfert 2 (Hernandez-Garcia et al. 2015). X-ray variability is found in all 15 nuclei over the aforementioned ranges of timescales. The main variability pattern is related to intrinsic changes in the sources, which are observed in ten nuclei. Changes in the column density are also frequent, as they are observed in six nuclei, and variations at soft energies, possibly related to scattered nuclear emission, are detected in six sources. X-ray intraday variations are detected in six out of the eight studied sources. Variations at UV frequencies are detected in seven out of nine sources. A comparison between the samples of Seyfert 1.8/1.9 and 2 shows that, even if the main variability pattern is due to intrinsic changes of the sources in the two families, these nuclei exhibit different variability properties in the UV and X-ray domains. In particular, variations in the broad X-ray band on short time-scales (days/weeks), and variations in the soft X-rays and UV on long time-scales (months/years) are detected in Seyfert 1.8/1.9 but not in Seyfert 2. Overall, we suggest that optically classified Seyfert 1.8/1.9 should be kept separated from Seyfert 2 galaxies in UV/X-ray studies of the obscured AGN population because their intrinsic properties might be different.
We consider weighted sums of independent random variables regulated by an increment sequence. We provide operative conditions that ensure strong law of large numbers for such sums to hold in both the centered and non-centered case. The existing criteria for the strong law are either implicit or assume some sufficient decay for the sequence of coefficients. In our set up we allow for arbitrary sequence of coefficients, possibly random, provided the random variables regulated by such increments satisfy some mild concentration conditions. In the non-centered case, convergence can be translated into the behavior of a deterministic sequence and it becomes a game of mass provided the expectation of the random variables is a function of the increments. We show how different limiting scenarios can emerge by identifying several classes of increments, for which concrete examples will be offered.
Forecasts and analyses of cosmological observations often rely on the assumption of a perfect theoretical model over a defined range of scales. We explore how model uncertainties and nuisance parameters in perturbative models of the matter and galaxy spectra affect constraints on neutrino mass and primordial non-Gaussianities. We provide a consistent treatment of theoretical errors and argue that their inclusion is a necessary step to obtain realistic cosmological constraints. We find that galaxy surveys up to high redshifts will allow a detection of the minimal neutrino mass and local non-Gaussianity of order unity, but improving the constraints on equilateral non-Gaussianity beyond the CMB limits will be challenging. We argue that similar considerations apply to analyses where theoretical models are based on simulations.
We study linear closure relations for the moments' method applied to simple kinetic equations. The equations are linear collisional models (velocity jump processes) which are well suited to this type of approximation. In this simplified, 1 dimensional setting, we are able to prove stability estimates for the method (with a kinetic interpretation by a BGK model). Moreover we are also able to obtain convergence rates which automatically increase with the smoothness of the initial data.
We study the magnetic properties of a mixed Ising ferrimagnetic system, in which the two interacting sublattices have spins $\sigma$, $(\pm 1/2)$ and spins $S$, $(\pm 3/2,\pm 1/2)$ in the presence of a random crystal field, with the mean field approach. The obtained results show the existence of some interesting phenomena, such as the appearance of a new ferrimagnetic phase namely the partly ferrimagnetic phase $(m_{\sigma}=\frac{-1}{2},m_S=+1)$ and consequently the existence of three topologically different types of phase diagrams. The effect of increasing the exchange interaction parameter $J$, at very low temperature is investigated. The transitions shown in these phase diagrams are in good agreement with those obtained in the ground state case.
We perform the investigations of the resonant tunneling via impurities embedded in the AlAs barrier of a single GaAs/AlGaAs heterostructure. In the $I(V)$ characteristics measured at 30mK, the contribution of individual donors is resolved and the fingerprints of phonon assistance in the tunneling process are seen. The latter is confirmed by detailed analysis of the tunneling rates and the modeling of the resonant tunneling contribution to the current. Moreover, fluctuations of the local structure of the DOS (LDOS) and Fermi edge singularities are observed.
We develop a theory of Coulomb drag in ultraclean double layers with strongly correlated carriers. In the regime where the equilibration length of the electron liquid is shorter than the interlayer spacing the main contribution to the Coulomb drag arises from hydrodynamic density fluctuations. The latter consist of plasmons driven by fluctuating longitudinal stresses, and diffusive modes caused by temperature fluctuations and thermal expansion of the electron liquid. We express the drag resistivity in terms of the kinetic coefficients of the electron fluid. Our results are nonperturbative in interaction strength and do not assume Fermi-liquid behavior of the electron liquid.
We carried out a search for unknown dwarf novae in a public data release of the Zwicky Transient Facility survey and suspected that the object ZTF18abdlzhd is a SU UMa-type star. Performed multicolor CCD observations permit us to follow its fading from an outburst in August and an entire superoutburst in October 2020. The duration of the superoutburst is 13 days. We detected superhumps with period P = 0.06918(3) d that are characteristic of UGSU type stars.
We embark on investigating the magneto-optical absorption in {\em spherical} quantum dots {\em completely} confined by a harmonic potential and exposed to an applied magnetic field in the symmetric gauge. This is done within the framework of Bohm-Pines' RPA that enables us to derive and discuss the full Dyson equation that takes proper account of the Coulomb interactions. Intensifying the confinement or magnetic field and reducing the dot-size yields a blue-shift in the absorption peaks. However, the size effects are seen to be predominant in this role. The magnetic field tends to maximize the localization of the particle, but leaves the peak position of the radial distribution intact. The intra-Landau level transitions are forbidden.
We study the Hubble parameter $H(z)$ in perturbed Friedmann universe and obtain an expression of the perturbed Hubble parameter $H(z,\textbf{n})$. We derive the Hubble parameter power spectrum by using the initial spectrum during inflation and the Bardeen transfer function. We obtain a semi-analytical expression in the case of cold dark matter (CDM) universe. Similar with luminosity distance, the Hubble parameter spectrum is suggested to be an useful observational tool to determine some cosmological parameters. In addition, we show that the Hubble parameter power spectrum could be used to check whether the expansion is accelerated by the second order small scale fluctuation.
We review (i) observations and numerical simulations of vortical flows in the solar atmosphere and (ii) measurements of the horizontal magnetic field in quiet Sun regions. First, we discuss various manifestations of vortical flows and emphasize the role of magnetic fields in mediating swirling motion created near the solar surface to the higher layers of the photosphere and to the chromosphere. We reexamine existing simulation runs of solar surface magnetoconvection with regard to vortical flows and compare to previously obtained results. Second, we review contradictory results and problems associated with measuring the angular distribution of the magnetic field in quiet Sun regions. Furthermore, we review the Stokes-V-amplitude ratio method for the lines Fe I 630.15 and 630.25 nm. We come to the conclusion that the recently discovered two distinct populations in scatter plots of this ratio must not bee interpreted in terms of 'uncollapsed' and 'collapsed' fields but they stem from weak granular magnetic fields and weak canopy fields located at the boundaries between granules and the intergranular space. Based on new simulation runs, we reaffirm earlier findings of a predominance of the horizontal field components over the vertical one, particularly in the upper photosphere and at the base of the chromosphere.
For a monic polynomial $D(X)$ of even degree, express $\sqrt D$ as a Laurent series in $X^{-1}$; this yields a continued fraction expansion (similar to continued fractions of real numbers): \[\sqrt D=a_0+\dfrac{1}{a_1+\dfrac{1}{a_2+\dfrac{1}{\ddots}}},\quad a_i\text{ polynomials in }X.\] Such continued fractions were first considered by Abel in 1826, and later by Chebyshev. It turns out they are rarely periodic unless $D$ is defined over a finite field.   Around 2001 van der Poorten studied non-periodic continued fractions of $\sqrt D$, with $D$ defined over the rationals, and simultaneously the continued fraction of $\sqrt D$ modulo a suitable prime $p$; the latter continued fraction is automatically periodic. He found that one recovers all the convergents (rational function approximations to $\sqrt D$ obtained by cutting off the continued fraction) of $\sqrt D \mod{p}$ by appropriately normalising and then reducing the convergents of $\sqrt D$.   By developing a general specialization theory for continued fractions of Laurent series, I produced a rigorous proof of this result stated by van der Poorten and further was able to show the following:   If $D$ is defined over the rationals and the continued fraction of $\sqrt D$ is non-periodic, then for all but finitely many primes $p \in \mathbb Z$, this prime $p$ occurs in the denominator of the leading coefficient of infinitely many $a_i$.   For $\mathrm{deg}\,D = 4$, I can even give a description of the orders in which the prime appears, and the $p$-adic Gauss norms of the $a_i$ and the convergents. These results also generalise to number fields.   Moreover, I derive optimised formulae for computing quadratic continued fractions, along with several example expansions. I discuss a few known results on the heights of the convergents, and explain some relations with the reduction of hyperelliptic curves and Jacobians.
Particle acceleration to suprathermal energies in strong astrophysical shock waves is a widespread phenomenon, generally explained by diffusive shock acceleration. Such shocks can also amplify upstream magnetic field considerably beyond simple compression. The complex plasma physics processes involved are often parameterized by assuming that shocks put some fraction $\epsilon_e$ of their energy into fast particles, and another fraction $\epsilon_B$ into magnetic field. Modelers of shocks in supernovae, supernova remnants, and gamma-ray bursters, among other locations, often assume typical values for these fractions, presumed to remain constant in time. However, it is rare that enough properties of a source are independently constrained that values of the epsilons can be inferred directly. Supernova remnants (SNRs) can provide such circumstances. Here we summarize results from global fits to spatially integrated emission in six young SNRs, finding $10^{-4} \le \epsilon_e \le 0.05$ and $0.001 \le \epsilon_B \le 0.1$. These large variations might be put down to the differing ages and environments of these SNRs, so we conduct a detailed analysis of a single remnant, that of Kepler's supernova. Both epsilons can be determined at seven different locations around the shock, and we find even larger ranges for both epsilons, as well as for their ratio (thus independent of the shock energy itself). We conclude that unknown factors have a large influence on the efficiency of both processes. Shock obliquity, upstream neutral fraction, or other possibilities need to be explored, while calculations assuming fixed values of the epsilons should be regarded as provisional.
Thermal fluctuations in the magnetization of interstellar grains will produce magnetic dipole emission at frequencies below ~100 GHz. We show how to calculate absorption and emission from small particles composed of magnetic materials. The Kramers-Kronig relations for a dusty medium are generalized to include the possibility of magnetic grains. The frequency-dependent magnetic permeability is discussed for candidate grain materials, including iron and magnetite.   We calculate emission spectra for various interstellar grain candidates. While paramagnetic grains or magnetite grains cannot account for the observed "anomalous" emission from dust in the 14-90 GHz range, stronger magnetic dipole emission will result if a fraction of the grain material is ferromagnetic, as could be the case given the high Fe content of interstellar dust. The observed emission from dust near 90 GHz implies that not more than 5% of interstellar Fe is in the form of metallic iron grains or inclusions (e.g., in "GEMS"). However, we show that if most interstellar Fe is in a moderately ferromagnetic material, it could contribute a substantial fraction of the observed 14-90 GHz emission, perhaps comparable to the contribution from spinning ultrasmall dust grains. The two emission mechanisms can be distinguished by measuring the emission from dark clouds. The expected polarization of magnetic dipole emission is discussed
In this note we complete a previous study, where we got existence results for the quasilinear elliptic equation \begin{equation*}   -\Delta w+ V\left( \left| x\right| \right) w - w \left( \Delta w^2 \right)= K(|x|) g(w) \quad \text{in }\mathbb{R}^{N},   \end{equation*} with singular or vanishing continuous radial potentials $V(r)$, $K(r)$. In our previuos study we assumed, for technical reasons, that $K(r)$ was vanishing as $r \rightarrow 0$, while in the present paper we remove this obstruction. To face the problem we apply a suitable change of variables $w=f(u)$ and we find existence of non negative solutions by the application of variational methods. Our solutions satisfy a weak formulations of the above equation, but they are in fact classical solutions in $\mathbb{R}^{N} \setminus \{0\}$. The nonlinearity $g$ has a double-power behavior, whose standard example is $g(t) = \min \{ t^{q_1 -1}, t^{q_2 -1} \}$ ($t>0$), recovering the usual case of a single-power behavior when $q_1 = q_2$.
We find an exact solution to the charged 2-body problem in $(1+1)$ dimensional lineal gravity which provides the first example of a relativistic system that generalizes the Majumdar-Papapetrou condition for static balance.
Using the methods developed for the Bianchi I case we have shown that a boostrap argument is also suitable to treat the future non-linear stability for reflection symmetric solutions of the Einstein-Vlasov system of Bianchi types II and VI$_0$. These solutions are asymptotic to the Collins-Stewart solution with dust and the Ellis-MacCallum solution respectively. We have thus generalized the results obtained by Rendall and Uggla in the case of locally rotationally symmetric Bianchi II spacetimes to the reflection symmetric case. However we needed to assume small data. For Bianchi VI$_0$ there is no analogous previous result.