ShantanuT01/DACTYL-Pretraining huggingface dataset:
We review the leading momentum, frequency and temperature dependences of the single particle self-energy and the corresponding term in the entropy of a two dimensional Fermi liquid (FL) with a free particle spectrum. We calculate the corrections to these leading dependences for the paramagnon model and the electron gas and find that the leading dependences are limited to regions of energy and temperature which decrease with decreasing number density of fermions. This can make it difficult to identify the frequency and temperature dependent characteristics of a FL ground state in experimental quantities in low density systems even when complications of band structure and other degrees of freedom are absent. This is an important consideration when the normal state properties of the undoped cuprate superconductors are analyzed.
In this paper we explicitly show the equivalence between the non-Abelian Born-Infeld action, which was proposed by Tseytlin as an effective action on several D-branes, and its noncommutative counterpart for slowly varying fields. This confirms the equivalence between the two descriptions of the D-branes using an ordinary gauge theory with a constant B field background and a noncommutative gauge theory, claimed by Seiberg and Witten. We also construct the general forms of the 2 n-derivative terms for non-Abelian gauge fields which are consistent with the equivalence in the approximation of neglecting (2 n+2)-derivative terms.
The results of the N/O abundance determination in a sample of low-metallicity blue compact dwarf (BCD) galaxies based on new spectroscopic observations with large telescopes (Keck, VLT, MMT, 4m KPNO) are presented. We show that the N/O abundance ratio is constant at lowest metallicities < Zsun/20, confirming previous findings and strongly supporting the origin of nitrogen as a primary element.
The ionization fraction plays a key role in the physics and chemistry of the neutral interstellar medium, from controlling the coupling of the gas to the magnetic field to allowing fast ion-neutral reactions that drive interstellar chemistry. Most estimations of the ionization fraction have relied on deuterated species such as DCO+, whose detection is limited to dense cores representing an extremely small fraction of the volume of the giant molecular clouds they are part of. As large field-of-view hyperspectral maps become available, new tracers may be found. We search for the best observable tracers of the ionization fraction based on a grid of astrochemical models. We build grids of models that sample randomly a large space of physical conditions (unobservable quantities such as gas density, temperature, etc.) and compute the corresponding observables (line intensities, column densities) and the ionization fraction. We estimate the predictive power of each potential tracer by training a Random Forest model to predict the ionization fraction from that tracer, based on these model grids. In both translucent medium and cold dense medium conditions, several observable tracers with very good predictive power for the ionization fraction are found. Several tracers in cold dense medium conditions are found to be better and more widely applicable than the traditional DCO+/HCO+ ratio. We also provide simpler analytical fits for estimating the ionization fraction from the best tracers, and for estimating the associated uncertainties. We discuss the limitations of the present study and select a few recommended tracers in both types of conditions. The method presented here is very general and can be applied to the measurement of any other quantity of interest (cosmic ray flux, elemental abundances, etc.) from any type of model (PDR models, time-dependent chemical models, etc.). (abridged)
We derive the chiral effective Lagrangian for excited heavy-light mesons from QCD under proper approximations. We focus on the chiral partners with $j_l^P=\frac{3}{2}^+$ and $j_l^P=\frac{3}{2}^-$ which amounts to ($1^+,2^+$) and ($1^-,2^-$) states respectively. The low energy constants including the masses of the chiral partners are calculated. The calculated spectrum for the excited mesons are found roughly consistent with experimental data. In addition, our results indicate that quantum numbers of $B_J(5970)$ can be identified with $1^-$ or $2^-$.
We derive a master equation for the motion of a polarizable particle weakly interacting with one or several strongly pumped cavity modes. We focus here on massive particles with complex internal structure such as large molecules and clusters, for which we assume a linear scalar polarizability mediating the particle-light interaction. The predicted friction and diffusion coefficients are in good agreement with former semiclassical calculations for atoms and small molecules in weakly pumped cavities, while the current rigorous quantum treatment and numerical assessment sheds a light on the feasibility of experiments that aim at optically manipulating beams of massive molecules with multimode cavities.
We discuss the relationship between exact solvability of the Schr\"{o}dinger equation with a position-dependent mass and the ordering ambiguity in the Hamiltonian operator within the frame of supersymmetric quantum mechanics. The one-dimensional Schr\"{o}dinger equation, derived from the general form of the effective mass Hamiltonian, is solved exactly for a system with exponentially changing mass in the presence of a potential with similar behaviour, and the corresponding supersymmetric partner Hamiltonians are related to the effective-mass Hamiltonians proposed in the literature.
One-variable thermostats are studied as a generalization of the Nos\'e--Hoover method which is aimed to achieve Gibbs' canonical distribution with conserving the time-reversibility. A condition for equations of motion for the system with the thermostats is derived in the form of a partial differential equation. Solutions of this equation construct a family of thermostats including the Nos\'e--Hoover method as the minimal solution. It is shown that the one-variable thermostat coupled with the one-dimensional harmonic oscillator loses its ergodicity with large enough relaxation time. The present result suggests that multi-variable thermostats are required to assure the ergodicity and to work as heatbath.
The AV_nO_{2n+1} mixed valence compounds (n=1, A=Na) are classified as dimerized layered system with strongly interacting d-electrons of vanadium ions. The derived band gaps, energy dispersion relations and density of electronic states are in a good agreement with available experimental and theoretical data. The correlated band gap provides the insulating state of the high-temperature alpha-NaV_2O_5 phase whereas the state, earlier misrepresented as the spin-Peierls state, is governed, in fact, by opening of the Coulomb gap.
We propose a new version of the Baade--Becker--Wesselink technique, which allows one to independently determine the colour excess and the intrinsic colour of a radially pulsating star, in addition to its radius, luminosity, and distance. It is considered to be a generalization of the Balona approach. The method also allows the function F(CI) = BC + 10 log (Teff) for the class of pulsating stars considered to be calibrated. We apply this technique to a number of classical Cepheids with very accurate light and radial-velocity curves and with bona fide membership in open clusters (SZ Tau, CF Cas, U Sgr, DL Cas, GY Sge), and find the results to agree well with the reddening estimates of the host open clusters. The new technique can also be applied to other pulsating variables, e.g. RR Lyrae and RV Tauri.
We suggest a scheme to reconstruct the covariance matrix of a two-mode state using a single homodyne detector plus a polarizing beam splitter and a polarization rotator. It can be used to fully characterize bipartite Gaussian states and to extract relevant informations on generic states.
We consider string theory on the Lorentzian Melvin geometry, which is obtained by analytically continuing the two-parameter Euclidean Melvin background. Because this model provides a solvable conformal field theory that describes time-dependent twisted string dynamics, we study the string one-loop partition function and the D-brane spectrum. We found that both the wrapping D2-brane and the codimension-one D-string emit winding strings, and this behavior can be traced to the modified open string Hamiltonian on these probe D-branes.
We study reflected solutions of one-dimensional backward doubly stochastic differential equations (BDSDEs in short). The "reflected" keeps the solution above a given stochastic process. We get the uniqueness and existence by penalization. For the existence of backward stochastic integral, our proof is different from [KKPPQ] slightly. We also obtain a comparison theorem for reflected BDSDEs.
This paper presents a family of rapidly convergent summation formulas for various finite sums of the form $\sum_{k=0}^{\lfloor x\rfloor}f(k)$, where $x$ is a positive real number.
In this paper, we study the hybrid problem of Hua's theorem and the Piatetski-Shapiro prime number theorem, and obtain results in this direction of the nonhomogeneous case $k=3$, which deepen the classical result of Hua.
Charge and heat transfer through a nanoscale conductor is not only determined by the transmission properties of the electrons, but can also be strongly impacted by coupling to other degrees of freedom in the environment of the conductor. Here, we analyze the influence of the electromagnetic environment on a simple, yet significant thermoelectric property, the thermopower, in the simple transport scenario of single-charge transfer across a tunnel junction. Considering both thermal and out-of-equilibrium steady-state environments, we find that the thermopower can be strongly affected by the environmental state and can, in turn, act as a sensitive probe of environmental properties.
We provide a series of rigidity results for a nonlocal phase transition equation. The prototype equation that we consider is of the form $$ (-\Delta)^{s/2} u=u-u^3,$$ with~$s\in(0,1)$. More generally, we can take into account equations like $$ L u = f(u),$$ where $f$ is a bistable nonlinearity and $L$ is an integro-differential operator, possibly of anisotropic type.   The results that we obtain are an improvement of flatness theorem and a series of theorems concerning the one-dimensional symmetry for monotone and minimal solutions, in the research line dictaded by a classical conjecture of E. De Giorgi.   Here, we collect a series of pivotal results, of geometric type, which are exploited in the proofs of the main results in the companion paper.
Fix a field $F$. In this paper, we study the sets $\D_F(n) \subset [0,n]$ defined by [\D_F(n):= {0 \leq m \leq n: T^n-1\text{has a divisor of degree $m$ in} F[T]}.] When $\D_F(n)$ consists of all integers $m$ with $0 \leq m \leq n$, so that $T^n-1$ has a divisor of every degree, we call $n$ an $F$-practical number. The terminology here is suggested by an analogy with the practical numbers of Srinivasan, which are numbers $n$ for which every integer $0 \leq m \leq \sigma(n)$ can be written as a sum of distinct divisors of $n$. Our first theorem states that, for any number field $F$ and any $x \geq 2$, [#{\text{$F$-practical $n\leq x$}} \asymp_{F} \frac{x}{\log{x}};] this extends work of the second author, who obtained this estimate when $F=\Q$.   Suppose now that $x \geq 3$, and let $m$ be a natural number in $[3,x]$. We ask: For how many $n \leq x$ does $m$ belong to $\D_F(n)$? We prove upper bounds in this problem for both $F=\Q$ and $F=\F_p$ (with $p$ prime), the latter conditional on the Generalized Riemann Hypothesis. In both cases, we find that the number of such $n \leq x$ is $\ll_{F} x/(\log{m})^{2/35}$, uniformly in $m$.
Consider a collection of particles whose state evolution is described through a system of interacting diffusions in which each particle is driven by an independent individual source of noise and also by a small amount of noise that is common to all particles. The interaction between the particles is due to the common noise and also through the drift and diffusion coefficients that depend on the state empirical measure. We study large deviation behavior of the empirical measure process which is governed by two types of scaling, one corresponding to mean field asymptotics and the other to the Freidlin-Wentzell small noise asymptotics. Different levels of intensity of the small common noise lead to different types of large deviation behavior, and we provide a precise characterization of the various regimes. We also study large deviation behavior of interacting particle systems approximating various types of Feynman-Kac functionals. Proofs are based on stochastic control representations for exponential functionals of Brownian motions and on uniqueness results for weak solutions of stochastic differential equations associated with controlled nonlinear Markov processes.
We study a finite SU(5) grand unified model based on the non-Abelian discrete symmetry A_4. This model leads to the democratic structure of the mass matrices for the quarks and leptons. In the soft supersymmetry breaking sector, the scalar trilinear couplings are aligned and the soft scalar masses are degenerate, thus solving the SUSY flavor problem.
We propose a linear optical scheme for the teleportation of unknown ionic states, the entanglement concentration for nonmaximally entangled states for ions via entanglement swapping and the remote preparation for ionic entangled states. The unique advantage of the scheme is that the joint Bell-state measurement needed in the previous schemes is not needed in the current scheme, i.e. the joint Bell-state measurement has been converted into the product of separate measurements on single ions and photons. In addition, the current scheme can realize the quantum information processes for ions by using linear optical elements, which simplify the implementation of quantum information processing for ions.
The definition of Simon tensor, originally given only in the Kerr spacetime and associated with the static family of observers, is generalized to any spacetime and to any possible observer family. Such generalization is obtained by a standard "3+1" splitting of the Bianchi identities, which are rewritten here as a "balance equation" between various spatial fields, associated with the kinematical properties of the observer congruence and representing the spacetime curvature.
We used an Artificial Neural Network (ANN) to derive the orbital parameters of spectroscopic binary stars. Using measured radial velocity data of seven double-lined spectroscopic binary systems V373 Cas, V2388 Oph, V401 Cyg, GM Dra, V523 Cas, AB And, and HD 141929, we found corresponding orbital and spectroscopic elements. Our numerical results are in good agreement with those obtained by others using more traditional methods.
We construct a family of multi-dyonically charged and rotating supersymmetric AdS$_2\times \Sigma$ solutions of $D=4$, $\mathcal{N}=4$ gauged supergravity, where $\Sigma$ is a sphere with two conical singularities known as a spindle. We argue that these arise as near horizon limits of extremal dyonically charged rotating and accelerating supersymmetric black holes in AdS$_4$, that we conjecture to exist. We demonstrate this in the non-rotating limit, constructing the accelerating black hole solutions and showing that the non-spinning spindle solutions arise as the near horizon limit of the supersymmetric and extremal sub-class of these black holes. From the near horizon solutions we compute the Bekenstein-Hawking entropy of the black holes as a function of the conserved charges, and show that this may equivalently be obtained by extremizing a simple entropy function. For appropriately quantized magnetic fluxes, the solutions uplift on $S^7$, or its ${\cal N}=4$ orbifolds $S^7/\Gamma$, to smooth supersymmetric solutions to $D=11$ supergravity, where the entropy is expected to count microstates of the theory on $N$ M2-branes wrapped on a spinning spindle, in the large $N$ limit.
In this article a new upper bounds for the multiple trigonometrical integrals are found. The method of the work based on a new method of estimation for the areas of algebraic surfaces.
It is believed that massive galaxies have quenched their star formation because of active galactic nucleus feedback. However, recent studies have shown that some massive galaxies are still forming stars. We analyze the morphology of star formation regions for galaxies of stellar mass larger than 10$^{11.3}$ M$_{\odot}$ at around redshift $z_r=0.5$ using $u-z$ color images. We find that about $20\%$ of the massive galaxies are star-forming (SF) galaxies, and most of them ($\sim 85\%$) have asymmetric structures induced by recent mergers. Moreover, for these asymmetric galaxies, we find that the asymmetry of the SF regions becomes larger for bluer galaxies. Using the Illustris simulation, we can qualitatively reproduce the observed relation between asymmetry parameter and color. Furthermore, using the merger trees in the simulation, we find a correlation between the color of the main branch galaxies at $z_r=0.5$ and the sum of the Star Formation Rates (SFRs) of the recently accreted galaxies, which implies that star formation of the accreted galaxies has contributed to the observed star formation of the massive (host) galaxies (ex situ star formation). Furthermore, we find two blue and symmetric galaxies, candidates for massive blue disks, in our observed sample, which indicates that about $\sim 10\%$ of massive SF galaxies are forming stars in the normal mode of disk star formation (in situ star formation). With the simulation, we find that the disk galaxies at $z_r \approx 0.5$ should have experienced few major mergers during the last 4.3 Gyrs.
The physics of excitons, electron-hole pairs that are bound together by their mutual Coulomb attraction, can to great extent be understood in the framework of the quantum-mechanical hydrogen model. This model has recently been challenged by spectroscopic measurements on two-dimensional transition-metal dichalchogenides that unveil strong deviations from a hydrogenic spectrum. Here, we show that this deviation is due to the particular relativistic character of electrons in this class of materials. Indeed, their electrons are no longer described in terms of a Schroedinger but a massive Dirac equation that intimately links electrons to holes. Dirac excitons therefore inherit a relativistic quantum spin-1/2 that contributes to the angular momentum and thus the exciton spectrum. Most saliently, the level spacing is strongly reduced as compared to the hydrogen model, in agreement with spectroscopic measurements and ab-initio calculations.
When assessing risks on a finite-time horizon, the problem can often be reduced to the study of a random sequence $C(N)=(C_1,\ldots,C_N)$ of random length $N$, where $C(N)$ comes from the product of a matrix $A(N)$ of random size $N \times N$ and a random sequence $X(N)$ of random length $N$. Our aim is to build a regular variation framework for such random sequences of random length, to study their spectral properties and, subsequently, to develop risk measures. In several applications, many risk indicators can be expressed from the asymptotic behavior of $\vert \vert C(N)\vert\vert$, for some norm $\Vert \cdot \Vert$. We propose a generalization of Breiman Lemma that gives way to an asymptotic equivalent to $\Vert C(N) \Vert$ and provides risk indicators such as the ruin probability and the tail index for Shot Noise Processes on a finite-time horizon. Lastly, we apply our final result to a model used in dietary risk assessment and in non-life insurance mathematics to illustrate the applicability of our method.
We reprove Saito's vanishing theorem for mixed Hodge modules by the method of Esnault and Viehweg. The main idea is to exploit the strictness of direct images on certain branched coverings.
A classical extremal, or Tur\'an-type problem asks to determine ${\rm ex}(G, H)$, the largest number of edges in a subgraph of a graph $G$ which does not contain a subgraph isomorphic to $H$. Alon and Shikhelman introduced the so-called generalized extremal number ${\rm ex}(G,T,H)$, defined to be the maximum number of subgraphs isomorphic to $T$ in a subgraph of $G$ that contains no subgraphs isomorphic to $H$. In this paper we investigate the case when $G = Q_n$, the hypercube of dimension $n$, and $T$ and $H$ are smaller hypercubes or cycles.
We use Burgos theory of arithmetic Chow groups to exhibit a realization of the degree zero part of the polylogarithm on abelian schemes in Deligne-Beilinson cohomology.
The ground-state deformations of the Ge isotopes are investigated in the framework of Gogny-Hartree-Fock-Bogoliubov (HFB) and Skyrme Hartree-Fock plus pairing in the BCS approximation. Five different Skyrme parametrizations are used to explore the influence of different effective masses and spin-orbit models. There is generally good agreement for binding energies and deformations (total quadrupole moment, triaxiality) with experimental data where available (i.e., in the valley of stability). All calculations agree in predicting a strong tendency for triaxial shapes in the Ge isotopes with only a few exceptions due to neutron (sub-)shell closures. The frequent occurrence of energetically very close shape isomers indicates that the underlying deformation energy landscape is very soft. The general triaxial softness of the Ge isotopes is demonstrated in the fully triaxial potential energy surface. The differences between the forces play an increasing role with increasing neutron number. This concerns particularly the influence of the spin-orbit model, which has a visible effect on the trend of binding energies towards the drip line. Different effective mass plays an important role in predicting the quadrupole and triaxial deformations. The pairing strength only weakly affects binding energies and total quadrupole deformations, but considerably influences triaxiality.
We present the discovery in TMC-1 of vinyl acetylene, CH2CHCCH, and the detection, for the first time in a cold dark cloud, of HCCN, HC4N, and CH3CH2CN. A tentative detection of CH3CH2CCH is also reported. The column density of vinyl acetylene is (1.2 +/- 0.2)e13 cm-2, which makes it one of the most abundant closed-shell hydrocarbons detected in TMC-1. Its abundance is only three times lower than that of propylene, CH3CHCH2. The column densities derived for HCCN and HC4N are (4.4 +/- 0.4)e11 cm-2 and (3.7 +/- 0.4)e11 cm-2, respectively. Hence, the HCCN/HC4N abundance ratio is 1.2 +/- 0.3. For ethyl cyanide we derive a column density of (1.1 +/- 0.3)e11 cm-2. These results are compared with a state-of-the-art chemical model of TMC-1, which is able to account for the observed abundances of these molecules through gas-phase chemical routes.