ShantanuT01/DACTYL-Pretraining huggingface dataset:
I revisit the exactly solvable Kipnis--Marchioro--Presutti model of heat conduction [J. Stat. Phys. 27 65 (1982)] and describe, for one-dimensional systems of arbitrary sizes whose ends are in contact with thermal baths at different temperatures, a systematic characterization of their non-equilibrium stationary states. These arguments avoid resorting to the analysis of a dual process and yield a straightforward derivation of Fourier's law, as well as higher-order static correlations, such as the covariant matrix. The transposition of these results to families of gradient models generalizing the KMP model is established and specific cases are examined.
We perform Jeans anisotropic modeling (JAM) on elliptical and spiral galaxies from the MaNGA DR13 sample. By comparing the stellar mass-to-light ratios estimated from stellar population synthesis (SPS) and from JAM, we find a similar systematic variation of the initial mass function (IMF) as in the earlier $\rm ATLAS^{3D}$ results. Early type galaxies (elliptical and lenticular) with lower velocity dispersions within one effective radius are consistent with a Chabrier-like IMF while galaxies with higher velocity dispersions are consistent with a more bottom heavy IMF such as the Salpeter IMF. Spiral galaxies have similar systematic IMF variations, but with slightly different slopes and larger scatters, due to the uncertainties caused by higher gas fractions and extinctions for these galaxies. Furthermore, we examine the effects of stellar mass-to-light ratio gradients on our JAM modeling, and find that the trends from our results becomes stronger after considering the gradients.
Polarized and unpolarized inelastic neutron scattering is used to study Haldane-gap excitations in the mixed-spin linear-chain antiferromagnet Nd2BaNiO5. The longitudinal mode, polarized along the direction of ordered moments, is observed for the first time. The model of isolated Haldane chains in a static staggered exchange field, that is known to work very well for static properties and transverse spin excitations in R2BaNiO5 compounds, fails to explain new results for the longitudinal spin gap.
Using the methods of the recently proposed Quantum Spectral Curve (QSC) originating from integrability of ${\cal N}=4$ Super--Yang-Mills theory we analytically continue the scaling dimensions of twist-2 operators and reproduce the so-called pomeron eigenvalue of the Balitsky-Fadin-Kuraev-Lipatov (BFKL) equation. Furthermore, we recovered the Faddeev-Korchemsky Baxter equation for Lipatov's spin chain and also found its generalization for the next-to-leading order in the BFKL scaling. Our results provide a non-trivial test of QSC describing the exact spectrum in planar ${\cal N}=4$ SYM at infinitely many loops for a highly nontrivial non-BPS quantity and also opens a way for a systematic expansion in the BFKL regime.
In this paper we give the classification of rank 3 vector bundles without "inner" cohomology on a quadric hypersurface \Q_n (n>3) by studying the associated monads.
In three dimensional spacetime with negative cosmology constant, the general relativity can be written as two copies of SO$(2,1)$ Chern-Simons theory. On a manifold with boundary the Chern-Simons theory induces a conformal field theory--WZW theory on the boundary. In this paper, it is show that with suitable boundary condition for BTZ black hole, the WZW theory can reduce to a massless scalar field on the horizon.
Let $E$ be an elliptic curve defined over ${\bf Q}$ and $K$ an imaginary quadratic field satisfying the Heegner hypothesis. A classical result of Kolyvagin states that, under suitable assumptions, if the basic Heegner point $y_K \in E(K)$ is not divisible by an odd prime $p$, then the groups $E(K)/{\bf Z} y_K$ and $\sha(E/K)$ are finite and their orders are prime to $p$. In this article we develop the following themes: firstly, we discuss improvements of Kolyvagin's result, following Cha (2005) and Lawson and Wuthrich (2016). Secondly, we prove an abstract Iwasawa-theoretical result which allows us to deduce, under several additional assumptions, that similar vanishing holds for all layers in the anticyclotomic ${\bf Z}_p$-extension of $K$. Analogous results hold for CM points on simple quotients of Jacobians of Shimura curves over totally real fields; this will be discussed in a separate article.
Meixner's historical remark in 1969 "... it can be shown that the concept of entropy in the absence of equilibrium is in fact not only questionable but that it cannot even be defined...." is investigated from today's insight. Several statements --such as the three laws of phenomenological thermodynamics, the embedding theorem and the adiabatical uniqueness-- are used to get rid of non-equilibrium entropy as a primitive concept. In this framework, Clausius inequality of open systems can be derived by use of the defining inequalities which establish the non-equilibrium quantities contact temperature and non-equilibrium molar entropy which allow to describe the interaction between the Schottky system and its controlling equilibrium environment.
Understanding crystal shapes is a fundamental subject in surface science. It is now well studied how chemical bondings determine crystal shapes via dependence of surface energies on surface orientations. Meanwhile, discoveries of topological materials have led us to a new paradigm in surface science, and one can expect that topological surface states may affect surface energies and crystal facets in an unconventional way. Here we show that the surface energy of glide-symmetric topological crystalline insulators (TCI) depends on the surface orientation in a singular way via the parity of the Miller index. This singular surface energy of the TCI affects equilibrium crystal shapes, resulting in emergence of unique crystal facets of the TCI. This singular dependence of the topological surface states is unique to the TCI protected by the glide symmetry in contrast to a TCI protected by a mirror symmetry. In addition, we show that such singular surface states of the TCI protected by the glide symmetries can be realized in KHgSb with first-principles calculations. Our results provide a basis for designs and manipulations of crystal facets by utilizing symmetry and topology.
Rubinstein and Sarnak investigated systems of inequalities of the form pi(x;q,a_1) > ... > pi(x;q,a_r), where pi(x;q,a) denotes the number of primes up to x that are congruent to a mod q. They showed, under standard hypotheses on the zeros of Dirichlet L-functions mod q, that the set of positive real numbers x for which these inequalities hold has positive (logarithmic) density delta_{q;a_1,dots,a_r} > 0. They also discovered the surprising fact that a certain distribution associated with these densities is not symmetric under permutations of the residue classes a_j in general, even if the a_j are all squares or all nonsquares mod q (a condition necessary to avoid obvious biases of the type first observed by Chebyshev). This asymmetry suggests, contrary to prior expectations, that the densities delta_{q;a_1,dots,a_r} themselves vary under permutations of the a_j.   In this paper, we derive (under the hypotheses used by Rubinstein and Sarnak) a general formula for the densities delta_{q;a_1,dots,a_r}, and we use this formula to calculate many of these densities when q <= 12 and r <= 4. For the special moduli q = 8 and q = 12, and for {a_1,a_2,a_3} a permutation of the nonsquares {3,5,7} mod 8 and {5,7,11} mod 12, respectively, we rigorously bound the error in our calculations, thus verifying that these densities are indeed asymmetric under permutation of the a_j. We also determine several situations in which the densities delta_{q;a_1,dots,a_r} remain unchanged under certain permutations of the a_j, and some situations in which they are provably different.
Quantitative phase analysis is one of the major applications of X-ray powder diffraction. The essential principle of quantitative phase analysis is that the diffraction intensity of a component phase in a mixture is proportional to its content. Nevertheless, the diffraction intensity of the component phases cannot be compared with each other directly since each phase has its specific diffraction power. The diffraction power of the unit cell of a crystal is well represented by the sum of the squared structure factors, which cannot be calculated directly when the structure data is unavailable. Here a method was demonstrated to calculate the diffraction power using only the chemical contents in the unit cell of a crystal, which enables quantitative phase analysis on a mixture sample consisting of crystalline phases with unknown atomic structures.
We discuss the response of a Bose-Einstein condensate to a change in the scattering length, which is experimentally realized by tuning the magnetic field near a Feshbach resonance. In particular, we consider the collapse of the condensate induced by a sudden change in the scattering length from a large positive to a small negative value. We also consider the condensate dynamics that results from a single pulse in the magnetic field, due to which the scattering length is rapidly increased from zero to a large value and then after some time rapidly decreased again to its initial value. We focus primarily on the consequences of the quantum evaporation process on the dynamics of the Bose-Einstein condensate, but also discuss the effects of atom-molecule coherence.
This paper is concerned with an inverse source problem for the three-dimensional Helmholtz equation by a single boundary measurement at a fixed frequency. We show the Lipschitz stability under the assumption that the source function is piecewise constant on a domain which is made of a union of disjoint convex polyhedral subdomains..
This paper is devoted to the analysis of non-negative solutions for a degenerate parabolic-elliptic Patlak-Keller-Segel system with critical nonlinear diffusion in a bounded domain with homogeneous Neumann boundary conditions. Our aim is to prove the existence of a global weak solution under a smallness condition on the mass of the initial data, there by completing previous results on nite blow-up for large masses. Under some higher regularity condition on solutions, the uniqueness of solutions is proved by using a classical duality technique.
Requiring that the matter fields are subject to the dominant energy condition, we establish the lower bound $(4\pi)^{-1} \kappa {\cal A}$ for the total mass $M$ of a static, spherically symmetric black hole spacetime. (${\cal A}$ and $\kappa$ denote the area and the surface gravity of the horizon, respectively.) Together with the fact that the Komar integral provides a simple relation between $M - (4\pi)^{-1} \kappa A$ and the strong energy condition, this enables us to prove that the Schwarzschild metric represents the only static, spherically symmetric black hole solution of a selfgravitating matter model satisfying the dominant, but violating the strong energy condition for the timelike Killing field $K$ at every point, that is, $R(K,K) \leq 0$. Applying this result to scalar fields, we recover the fact that the only black hole configuration of the spherically symmetric Einstein-Higgs model with arbitrary non-negative potential is the Schwarzschild spacetime with constant Higgs field. In the presence of electromagnetic fields, we also derive a stronger bound for the total mass, involving the electromagnetic potentials and charges. Again, this estimate provides a simple tool to prove a ``no-hair'' theorem for matter fields violating the strong energy condition.
The report of a significant deviation of the CMB temperature anisotropies distribution from Gaussianity (soon after the public release of the WMAP data in 2003) has become one of the most solid WMAP anomalies. This detection grounds on an excess of the kurtosis of the Spherical Mexican Hat Wavelet coefficients at scales of around 10 degrees. At these scales, a prominent feature --located in the southern Galactic hemisphere-- was highlighted from the rest of the SMHW coefficients: the Cold Spot. This article presents a comprehensive overview related to the study of the Cold Spot, paying attention to the non-Gaussianity detection methods, the morphological characteristics of the Cold Spot, and the possible sources studied in the literature to explain its nature. Special emphasis is made on the Cold Spot compatibility with a cosmic texture, commenting on future tests that would help to give support or discard this hypothesis.
Based on the general description for Z'-Z-\gamma mixing as derived from the electroweak chiral Lagrangian, we characterize and classify the various new physics models involving the Z' boson that have appeared in the literature into five classes: 1. Models with minimal Z'-Z mass mixing; 2. Models with minimal Z'-Z kinetic mixing; 3. Models with general Z'-Z mixing; 4. Models with Z'-\gamma kinetic and Z'-Z mixing; and 5. Models with Stueckelberg-type mixing. The corresponding mixing matrices are explicitly evaluated for each of these classes. We constrain and classify the Z' boson charges with respect to quark-leptons by anomaly cancellation conditions.
This letter proposes a new scenario to solve the structural or conceptual problems remained in quantum mechanics, and gives an overview of the theory proposed in quant-ph/9906130 (including quant-ph/9909025 and quant-ph/0001015).
We show that the distribution of elliptic curves in isogeny classes of curves with a given value of the Frobenius trace $t$ becomes close to uniform even when $t$ is averaged over very short intervals inside the Hasse-Weil interval.
We use recent work of Jonah Blasiak (2012) to prove a stability result for the coefficients in the Kronecker product of two Schur functions: one indexed by a hook partition and one indexed by a rectangle partition. We also give bounds for the size of the partition starting with which the Kronecker coefficients are stable. Moreover, we show that once the bound is reached, no new Schur functions appear in the decomposition of Kronecker product, thus allowing one to recover the decomposition from the smallest case in which the stability holds.
Extending a recent result of S.B. Giddings, F. Hacquebord and H. Verlinde, we show that in the U(N) SYM Matrix theory there exist classical BPS instantons which interpolate between different closed string configurations via joining/splitting interactions similar to those of string field theory. We construct them starting from branched coverings of Riemann surfaces. For the class of them which we analyze in detail the construction can be made explicit in terms U(N) affine Toda field theories.
We study an effect of moderate magnetic field on variable range hopping conductivity in arrays of ferromagnetic granules separated by tunnel barriers. It is shown that the resulting magnetoresistance can be significantly larger than the standard "giant" magnetoresistance in Fe-N-Fe-N... multilayers. The effect is related to a gain in densities of states available for the virtual processes within the intermediate granules due to magnetic-field induced alignment of the granule magnetizations.
The \textit{sepr-sequence} of an $n\times n$ real matrix $A$ is $(s_1,\ldots,s_n)$, where $s_k$ is the subset of those signs of $+,-,0$ that appear in the values of the $k\times k$ principal minors of $A$. The $12\times 12$ matrix $$\left(\begin{array}{cccccc|ccc|ccc} 0&0&0&0&0&0&0&0&0&a_1&0&0\\ 0&0&0&0&0&0&0&0&0&0&a_2&0\\ 0&0&0&0&0&0&0&0&0&0&0&a_3\\ 0&0&0&0&0&0&0&0&0&0&0&a_4\\ 0&0&0&0&0&0&0&0&0&0&0&a_5\\ 0&0&0&0&0&0&0&0&0&0&0&a_6\\\hline b_1&b_2&0&0&0&0&0&0&0&0&0&0\\ b_3&b_4&0&0&b_5&-b_6&0&0&0&0&0&0\\ 0&b_7&b_8&-b_9&b_{10}&b_{11}&0&0&0&0&0&0\\\hline 0&0&0&0&0&0&c_1&0&0&0&0&0\\ 0&0&0&0&0&0&0&c_2&0&0&0&0\\ 0&0&0&0&0&0&0&0&c_3&0&0&0 \end{array}\right)$$ does always have $s_k=\{0,+,-\}$ if $k=3,6,9$ and $s_k=\{0\}$ otherwise, provided that the variables are positive. However, every principal $9\times 9$ minor that is not identically zero can take values of both signs.
V. I. Vasyunin has introduced special sequences of step functions related to the strong Nyman-Beurling criterion that converge pointwise to 1 in $[1,\infty)$. We show here that the first and simplest such sequence considered by Vasyunin diverges in $L_1((1,\infty),x^{-2}dx)$, which of course precludes the $L_2((1,\infty),x^{-2}dx)$-convergence needed for the Riemann hypothesis. Whether all sequences considered by this author also diverge remains an interesting open question.
Four well-sampled spectral energy distributions (SEDs) of PMN J0948+0022 are fitted with the syn+SSC+EC model to derive the physical parameters of its jets and to investigate the spectral variations of its SEDs. A tentative correlation between the peak luminosity L_c and peak frequency nu_c of its inverse Compton (IC) bump is found in both the observer and co-moving frames, indicating that the variations of luminosity are accompanied with the spectral shift. A correlation between L_c and delta is found, and thus the magnification of the external photon field by the bulk motion of the radiation regions is an essential reason for the spectral variation since the IC bump of PMN J0948+0022 is dominated by the EC process.
We present the results of simultaneous Suzaku and NuSTAR observations of the nearest Low-Luminosity Active Galactic Nucleus (LLAGN), M81*. The spectrum is well described by a cut-off power law plus narrow emission lines from Fe K$\alpha$, Fe XXV and Fe XXVI. There is no evidence of Compton reflection from an optically thick disc, and we obtain the strongest constraint on the reflection fraction in M81* to date, with a best-fit value of $R = 0.0$ with an upper limit of $R < 0.1$. The Fe K$\alpha$ line may be produced in optically thin, $N_H = 1 \times 10^{23}$ cm$^{-2}$, gas located in the equatorial plane that could be the broad line region. The ionized iron lines may originate in the hot, inner accretion flow. The X-ray continuum shows significant variability on $\sim 40$ ks timescales suggesting that the primary X-ray source is $\sim 100$s of gravitational radii in size. If this X-ray source illuminates any putative optically thick disc, the weakness of reflection implies that such a disc lies outside a few $\times 10^3$ gravitational radii. An optically thin accretion flow inside a truncated optically thick disc appears to be a common feature of LLAGN that are accreting at only a tiny fraction of the Eddington limit.
For a specific choice of the diffusion, the parabolic-elliptic Patlak-Keller-Segel system with non-linear diffusion (also referred to as the quasi-linear Smoluchowski-Poisson equation) exhibits an interesting threshold phenomenon: there is a critical mass $M_c>0$ such that all the solutions with initial data of mass smaller or equal to $M_c$ exist globally while the solution blows up in finite time for a large class of initial data with mass greater than $M_c$. Unlike in space dimension 2, finite mass self-similar blowing-up solutions are shown to exist in space dimension $d?3$.
We present a complete set of analytical and invariant expressions for the steady-state density matrix of atoms in a resonant radiation field with arbitrary intensity and polarization. The field drives the closed dipole transition with arbitrary values of the angular momenta $J_{g}$ and $J_{e}$ of the ground and excited state. The steady-state density matrix is expressed in terms of spherical harmonics of a complex direction given by the field polarization vector. The generalization to the case of broad-band radiation is given. We indicate various applications of these results.
We derive a quantum-mechanical formula of the orbital magnetic quadrupole moment (MQM) in periodic systems by using the gauge-covariant gradient expansion. This formula is valid for insulators and metals at zero and finite temperature. We also prove a direct relation between the MQM and magnetoelectric (ME) susceptibility for insulators at zero temperature. It indicates that the MQM is a microscopic origin of the ME effect. Using the formula, we quantitatively estimate these quantities for room-temperature antiferromagnetic semiconductors BaMn$_2$As$_2$ and CeMn$_2$Ge$_{2 - x}$Si$_x$. We find that the orbital contribution to the ME susceptibility is comparable with or even dominant over the spin contribution.
It has been postulated that globular clusters could be sources of Very-High Energy (VHE) gamma rays, powered by milli-second pulsars. This could be due to cumulative direct emission or to plerion-type emission driven by colliding winds. In particular the southern hemisphere globular cluster 47 Tuc has been singled out as a potential source in both models. In light of the recent detection by the Fermi Gamma-ray Space Telescope (FGST) of 47 Tuc, the first detection of any globular cluster as a gamma-ray source, we present the results of observations of northern hemisphere globular clusters by VERITAS. Three globular clusters have been observed: M15, M13 and M5. Of these, M15 and M13 have been explicitly proposed as VHE gamma-ray sources and M5 possess similarities with them.
We investigate how symmetry and topological order are coupled in the ${2+1}$d $\mathbb{Z}_{N}$ rank-2 toric code for general $N$, which is an exactly solvable point in the Higgs phase of a symmetric rank-2 $U(1)$ gauge theory. The symmetry enriched topological order present has a non-trivial realization of square-lattice translation (and rotation/reflection) symmetry, where anyons on different lattice sites have different types and belong to different superselection sectors. We call such particles "position-dependent excitations." As a result, in the rank-2 toric code anyons can hop by one lattice site in some directions while only by $N$ lattice sites in others, reminiscent of fracton topological order in ${3+1}$d. We find that while there are $N^2$ flavors of $e$ charges and $2N$ flavors of $m$ fluxes, there are not $N^{N^{2} + 2N}$ anyon types. Instead, there are $N^{6}$ anyon types, and we can use Chern-Simons theory with six $U(1)$ gauge fields to describe all of them. While the lattice translations permute anyon types, we find that such permutations cannot be expressed as transformations on the six $U(1)$ gauge fields. Thus the realization of translation symmetry in the $U^6(1)$ Chern-Simons theory is not known. Despite this, we find a way to calculate the translation-dependent properties of the theory. In particular, we find that the ground state degeneracy on an ${L_{x}\times L_{y}}$ torus is ${N^{3}\gcd(L_{x},N) \gcd(L_{y},N) \gcd(L_{x},L_{y},N)}$, where $\gcd$ stands for "greatest common divisor." We argue that this is a manifestation of UV/IR mixing which arises from the interplay between lattice symmetries and topological order.
We present detections of stellar flares of Wolf\,359, an M6.5 dwarf in the solar neighborhood (2.41~pc) known to be prone to flares due to surface magnetic activity. The observations were carried out from 2020 April 23 to 29 with a 1-m and a 0.5-m telescope separated by nearly 300~km in Xinjiang, China. In 27~hr of photometric monitoring, a total of 13 optical flares were detected, each with a total energy of $\gtrsim 5 \times 10^{29}$~erg. The measured event rate of about once every two hours is consistent with those reported previously in radio, X-ray and optical wavelengths for this star. One such flare, detected by both telescopes on 26 April, was an energetic event with a released energy of nearly $10^{33}$~erg. The two-telescope lightcurves of this major event sampled at different cadences and exposure timings enabled us to better estimate the intrinsic flare profile, which reached a peak of up to 1.6 times the stellar quiescent brightness, that otherwise would have been underestimated in the observed flare amplitudes of about $0.4$ and $0.8$, respectively, with single telescopes alone. The compromise between fast sampling so as to resolve a flare profile versus a longer integration time for higher photometric signal-to-noise provides a useful guidance in the experimental design of future flare observations.