ShantanuT01/DACTYL-Pretraining huggingface dataset:
The concept of temperature is one of the key ideas in describing the thermodynamical properties of a physical system. In classical statistical mechanics of ideal gases, the notion of temperature can be described in two different ways, the kinetic temperature and the thermodynamic temperature. For the Boltzmann distribution, the two notions lead to the same result. However, for a general probability density function, while the kinetic temperature has been commonly used, there appears to be no corresponding general definition of thermodynamic temperature. In this paper, we propose such a definition and show that it is connected to the Fisher information associated with the distribution of the momenta.
Our light-traces-mass (LTM) strong-lensing model for MACS J1149.5+2223 has played several key roles over the last decade: it aided the identification of multiple images in this cluster and the study of MACS1149-JD1 at redshift $z\simeq9$, it was used to estimate the properties of the first multiply imaged supernova, Refsdal, in its discovery paper, and of the first caustic crossing event by a cluster, Lensed Star 1. Supernova Refsdal supplied an invaluable opportunity to conduct a blind test of the ability of common lens-modeling techniques to accurately describe the properties of SN Refsdal's images and predict the reappearance of one of its counter images that was due about a year post-discovery of the original Einstein cross. Thanks to this practice, in which our submitted model yielded some outlying results, we located a numerical artifact in the time delay (TD) calculation part of the code, which was now fixed. This artifact did not influence the reproduction of multiple images (i.e., the deflection fields -- which are those constrained directly from the observations) or the derived mass model, and so it remained unnoticed prior to supernova Refsdal, emphasizing the importance of blind tests in astronomy. Here we update our model and present revised LTM measurements for Refsdal. These are important not only for completing the LTM view of the Refsdal event, but also because they affect the range of values predicted from different lens-modeling techniques and thus the range of systematic uncertainties for the TD calculation and the resulting Hubble constant.
We give many examples in which there exist infinitely many divisorial conditions on the moduli space of polarized K3 surfaces $(S,H)$ of degree $H^2=2g-2$, $g \geq 3$, and Picard number $rk N(S)=\rho(S)=2$ such that for a general K3 surface $S$ satisfying these conditions the moduli space of sheaves $M_S(r,H,s)$ is birationally equivalent to the Hilbert scheme $S[g-rs]$ of zero-dimensional subschemes of $S$ of lenght equal to $g-rs$. This result generalizes the main result of \cite{Nik1} when $g=rs+1$ and of \cite{Monat} when $r=s=2$, $g \geq 5$.
Large deviations principles characterize the exponential decay rates of the probabilities of rare events. Cerrai and Rockner [13] proved that systems of stochastic reaction-diffusion equations satisfy a large deviations principle that is uniform over bounded sets of initial data.   This paper proves uniform large deviations results for a system of stochastic reaction--diffusion equations in a more general setting than Cerrai and Rockner. Furthermore, this paper identifies two common situations where the large deviations principle is uniform over unbounded sets of initial data, enabling the characterization of Freidlin-Wentzell exit time and exit shape asymptotics from unbounded sets.
We study the existence of regular solutions of the incompressible stationary Navier-Stokes equations in $n$-dimensional Euclidean space with a given bounded external force of compact support. In dimensions $n\le 5$, the existence of such solutions was known. In this paper, we extend it to dimensions $n\le 15$.
High resolution X-ray observations indicate that the entropy profiles in the central regions of some massive cooling flow clusters are well approximated by powerlaws. McCarthy and coworkers recently accounted for this trend with an analytic model that includes the detailed effects of radiative cooling. Interestingly, these authors found that cooling (and subsequent inflow of the gas) naturally establishes approximate steady-state powerlaw entropy profiles in the cores of clusters. However, the origin of this behavior and its dependence on initial conditions have yet to be elucidated. In the present study, we explain this trend in the context of the self-similar cooling wave model developed previously by Bertschinger (1989). It is shown that the logarithmic slope of the entropy profile in the cores of relaxed cooling flow clusters is given by a simple analytic function that depends only on the logarithmic slopes of the local gravitational potential and the cooling function. We discuss a number of potentially interesting uses of the above result, including: (1) a way of measuring the shapes of gravitational potentials of cooling flow clusters (which may, for example, be compared with the results of the standard hydrostatic equilibrium method); (2) a simple method for constructing realistic analytic cluster models that include the effects of radiative cooling; and (3) a test of the reliability of cooling routines implemented in analytic models and hydrodynamic simulations.
Redshifted 21cm-line signal from neutral hydrogens in the intergalactic medium (IGM) gives a direct probe of the epoch of reionization (EoR). In this paper, we investigate the potential of the variance and skewness of the probability distribution function of the 21cm brightness temperature for constraining EoR models. These statistical quantities are simple, easy to calculate from the observed visibility and thus suitable for the early exploration of the EoR with ongoing telescopes such as the Murchison Widefield Array (MWA) and LOw Frequency ARray (LOFAR). We show, by performing Fisher analysis, that the variance and skewness at $z=7-9$ are complementary to each other to constrain the EoR model parameters such as the minimum virial temperature of halos which host luminous objects, ionizing efficiency and mean free path of ionizing photons in the IGM. Quantitatively, the constraining power highly depends on the quality of the foreground subtraction and calibration. We give a best case estimate of the constraints on the parameters, neglecting the systematics other than the thermal noise.
The concepts of deconfinement and topological order are of great current interest for quantum information science and for our understanding of quantum materials. Here, we introduce a simple model of three antiferromagnetically coupled Kondo impurities, a Kondo triangle, which can be used to further extend the application of these concepts to electronic systems. We show that, by tuning the magnetic frustration, the Kondo triangle undergoes a quantum phase transition between two phases of unbroken symmetry, signaling a phase transition beyond the Landau paradigm. We demonstrate that the frustrated spin liquid phase is described by a three-channel Kondo (3CK) fixed point and thus displays an irrational ground state degeneracy. Using an Abrikosov pseudofermion representation, this quantum state is categorized by an emergent U(1) gauge field and its projective symmetry group. The gauge theory is deconfining in the sense that a miniature Wilson loop orders and topological defects (instantons in the gauge field) are expelled. This phase persists in the presence of moderate Kondo screening until proliferation of topological defects leads to a quantum phase transition to an unfrustrated Fermi liquid phase. Based on this evidence, we propose that the 3CK phase displays topological order in a similar sense as gapless spin liquids.
We present and analyze Raman spectra of the Mott insulator Ca$_2$RuO$_4$, whose quasi-two-dimensional antiferromagnetic order has been described as a condensate of low-lying spin-orbit excitons with angular momentum $J_{eff}=1$. In the $A_g$ polarization geometry, the amplitude (Higgs) mode of the spin-orbit condensate is directly probed in the scalar channel, thus avoiding infrared-singular magnon contributions. In the $B_{1g}$ geometry, we observe a single-magnon peak as well as two-magnon and two-Higgs excitations. Model calculations using exact diagonalization quantitatively agree with the observations. Together with recent neutron scattering data, our study provides strong evidence for excitonic magnetism in Ca$_2$RuO$_4$ and points out new perspectives for research on the Higgs mode in two dimensions.
In this paper the results of AGASA experiment is discussed. It is argued that the UHECR radiation is composed of long lived particles with mass, where is the proton mass. Keywords: UHECR; Modified Lorentz transformation; New particles. PACS: 96.50.S, 96.50sb, 13.85Tp
We examine if the cosmological relaxation mechanism, which was proposed recently as a new solution to the hierarchy problem, can be compatible with high reheating temperature well above the weak scale. As the barrier potential disappears at high temperature, the relaxion rolls down further after the reheating, which may ruin the successful implementation of the relaxation mechanism. It is noted that if the relaxion is coupled to a dark gauge boson, the new frictional force arising from dark gauge boson production can efficiently slow down the relaxion motion, which allows the relaxion to be stabilized after the electroweak phase transition for a wide range of model parameters, while satisfying the known observational constraints.
Let $K$ be a field of characteristic $\ne 2$ and let $X$ be the affine variety over $K$ defined by the equation $$ X:\ a_0x_0^2 + \cdots + a_nx_n^2 = 1 $$ where $n\ge 0$ and $a_i\in K$. In this paper we compute the lowest mod 2 \'{e}tale homological obstruction class to the existence of a $K$-rational point on $X$, and show that it is the cup product of the form $$ o_{n+1} = [a_0]\cup\cdots\cup[a_n]. $$   Our computation is an \'{e}tale-homotopy analogue of the topological fact that Stiefel-Whitney classes are the homological obstructions to find a section to the unit sphere bundle of a real vector bundle.
We compare different methods of computing the orbital eccentricity of quasi-circular binary black hole systems using the orbital variables and gravitational wave phase and frequency. For eccentricities of about a per cent, most methods work satisfactorily. For small eccentricity, however, the gravitational wave phase allows a particularly clean and reliable measurement of the eccentricity. Furthermore, we measure the decay of the orbital eccentricity during the inspiral and find reasonable agreement with post-Newtonian results. Finally, we measure the periastron advance of non-spinning binary black holes, and we compare them to post-Newtonian approximations. With the low uncertainty in the measurement of the periastron advance, we positively detect deviations between fully numerical simulations and post-Newtonian calculations.
Vacuum and medium modified fragmentation functions are used to study the properties of hadrons produced in hard interactions, in $p$-$p$ and $A$-$A$ collisions, respectively. We study the modification of reconstructed jets and high transverse momentum (high-$p_\mathrm{T}$) hadrons as they propagate through a dense medium. Jets and jet modification are studied within the framework of a factorized jet function. The vacuum jet function is found consistent with PYTHIA simulations. Both the modification of the fragmentation function and the jet function are carried out within the identical higher-twist energy loss formalism. This approach is then extended to di-hadron production within a jet. Its further extension to a "di-prong" function and its application to the soft-drop measurements are discussed. The methodology of extending these semi-analytical calculations to full Monte-Carlo simulations is outlined. All calculations are carried out within a (2+1)-D viscous hydrodynamic simulation and compared to experimental data from a variety of collision energies.
The pulsar profile is characterised by two distinct emission components, the core and the cone. The standard model of a pulsar radio emission beam originating from dipolar magnetic fields, places the core at the centre surrounded by concentric layers of inner and outer conal components. The core emission is expected to have steeper spectra compared to the cones. We present a detailed analysis of the relative differences in spectra between the core and conal emission from a large sample of 53 pulsars over a wide frequency range between 100 MHz and 10 GHz. The core was seen to be much steeper than the cones particularly between 100 MHz and 1 GHz with a relative difference between the spectral index $\Delta\alpha_{core/cone}\sim$ -1.0. In addition we also found the spectra of the outer conal components to be steeper than the inner cone with relative difference in the spectral index $\Delta\alpha_{in/out}\sim$ +0.5. The flattening of the spectra from the magnetic axis towards the edge of the open field line region with increasing curvature of the field lines is a natural outcome of the coherent curvature radiation from charged soliton bunches, and explains the difference in spectra between the core and the cones. In addition due to the relativistic beaming effect, the radiation is only visible when it is directed towards the observer over a narrow angle $\theta\leq 1/\gamma$, where $\gamma$ is the Lorentz factor of the outflowing plasma clouds. This restricts the emission particularly from outer cones, that are associated with field lines with larger curvature thereby making the spectra steeper than the inner cones.
An analysis is given connecting event rates for the direct detection of neutralino dark matter with the possible signatures of supersymmetry at the LHC. It is shown that if an effect is seen in the direct detection experiments at a level of $O(10^{-44})$ cm$^2$ for the neutralino-proton cross section, then within the mSUGRA model the next heavier particle above the neutralino is either a stau, a chargino, or a CP odd/CP even (A/H) Higgs boson. Further, the collider analysis shows that models with a neutralino-proton cross section at the level of $(1-5)\times 10^{-44}$ cm$^2$ could be probed with as little as 1 fb$^{-1}$ of integrated luminosity at the LHC at $\sqrt s=10$ TeV. The most recent limit from the five tower CDMS II result on WIMP-nucleon cross section is discussed in this context. It is argued that the conclusions of the analysis given here are more broadly applicable with inclusion of non-universalities in the SUGRA models.
We analyze the behavior of an itinerant Fermi system near a charge nematic(n=2) Pomeranchuk instability in terms of the Landau Fermi liquid (FL) theory. The main object of our study is the fully renormalized vertex function $\Gamma\Omega$, related to the Landau interaction function. We derive $\Gamma^\Omega$ for a model case of the long-range interaction in the nematic channel. Already within the Random Phase Approximation (RPA), the vertex is singular near the instability. The full vertex, obtained by resumming the ladder series composed of the RPA vertices, differs from the RPA result by a multiplicative renormalization factor $Z_\Gamma$, related to the single-particle residue $Z$ and effective mass renormalization $m^*/m$. We employ the Pitaevski-Landau identities, which express the derivatives of the self-energy in terms of $\Gamma^\Omega$, to obtain and solve a set of coupled non-linear equations for $Z_\Gamma$, $Z$, and $m^*/m$. We show that near the transition the system enters a critical FL regime, where $Z_\Gamma \sim Z \propto (1 + g_{c,2})^{1/2}$ and $m^*/m \approx 1/Z$, where $g_{c,2}$ is the $n=2$ charge Landau component which approaches -1 at the instability. We construct the Landau function of the critical FL and show that all but $g_{c,2}$ Landau components diverge at the critical point. We also show that in the critical regime the one-loop result for the self-energy $\Sigma (K) \propto \int dP G(P) D (K-P)$ is asymptotically exact if one identifies the effective interaction $D$ with the RPA form of $\Gamma^\Omega$.
The equation of state for matter with energy density above 2 x10^14 g/cm^3 is parametrized by P = kN^Gamma, where N is the number density, Gamma is the adiabatic index, and k a constant. Using this scheme to generate thousands of models, together with data on neutron star masses, it is found, for a core region with a constant adiabatic index, that the central density must satisfy 10^15 gm/cm^3 < rho_c < 10^16 gm/cm^3, with Gamma > 2.2. Further preliminary results indicate, based on the observed neutrino flux from supernova 1987a, that this number must be considerably higher, on the order of 3.5. These results provide evidence for a hard equation of state in the cores of neutron stars.
If V is the vertex sequence of a symmetric 2t-cycle in the hypercube graph with the vertices {1,-1}^t, then for any vertex T of the graph there exists a unique inclusion-minimal subset of V such that T is the sum of its elements. We present a simple combinatorial statistic on decompositions of vertices of the hypercube graphs with respect to symmetric cycles and describe their basic metric properties.
We recently suggested a nonlocal modification of Einstein's field equations in which Newton's constant $G$ was promoted to a covariant differential operator $G_\Lambda(\Box_g)$. The latter contains two independent contributions, which operate respectively in the infrared (IR) and ultraviolet (UV) energy regimes. In the light of the recent direct gravitational radiation measurements we aim to determine the UV-modified 1.5 post-Newtonian radiative quadrupole moment of a generic $n$-body system. We eventually use these initial results in the particular context of a binary system and observe that in the limit vanishing UV parameters we precisely recover the corresponding general relativistic results. Moreover we observe that the leading order deviation of the UV-modified radiative quadrupole moment numerically coincides with findings obtained in the framework of calculations performed previously in the context of possible deviations of the perihelion precession of Mercury.
Moduli spaces of semistable sheaves on a K3 or abelian surface with respect to a general ample divisor are shown to be locally factorial, with the exception of symmetric products of a K3 or abelian surface and the class of moduli spaces found by O'Grady. Consequently, since singular moduli space that do not belong to these exceptional cases have singularities in codimension $\geq4$ they do no admit projective symplectic resolutions.
We consider a random variable $X$ that takes values in a (possibly infinite-dimensional) topological vector space $\mathcal{X}$. We show that, with respect to an appropriate "normal distance" on $\mathcal{X}$, concentration inequalities for linear and non-linear functions of $X$ are equivalent. This normal distance corresponds naturally to the concentration rate in classical concentration results such as Gaussian concentration and concentration on the Euclidean and Hamming cubes. Under suitable assumptions on the roundness of the sets of interest, the concentration inequalities so obtained are asymptotically optimal in the high-dimensional limit.
We use the three-scale framework of Hu et al. to show how the Cosmic Microwave Background anisotropy spectrum depends on the fundamental constants. As expected, the spectrum depends only on \emph{dimensionless} combinations of the constants, and we emphasize the points that make this generally true for cosmological observables. Our analysis suggests that the CMB spectrum shape is mostly determined by $\alpha^2m_e/m_p$ and the proton-CDM-particle mass ratio, $m_p/\mchi$. The distance to the last-scattering surface depends on $Gm_p\mchi/\hbar c$, so published CMB observational limits on time variations of the constants implicitly assume the time-independence of this quantity, as well as assuming a flat-\lcdm~cosmological model. On the other hand, low-redshift BAO, $H_0$ and baryon-mass-fraction measurements can be combined with the \emph{shape} of the CMB spectrum to give information that is largely independent of these assumptions. In particular we show that the pre-recombination values of $G\mchi^2/\hbar c$, $m_p/\mchi$ and $\alpha^2m_e/m_p$ are equal to their present values at a precision of $\sim15\%$.
We present a general conjecture on congruences between Hecke eigenvalues of parabolically induced and cuspidal automorphic representations of split reductive groups, modulo divisors of critical values of certain $L$-functions. We examine the consequences in several special cases, and use the Bloch-Kato conjecture to further motivate a belief in the congruences.
Let M be a smooth and compact moduli space of stable coherent sheaves on a projective surface S with an effective (or trivial) anti-canonical line bundle. We find generators for the cohomology ring of M, with integral coefficients. When S is simply connected and a universal sheaf E exists over SxM, then its class [E] admits a Kunneth decomposition as a class in the tensor product of the topological K-rings K(S) and K(M). The generators are the Chern classes of the Kunneth factors of [E] in K(M). The general case is similar
Inspired by a class of algorithms proposed by Farhi et al. (arXiv:1411.4028), namely the quantum approximate optimization algorithm (QAOA), we present a circuit-based quantum algorithm to search for a needle in a haystack, obtaining the same quadratic speedup achieved by Grover's original algorithm. In our algorithm, the problem Hamiltonian (oracle) and a transverse field are applied alternately to the system in a periodic manner. We introduce a technique, based on spin-coherent states, to analyze the composite unitary in a single period. This composite unitary drives a closed transition between two states that have high degrees of overlap with the initial state and the target state, respectively. The transition rate in our algorithm is of order $\Theta(1/\sqrt N)$, and the overlaps are of order $\Theta(1)$, yielding a nearly optimal query complexity of $T\simeq \sqrt N (\pi/2\sqrt 2\,)$. Our algorithm is a QAOA circuit that demonstrates a quantum advantage with a large number of iterations that is not derived from Trotterization of an adiabatic quantum optimization (AQO) algorithm. It also suggests that the analysis required to understand QAOA circuits involves a very different process from estimating the energy gap of a Hamiltonian in AQO.
We use the newly published 28 observational Hubble parameter data ($H(z)$) and current largest SNe Ia samples (Union2.1) to test whether the universe is transparent. Three cosmological-model-independent methods (nearby SNe Ia method, interpolation method and smoothing method) are proposed through comparing opacity-free distance modulus from Hubble parameter data and opacity-dependent distance modulus from SNe Ia . Two parameterizations, $\tau(z)=2\epsilon z$ and $\tau(z)=(1+z)^{2\epsilon}-1$ are adopted for the optical depth associated to the cosmic absorption. We find that the results are not sensitive to the methods and parameterizations. Our results support a transparent universe.