ShantanuT01/DACTYL-Pretraining huggingface dataset:
A detailed analysis of the galaxy distribution in the Southern Sky Redshift Survey (SSRS) by means of the multifractal or scaling formalism is presented. It is shown that galaxies cluster in different ways according to their morphological type as well as their size. Ellipticals are more clustered than spirals, even at scales up to 15 h$^{-1}$ Mpc, whereas no clear segregation between early and late spirals is found. It is also shown that smaller galaxies distribute more homogeneously than larger galaxies.
Let $k$ be an algebraically closed field of characteristic $p > 0$. Let $X$ be an irreducible smooth projective curve of genus $g$ over $k$. Fix an integer $n \geq 2$, and let $S^n(X)$ be the $n$-fold symmetric product of $X$. In this article we find the $S$-fundamental group scheme and Nori's fundamental group scheme of $S^n(X)$.
We study the phase diagram of a one-dimensional version of the Kitaev spin-1/2 model with an extra ``$\Gamma$-term", using analytical, density matrix renormalization group and exact diagonalization methods. Two intriguing phases are found. In the gapless phase, although the exact symmetry group of the system is discrete, the low energy theory is described by an emergent SU(2)$_1$ Wess-Zumino-Witten (WZW) model. On the other hand, the spin-spin correlation functions exhibit SU(2) breaking prefactors, even though the exponents and the logarithmic corrections are consistent with the SU(2)$_1$ predictions. A modified nonabelian bosonization formula is proposed to capture such exotic emergent ``partial" SU(2) symmetry. In the ordered phase, there is numerical evidence for an $O_h\rightarrow D_4$ spontaneous symmetry breaking.
Ultra-massive hydrogen-rich (DA) white dwarfs (WD) are expected to have a substantial portion of their cores in a crystalline state at the effective temperatures characterizing the ZZ Ceti instability strip, as a result of Coulomb interactions. Asteroseismological analyses of these WDs can provide valuable information related to the crystallization process, the core chemical composition and the evolutionary origin of these stars. We present a thorough asteroseismological analysis of the ultra-massive ZZ Ceti star BPM~37093, which exhibits a rich period spectrum, on the basis of a complete set of fully evolutionary models that represent ultra-massive oxygen/neon(ONe)-core DA WD stars harbouring a range of hydrogen (H) envelope thicknesses. We also carry out preliminary asteroseismological inferences on two other ultra-massive ZZ Ceti stars that exhibit fewer periods, GD~518, and SDSS~J0840+5222. We found a mean period spacing of $\Delta \Pi \sim 17$ s in the data of BPM~37093, associated to $\ell= 2$ modes. We found asteroseismological models for the three objects under analysis, two of them (BPM~37093 and GD~518) characterized by canonical (thick) H envelopes, and the third one (SDSS~J0840+5222) with a thinner H envelope. We also derive asteroseismological distances which are somewhat different to the astrometric measurements of {\it Gaia} for these stars. Asteroseismological analyses like the one presented in this paper could lead to a more complete knowledge of the processes occurring during crystallization inside WDs. Also, they could make it possible to deduce the core chemical composition of ultra-massive WDs, and in this way, to infer their evolutionary origin, i.e., if the star has a ONe core and then is the result of single-star evolution, or if it harbour a carbon/oxygen (CO) core and is the product of a merger of the two components of a binary system.
The dependence of the magnetic ordering temperature To of Sm metal was determined through four-point electrical resistivity measurements to pressures as high as 150 GPa. A strong increase in To with pressure is observed above 85 GPa. In this pressure range Sm ions alloyed in dilute concentration with superconducting Y exhibit giant Kondo pair breaking. Taken together, these results suggest that for pressures above 85 GPa Sm is in a highly correlated electron state, like a Kondo lattice, with an unusually high value of To. A detailed comparison is made with similar results obtained earlier on Nd, Tb and Dy and their dilute magnetic alloys with superconducting Y.
We compute the frequency dependent conductivity of the two dimensional square lattice Hubbard model at zero temperature as a function of density to second order in the interaction strength, and compare the results to the predictions of single-site dynamical mean field theory computed at the same order. We find that despite the neglect of vertex corrections, the single site dynamical mean field approximation produces semiquantitatively accurate results for most carrier concentrations, but fails qualitatively for the nearly empty or nearly filled band cases where the theory exhibits an emergent Galilean invariance. The theory also becomes qualitatively inaccurate very near half filling if nesting is important.
We present a unitary correlation operator that explicitly induces into shell model type many-body states short ranged two-body correlations caused by the strong repulsive core and the pronounced tensor part of the nucleon-nucleon interaction. Alternatively an effective Hamiltonian can be defined by applying this unitary correlator to the realistic nucleon-nucleon interaction.   The momentum space representation shows that realistic interactions which differ in their short range behaviour are mapped on the same correlated Hamiltonian, indicating a successful provision for the correlations at high momenta. Calculations for He4 using the one- and two-body part of the correlated Hamiltonian compare favorably with exact many-body methods. For heavier nuclei like O16 and Ca40 where exact many-body calculations are not possible we compare our results with other approximations. The correlated single-particle momentum distributions describe the occupation of states above the Fermi momentum. The Unitary Correlation Operator Method (UCOM) can be used in mean-field and shell model configuration spaces that are not able to describe these repulsive and tensor correlations explicitly.
This paper is the third in a series of papers working towards the construction of a realistic, evolving, non-linear force-free coronal field model for the solar magnetic carpet. Here, we present preliminary results of 3D time-dependent simulations of the small-scale coronal field of the magnetic carpet. Four simulations are considered, each with the same evolving photospheric boundary condition: a 48 hr time series of synthetic magnetograms produced from the model of Meyer, Mackay, van Ballegooijen and Parnell, 2011, Solar Phys., 272, 29. Three simulations include a uniform, overlying coronal magnetic field of differing strength, the fourth simulation includes no overlying field. The build-up, storage and dissipation of magnetic energy within the simulations is studied. In particular, we study their dependence upon the evolution of the photospheric magnetic field and the strength of the overlying coronal field. We also consider where energy is stored and dissipated within the coronal field. The free magnetic energy built up is found to be more than sufficient to power small-scale, transient phenomena such as nanoflares and X-ray bright points, with the bulk of the free energy found to be stored low down, between 0.5-0.8 Mm. The energy dissipated is presently found to be too small to account for the heating of the entire quiet Sun corona. However, the form and location of energy dissipation regions are in qualitative agreement with what is observed on small scales on the Sun. Future MHD modelling using the same synthetic magnetograms may lead to a higher energy release.
We prove existence of static solutions to the cylindrically symmetric Einstein-Vlasov system, and we show that the matter cylinder has finite extension. The same results are also proved for a quite general class of equations of state for perfect fluids coupled to the Einstein equations, extending the class of equations of state considered in \cite{BL}. We also obtain this result for the Vlasov-Poisson system.
We compute quantitative bounds for measuring the discrepancy between the distribution of two min-max statistics involving either pairs of Gaussian random matrices, or one Gaussian and one Gaussian-subordinated random matrix. In the fully Gaussian setup, our approach allows us to recover quantitative versions of well-known inequalities by Gordon (1985, 1987, 1992), thus generalising the quantitative version of the Sudakov-Fernique inequality deduced in Chatterjee (2005). On the other hand, the Gaussian-subordinated case yields generalizations of estimates by Chernozhukov et al. (2015) and Koike (2019). As an application, we establish fourth moment bounds for matrices of multiple stochastic Wiener-It\^o integrals, that we illustrate with an example having a statistical flavour.
In the effective Ising spin-1/2 antiferromagnetic chain system BaCo$_2$V$_2$O$_8, the magnetic-field influence is highly anisotropic. For magnetic fields along the easy axis $c$, the N\'{e}el order is strongly suppressed already for low fields and an incommensurate order is entered above 4 T. We present a detailed study of the magnetic phase diagrams for different magnetic field directions, which are derived from magnetization data, high-resolution thermal expansion and magnetostriction measurements as well as from the thermal conductivity. Zero-field thermal expansion data reveal that the magnetic transition is accompanied by an orthorhombic distortion within the $ab$ plane. Under ambient conditions the crystals are heavily twinned, but the domain orientation can be influenced either by applying uniaxial pressure or a magnetic field along the [100] direction. In addition, our data reveal a pronounced in-plane magnetic anisotropy for fields applied within the $ab$ plane. For $H || [110]$, the magnetic field influence on T$_N$ is weak, whereas for magnetic fields applied along [100], T$_N$ vanishes at about 10 T and the zero-field N\'{e}el order is completely suppressed as is confirmed by neutron diffraction data. The second-order phase transition strongly suggests a quantum critical point being present at $H\simeq 10$ T parallel [100], where the N\'{e}el order probably changes to a spin-liquid state.
Using a cube tiling of $\mathbb{R}^n$ constructed by Lagarias and Shor a tiling proof of three well-known binomial identities related to the Lucas cube is given.
Tight frames and rank-one quantum measurements are shown to be intimately related. In fact, the family of normalized tight frames for the space in which a quantum mechanical system lies is precisely the family of rank-one generalized quantum measurements (POVMs) on that space. Using this relationship, frame-theoretical analogues of various quantum-mechanical concepts and results are developed.   The analogue of a least-squares quantum measurement is a tight frame that is closest in a least-squares sense to a given set of vectors. The least-squares tight frame is found for both the case in which the scaling of the frame is specified (constrained least-squares frame (CLSF)) and the case in which the scaling is free (unconstrained least-squares frame (ULSF)). The well-known canonical frame is shown to be proportional to the ULSF and to coincide with the CLSF with a certain scaling.   Finally, the canonical frame vectors corresponding to a geometrically uniform vector set are shown to be geometrically uniform and to have the same symmetries as the original vector set.
To study the problem of the assigned Gauss curvature with conical singularities on Riemanian manifolds, we consider the Liouville equation with a single Dirac measure on the two-dimensional sphere. By a stereographic projection, we reduce the problem to a Liouville equation on the euclidean plane. We prove new multiplicity results for bounded radial solutions, which improve on earlier results of C.-S. Lin and his collaborators. Based on numerical computations, we also present various conjectures on the number of unbounded solutions. Using symmetries, some multiplicity results for non radial solutions are also stated.
A digitalized temperature map is recovered from the first light sky survey image published by the Planck team, from which an angular power spectrum is derived. The amplitudes of the low multipoles measured from the preliminary Planck power spectrum are significantly lower than that reported by the WMAP team. Possible systematical effects are far from enough to explain the observed low-l differences.
A spiral spin structure with a nesting vector is expected to be the ground normal state of $Sr_2RuO_4$. It might be observable with use of the ARPES method with circularly polarised photons desighned by A.Kaminsky et al. (cond-mat/0203133).
While techniques to compute thermal fluctuation induced, or pseudo-Casimir, forces in equilibrium systems are well established, the same is not true for non-equilibrium cases. We present a general formalism that allows us to unambiguously compute non-equilibrium fluctuation induced forces by specifying the energy of interaction of the fluctuating fields with the boundaries. For a general class of classical fields with dissipative dynamics, we derive a very general relation between the Laplace transform of the time-dependent force and the static partition function for a related problem with a different Hamiltonian. In particular, we demonstrate the power of our approach by computing, for the first time, the explicit time dependence of the non-equilibrium pseudo-Casimir force induced between two parallel plates, upon a sudden change in the temperature of the system. We also show how our results can be used to determine the steady-state behavior of the non-equilibrium force in systems where the fluctuations are driven by colored noise.
The temperature dependence of the electron spin life-time, T_1 and the g-factor are anomalous in alkali fullerides (K,Rb)_3C_60, which cannot be explained by the canonical Elliott-Yafet theory. These materials are archetypes of strongly correlated and narrow band metals. We introduce the concept of "complex electron spin resonance frequency shift" to treat these measurables in a unified manner within the Kubo formalism. The theory is applicable for metals with nearly degenerate conduction bands and large momentum scattering even with an anomalous temperature dependence and sizeable residual value.
We study the properties of finite graphs in which the ball of radius $r$ around each vertex induces a graph isomorphic to some fixed graph $F$. This is a natural extension of the study of regular graphs, and of the study of graphs of constant link. We focus on the case where $F$ is $\mathbb{L}^d$, the $d$-dimensional square lattice. We obtain a characterisation of all the finite graphs in which the ball of radius $3$ around each vertex is isomorphic to the ball of radius $3$ in $\mathbb{L}^d$, for each integer $d \geq 3$. These graphs have a very rigidly proscribed global structure, much more so than that of $(2d)$-regular graphs. (They may be viewed as quotient lattices of $\mathbb{L}^d$ in various compact orbifolds.) In the $d=2$ case, our methods yield new proofs of structure theorems of Thomassen and of M\'arquez, de Mier, Noy and Revuelta, and also yield short, `algebraic' restatements of these theorems. Our proofs use a mixture of techniques and results from combinatorics, algebraic topology and group theory.
In this paper, we establish several geometric properties of boundary sections of convex solutions to the Monge-Amp\`ere equations: the engulfing and separating properties and volume estimates. As applications, we prove a covering lemma of Besicovitch type, a covering theorem and a strong type $p-p$ estimate for the maximal function corresponding to boundary sections. Moreover, we show that the Monge-Amp\`ere setting forms a space of homogeneous type.
Massive compact galaxies seem to be more common at high redshift than in the local universe, especially in denser environments. To investigate the fate of such massive galaxies identified at z~2 we analyse the evolution of their properties in three cosmological hydrodynamical simulations that form virialised galaxy groups of mass ~10^13 Msun hosting a central massive elliptical/S0 galaxy by redshift zero. We find that at redshift ~2 the population of galaxies with M_*> 2 10^10 Msun is diverse in terms of mass, velocity dispersion, star formation and effective radius, containing both very compact and relatively extended objects. In each simulation all the compact satellite galaxies have merged into the central galaxy by redshift 0 (with the exception of one simulation where one of such satellite galaxy survives). Satellites of similar mass at z = 0 are all less compact than their high redshift counterparts. They form later than the galaxies in the z = 2 sample and enter the group potential at z < 1, when dynamical friction times are longer than the Hubble time. Also, by z = 0 the central galaxies have increased substantially their characteristic radius via a combination of in situ star formation and mergers. Hence in a group environment descendants of compact galaxies either evolve towards larger sizes or they disappear before the present time as a result of the environment in which they evolve. Since the group-sized halos that we consider are representative of dense environments in the LambdaCDM cosmology, we conclude that the majority of high redshift compact massive galaxies do not survive until today as a result of the environment.
We consider quantum key distribution (QKD) and entanglement distribution using a single-sender multiple-receiver pure-loss bosonic broadcast channel. We determine the unconstrained capacity region for the distillation of bipartite entanglement and secret key between the sender and each receiver, whenever they are allowed arbitrary public classical communication. A practical implication of our result is that the capacity region demonstrated drastically improves upon rates achievable using a naive time-sharing strategy, which has been employed in previously demonstrated network QKD systems. We show a simple example of the broadcast QKD protocol overcoming the limit of the point-to-point strategy. Our result is thus an important step toward opening a new framework of network channel-based quantum communication technology.
In this thesis we study the phenomenon of superradiance and its implications to the stability of black-holes (BH) and perfect-fluid stars.   Superradiance is a radiation enhancement process that involves rotating dissipative systems. In BH spacetimes, superradiance is due to dissipation at the event horizon, with interesting associated phenomena, namely floating orbits and BH-bombs. BH superradiance is a very interdisciplinary topic, and its study allows us to obtain important results in the area of particle physics. The scattering of a scalar field by a rotating BH leads to the formation of quasi-boundstates. In rotational systems, these states can give rise to superradiant instabilities. These results were recently used to impose constraints to the mass of fundamental particles and darkmatter candidates.   In this work, it is shown that, when dissipation is properly included, similar results are achievable in self-gravitating systems other than black-holes, such as perfect fluid stars. It is also demonstrated that the relativistic effects related to the phenomenon of frame-dragging are neglectable in this calculation.
We analyze the supersymmetry conditions for a class of SU(2) structure backgrounds of Type IIB supergravity, corresponding to a specific ansatz for the supersymmetry parameters. These backgrounds are relevant for the AdS/CFT correspondence since they are suitable to describe mass deformations or beta-deformations of four-dimensional superconformal gauge theories. Using Generalized Complex Geometry we show that these geometries are characterized by a closed nowhere-vanishing vector field and a modified fundamental form which is also closed. The vector field encodes the information about the superpotential and the type of deformation - mass or beta respectively. We also show that the Pilch-Warner solution dual to a mass-deformation of N =4 Super Yang-Mills and the Lunin-Maldacena beta-deformation of the same background fall in our class of solutions.
Swift's remarkable ability to quickly localize gamma-ray bursts has led to the accumulation of a sizable burst sample for which both angular locations and redshifts are measured. This sample has become large enough that it can potentially be used to probe angular anisotropies indicative of large-scale universal structure. In a previous work, a large clustering of gamma-ray bursts at redshift z about 2 was reported in the general direction of the constellations of Hercules and Corona Borealis. Since that report, a 42 per cent increase in the number of z about 2 gamma-ray bursts has been observed, warranting an updated analysis. Surprisingly, the cluster is more pronounced now than it was when it was first reported.
The Chord Length Sampling (CLS) algorithm is a powerful Monte Carlo method that models the effects of stochastic media on particle transport by generating on-the-fly the material interfaces seen by the random walkers during their trajectories. This annealed disorder approach, which formally consists of solving the approximate Levermore-Pomraning equations for linear particle transport, enables a considerable speed-up with respect to transport in quenched disorder, where ensemble-averaging of the Boltzmann equation with respect to all possible realizations is needed. However, CLS intrinsically neglects the correlations induced by the spatial disorder, so that the accuracy of the solutions obtained by using this algorithm must be carefully verified with respect to reference solutions based on quenched disorder realizations. When the disorder is described by Markov mixing statistics, such comparisons have been attempted so far only for one-dimensional geometries, of the rod or slab type. In this work we extend these results to Markov media in two-dimensional (extruded) and three-dimensional geometries, by revisiting the classical set of benchmark configurations originally proposed by Adams, Larsen and Pomraning, and extended by Brantley. In particular, we examine the discrepancies between CLS and reference solutions for scalar particle flux and transmission/reflection coefficients as a function of the material properties of the benchmark specifications and of the system dimensionality.
The classical Hadwiger conjecture dating back to 1940's states that any graph of chromatic number at least $r$ has the clique of order $r$ as a minor. Hadwiger's conjecture is an example of a well studied class of problems asking how large a clique minor one can guarantee in a graph with certain restrictions. One problem of this type asks what is the largest size of a clique minor in a graph on $n$ vertices of independence number $\alpha(G)$ at most $r$. If true Hadwiger's conjecture would imply the existence of a clique minor of order $n/\alpha(G)$. Results of Kuhn and Osthus and Krivelevich and Sudakov imply that if one assumes in addition that $G$ is $H$-free for some bipartite graph $H$ then one can find a polynomially larger clique minor. This has recently been extended to triangle free graphs by Dvo\v{r}\'ak and Yepremyan, answering a question of Norin. We complete the picture and show that the same is true for arbitrary graph $H$, answering a question of Dvo\v{r}\'ak and Yepremyan. In particular, we show that any $K_s$-free graph has a clique minor of order $c_s(n/\alpha(G))^{1+\frac{1}{10(s-2) }}$, for some constant $c_s$ depending only on $s$. The exponent in this result is tight up to a constant factor in front of the $\frac{1}{s-2}$ term.