ShantanuT01/DACTYL-Pretraining huggingface dataset:
The notion of pseudocyclic association scheme is generalized to the non-commutative case. It is proved that any pseudocyclic scheme the rank of which is much more than the valency is the scheme of a Frobenius group and is uniquely determined up to isomorphism by its intersection number array. An immediate corollary of this result is that any scheme of prime degree, valency $k$ and rank at least $k^4$ is schurian.
Let $k $ be the algebraic closure of a finite field of odd characteristic $p$ and $X$ a smooth projective scheme over the Witt ring $W(k)$ which is geometrically connected in characteristic zero. We introduce the notion of Higgs-de Rham flow and prove that the category of periodic Higgs-de Rham flows over $X/W(k)$ is equivalent to the category of Fontaine modules, hence further equivalent to the category of crystalline representations of the \'{e}tale fundamental group $\pi_1(X_K)$ of the generic fiber of $X$, after Fontaine-Laffaille and Faltings. Moreover, we prove that every semistable Higgs bundle over the special fiber $X_k$ of $X$ of rank $\leq p$ initiates a semistable Higgs-de Rham flow and thus those of rank $\leq p-1$ with trivial Chern classes induce $k$-representations of $\pi_1(X_K)$. A fundamental construction in this paper is the inverse Cartier transform over a truncated Witt ring. In characteristic $p$, it was constructed by Ogus-Vologodsky in the nonabelian Hodge theory in positive characteristic; in the affine local case, our construction is related to the local Ogus-Vologodsky correspondence of Shiho.
We show that a two-dimensional polaritonic crystal, made of metallic rods that support well defined plasmon oscillations, can act in a narrow frequency range as a medium in which a negative refraction and subwavelength lensing can occur. We show that surface modes are excited on the surface of the lens, and that they facilitate restoration of the evanescent waves, which carry the subwavelength image information. We demonstrate that this can occur in the visible frequency range, for a wide range of materials, including silver and aluminum rods, and carbon nanotubes. This flexibility should allow for an experimental demonstration of this phenomenon in the visible frequency range.
We present transport measurements of the Kondo effect in a double quantum dot charged with only one or two electrons, respectively. For the one electron case we observe a surprising quasi-periodic oscillation of the Kondo conductance as a function of a small perpendicular magnetic field |B| \lesssim 50mT. We discuss possible explanations of this effect and interpret it by means of a fine tuning of the energy mismatch of the single dot levels of the two quantum dots. The observed degree of control implies important consequences for applications in quantum information processing.
For the relativistic string with massive ends (the meson model) and four various string baryon models (q-qq, q-q-q, Y and $\Delta$) we consider the classical quasirotational motions, which are small disturbances of the planar uniform rotations of these systems. For the string meson model the two types of these solutions are obtained. They describe oscillatory motions in the form of stationary waves in the rotational plane and in the orthogonal direction. This approach and the suggested method of determining an arbitrary motion of the system on the base of initial data let us solve the stability problem for the rotational motions for all mentioned string configurations. It is shown that the classic rotational motions are {\it stable} for the string meson model (or its analog q-qq) and for the $\Delta$ baryon configuration, but they are {\it unstable} for the string baryon models Y and q-q-q. For the latter two systems any small asymmetric disturbances grow with growing time. The motion of the q-q-q configuration become more complicated and quasiperiodic but quarks do not merge. In the case of Y model the evolution of disturbances results in falling a quark into the junction. These features of the classic behavior are important for describing the hadron states on the Regge trajectories and for choosing and developing the most adequate QCD-based string hadron models.
We show that in high dimensional Bernoulli percolation, removing from a thin infinite cluster a much thinner infinite cluster leaves an infinite component. This observation has implications for the van den Berg-Brouwer forest fire process, also known as self-destructive percolation, for dimension high enough.
We present late-time radio/millimeter (as well as optical/UV and X-ray) detections of the tidal disruption event (TDE) AT2018hyz, spanning $970 - 1300$ d after optical discovery. In conjunction with earlier deeper limits, including at $\approx 700$ d, our observations reveal rapidly rising emission at $0.8-240$ GHz, steeper than $F_\nu\propto t^5$ relative to the time of optical discovery. Such a steep rise cannot be explained in any reasonable scenario of an outflow launched at the time of disruption (e.g., off-axis jet, sudden increase in the ambient density), and instead points to a delayed launch. Our multi-frequency data allow us to directly determine the radius and energy of the radio-emitting outflow, showing that it was launched $\approx 750$ d after optical discovery. The outflow velocity is mildly relativistic, with $\beta\approx 0.25$ and $\approx 0.6$ for a spherical and a $10^\circ$ jet geometry, respectively, and the minimum kinetic energy is $E_K\approx 5.8\times 10^{49}$ and $\approx 6.3\times 10^{49}$ erg, respectively. This is the first definitive evidence for the production of a delayed mildly-relativistic outflow in a TDE; a comparison to the recently-published radio light curve of ASASSN-15oi suggests that the final re-brightening observed in that event (at a single frequency and time) may be due to a similar outflow with a comparable velocity and energy. Finally, we note that the energy and velocity of the delayed outflow in AT2018hyz are intermediate between those of past non-relativistic TDEs (e.g., ASASSN-14li, AT2019dsg) and the relativistic TDE Sw\,J1644+57. We suggest that such delayed outflows may be common in TDEs.
We assess the robustness of the two highest rungs of the "cosmic distance ladder" for Type Ia supernovae and the determination of the Hubble-Lema\^itre constant. In this analysis, we hold fixed Rung 1 as the distance to the LMC determined to 1 % using Detached Eclipsing Binary stars. For Rung 2 we analyze two methods, the TRGB and Cepheid distances for the luminosity calibration of Type Ia supernovae in nearby galaxies. For Rung 3 we analyze various modern digital supernova samples in the Hubble flow, such as the Cal\'an-Tololo, CfA, CSP, and Supercal datasets. This metadata analysis demonstrates that the TRGB calibration yields smaller $H_0$ values than the Cepheid calibration, a direct consequence of the systematic difference in the distance moduli calibrated from these two methods. Selecting the three most independent possible methodologies/bandpasses ($B$, $V$, $J$), we obtain $H_{0}=69.9 \pm 0.8$ and $H_{0} =73.5 \pm 0.7$ km s$^{-1}$ Mpc$^{-1}$ from the TRGB and Cepheid calibrations, respectively. Adding in quadrature the systematic uncertainty in the TRGB and Cepheid methods of 1.1 and 1.0 km s$^{-1}$ Mpc$^{-1}$, respectively, this subset reveals a significant 2.0 $\sigma$ systematic difference in the calibration of Rung 2. If Rung 1 and Rung 2 are held fixed, the different formalisms developed for standardizing the supernova peak magnitudes yield consistent results, with a standard deviation of 1.5 km s$^{-1}$ Mpc$^{-1}$, that is, Type Ia supernovae are able to anchor Rung 3 with 2 % precision. This study demonstrates that Type Ia supernovae have provided a remarkably robust calibration of R3 for over 25 years.
The discovery of correlated electronic phases, including Mott-like insulators and superconductivity, in twisted bilayer graphene (TBLG) near the magic angle, and the intriguing similarity of their phenomenology to that of the high-temperature superconductors, has spurred a surge of research to uncover the underlying physical mechanism. Local spectroscopy, which is capable of accessing the symmetry and spatial distribution of the spectral function, can provide essential clues towards unraveling this puzzle. Here we use scanning tunneling microscopy (STM) and spectroscopy (STS) in magic angle TBLG to visualize the local density of states (DOS) and charge distribution. Doping the sample to partially fill the flat band, where low temperature transport measurements revealed the emergence of correlated electronic phases, we find a pseudogap phase accompanied by a global stripe charge-order whose similarity to high-temperature superconductors provides new evidence of a deeper link underlying the phenomenology of these systems.
In order to complete the knowledge of the magnetic field and of its influence during the transition from Asymptotic Giant Branch to Planetary Nebulae stages, we have undertaken a search for magnetic fields at the surface of Mira stars. We used spectropolarimetric observations, collected with the Narval instrument at TBL, in order to detect - with Least Squares Deconvolution method - a Zeeman signature in the visible part of the spectrum. We present the first spectropolarimetric observations of the S-type Mira star chi Cyg, performed around its maximum light. We have detected a polarimetric signal in the Stokes V spectra and we have established its Zeeman origin. We claim that it is likely to be related to a weak magnetic field present at the photospheric level and in the lower part of the stellar atmosphere. We have estimated the strength of its longitudinal component to about 2-3 Gauss. This result favors a 1/r law for the variation of the magnetic field strength across the circumstellar envelope of chi Cyg. This is the first detection of a weak magnetic field at the stellar surface of a Mira star and we discuss its origin in the framework of shock waves periodically propagating throughout the atmosphere of these radially pulsating stars. At the date of our observations of chi Cyg, the shock wave reaches its maximum intensity, and it is likely that the shock amplifies a weak stellar magnetic field during its passage through the atmosphere. Without such an amplification by the shock, the magnetic field strength would have been too low to be detected. For the first time, we also report strong Stokes Q and U signatures (linear polarization) centered onto the zero velocity (i.e., at the shock front position). They seem to indicate that the radial direction would be favored by the shock during its propagation throughout the atmosphere.
Recently, diverse phase transition (PT) types have been obtained in multiplex networks, such as discontinuous, continuous, and mixed-order PTs. However, they emerge from individual systems, and there is no theoretical understanding of such PTs in a single framework. Here, we study a spin model called the Ashkin-Teller (AT) model in a mono-layer scale-free network; this can be regarded as a model of two species of Ising spin placed on each layer of a double-layer network. The four-spin interaction in the AT model represents the inter-layer interaction in the multiplex network. Diverse PTs emerge depending on the inter-layer coupling strength and network structure. Especially, we find that mixed-order PTs occur at the critical end points. The origin of such behavior is explained in the framework of Landau-Ginzburg theory.
Renormalization plays an important role in the theoretically and mathematically careful analysis of models in condensed-matter physics. I review selected results about correlated-fermion systems, ranging from mathematical theorems to applications in models relevant for materials science, such as the prediction of equilibrium phases of systems with competing ordering tendencies, and quantum criticality.
According to the shock jump conditions, the total fluid's mass, momentum, and energy should be conserved in the entire simulation box. We perform the dynamical Monte Carlo simulations with the multiple scattering law for energy analysis. The various energy functions of time are obtained by monitoring the total particles' mass, momentum, and energy in the simulation box. In conclusion, the energy analysis indicates that the smaller energy losses in the prescribed scattering law are, the harder the energy spectrum produced is.
In this paper we derive LPS's criterion for the breakdown of classical solutions to the incompressible nematic liquid crystal flow, a simplified version of Ericksen-Leslie system modeling the hydrodynamic evolution of nematic liquid crystals in $\mathbb R^3$. We show that if $0<T<+\infty$} is the maximal time interval for the unique smooth solution $u\in   C^\infty([0,T),\mathbb   R^3)$, then $|u|+|\nabla d|\notin L^q([0,T],L^p(\mathbb   R^3))$, where $p$ and $q$ safisfy the Ladyzhenskaya-Prodi-Serrin's condition: $\frac{3}{p}+\frac{2}{q}=1$ and $p\in(3,+\infty]$
The method of the nonequilibrium statistical operator developed by D. N. Zubarev is employed to analyse and derive generalized transport and kinetic equations. The degrees of freedom in solids can often be represented as a few interacting subsystems (electrons, spins, phonons, nuclear spins, etc.). Perturbation of one subsystem may produce a nonequilibrium state which is then relaxed to an equilibrium state due to the interaction between particles or with a thermal bath. The generalized kinetic equations were derived for a system weakly coupled to a thermal bath to elucidate the nature of transport and relaxation processes. It was shown that the "collision term" had the same functional form as for the generalized kinetic equations for the system with small interactions among particles. The applicability of the general formalism to physically relevant situations is investigated. It is shown that some known generalized kinetic equations (e.g. kinetic equation for magnons, Peierls equation for phonons) naturally emerges within the NSO formalism. The relaxation of a small dynamic subsystem in contact with a thermal bath is considered on the basis of the derived equations. The Schrodinger-type equation for the average amplitude describing the energy shift and damping of a particle in a thermal bath and the coupled kinetic equation describing the dynamic and statistical aspects of the motion are derived and analysed. The equations derived can help in the understanding of the origin of irreversible behavior in quantum phenomena.
We consider zitterbewegung (ZB) effect in four and five-dimensional space in the vicinity of the Chern-Simons black hole with torsion. The metric is taken in the traditional spherically symmetric form. We consider the equation for the current in the framework of the Schr\"odinger representation. Dependences of the electric current density on time is calculated for different dimension of space. In particular, it is shown that, with an increase in the space dimension, the effect of trembling motion qualitatively coincides. As the dimension increases, the amplitude of this effect decreases. Also, we investigate the dependence of the current on the radial coordinate for different dimensions of space. We obtain that when away from the event horizon the current ZB increases.
Globular cluster populations of supergiant elliptical galaxies are known to vary widely, from extremely populous systems like that of UGC 9799, the centrally dominant galaxy in Abell 2052, to globular-cluster-poor galaxies such as NGC 5629 in Abell 2666. Here we propose that these variations point strongly to the existence of a population of globular clusters that are not bound to individual galaxies, but rather move freely throughout the cores of clusters of galaxies. Such intracluster globular clusters may have originated as tidally stripped debris from galaxy interactions and mergers, or alternatively they may have formed in situ in some scenarios of globular cluster formation.
In a previous paper (arXiv:1410.5207) certain birational transformations were constructed between the noncommutative schemes associated to quadratic and cubic three dimensional Sklyanin algebras. In the current paper we consider the inverse birational transformations and show that they are of the same type. Moreover we extend everything to the $\mathbb{Z}$-algebras context, which allows us to incorporate the noncommutative quadrics introduced by Van den Bergh.
We study the correlation between galaxy structure and the quenching of star formation using a sample of SDSS central galaxies with stellar masses 9.75< log M_*/M_sun<11.25 and redshifts z<0.075. GALEX UV data are used to cleanly divide the sample into star-forming and quenched galaxies, and to identify galaxies in transition (the green valley). Despite a stark difference in visual appearance between blue and red galaxies, their average radial stellar mass density profiles are remarkably similar (especially in the outer regions) at fixed mass. The inner stellar mass surface density within a radius of 1 kpc, \Sigma_1, is used to quantify the growth of the bulge as galaxies evolve. When galaxies are divided into narrow mass bins, their distribution in the color-\Sigma_1 plane at fixed mass forms plausible evolutionary tracks. \Sigma_1 seems to grow as galaxies evolve through the blue cloud, and once it crosses a threshold value, galaxies are seen to quench at fixed \Sigma_1. The \Sigma_1 threshold for quenching grows with stellar mass, \Sigma_1 ~ M_*^{0.64}. However, the existence of some star-forming galaxies above the threshold \Sigma_1 implies that a dense bulge is necessary but not sufficient to quench a galaxy fully. This would be consistent with a two-step quenching process in which gas within a galaxy is removed or stabilized against star formation by bulge-driven processes (such as a starburst, AGN feedback, or morphological quenching), whereas external gas accretion is suppressed by separate halo-driven processes (such as halo gas shock heating). Quenching thus depends on an interplay between the inner structure of a galaxy and its surrounding dark matter halo, and lack of perfect synchrony between the two could produce the observed scatter in color vs. \Sigma_1. (Abridged)
Mounting observational data confirm that about 73% of the energy density consists of dark energy which is responsible for the current accelerated expansion of the Universe. We present observational evidences and dark energy projects. We then review various theoretical ideas that have been proposed to explain the origin of dark energy; they contain the cosmological constant, modified matter models, modified gravity models and the inhomogeneous model. The cosmological constant suffers from two major problems: one regarding fine-tuning and the other regarding coincidence. To solve them there arose modified matter models such as quintessence, k-essence, coupled dark energy, and unified dark energy. We compare those models by presenting attractive aspects, new rising problems and possible solutions. Furthermore we review modified gravity models that lead to late-time accelerated expansion without invoking a new form of dark energy; they contain f(R) gravity and the Dvali-Gabadadze-Porrati model. We also discuss observational constraints on those models and on future modified gravity theories. Finally we review the inhomogeneous Lemaitre-Tolman-Bondi model that drops an assumption of the spatial homogeneity of the Universe. We also present basics of cosmology and scalar field theory, which are useful especially for students and novices to understand dark energy models.
The temperature and magnetic field behavior of non-uniform diamagnetic phase of strongly correlated electron gas at the conditions of dHvA effect is analyzed. It is shown, that in the framework of Lifschitz-Kosevich-Shoenberg approximation the magnetic induction splitting, as well as the range of existence of Condon domains, are characterized by strong dependencies on temperature, magnetic field and impurities of the sample.
The precise positioning of dopant atoms within bulk crystal lattices could enable novel applications in areas including solid-state sensing and quantum computation. Established scanning probe techniques are capable tools for the manipulation of surface atoms, but at a disadvantage due to their need to bring a physical tip into contact with the sample. This has prompted interest in electron-beam techniques, followed by the first proof-of-principle experiment of bismuth dopant manipulation in crystalline silicon. Here, we use first principles modeling to discover a novel indirect exchange mechanism that allows electron impacts to non-destructively move dopants with atomic precision within the silicon lattice. However, this mechanism only works for the two heaviest group V donors with split-vacancy configurations, Bi and Sb. We verify our model by directly imaging these configurations for Bi, and by demonstrating that the promising nuclear spin qubit Sb can be manipulated using a focused electron beam.
We define linear stochastic heat equations (SHE) on p.c.f.s.s. sets equipped with regular harmonic structures. We show that if the spectral dimension of the set is less than two, then function-valued "random-field" solutions to these SPDEs exist and are jointly H\"older continuous in space and time. We calculate the respective H\"older exponents, which extend the well-known results on the H\"older exponents of the solution to SHE on the unit interval. This shows that the "curse of dimensionality" of the SHE on $\mathbb{R}^n$ depends not on the geometric dimension of the ambient space but on the analytic properties of the operator through the spectral dimension. To prove these results we establish generic continuity theorems for stochastic processes indexed by these p.c.f.s.s. sets that are analogous to Kolmogorov's continuity theorem. We also investigate the long-time behaviour of the solutions to the fractal SHEs.
We discuss the Jaynes-Cummings-Hubbard model (JCHM) describing the superfluid-Mott insulator transition of polaritons (i.e., dressed photon-qubit states) in coupled qubit-cavity arrays in the crossover from strong to weak correlations. In the strongly correlated regime the phase diagram and the elementary excitations of lattice polaritons near the Mott lobes are calculated analytically using a slave boson theory (SBT). The opposite regime of weakly interacting polariton superfluids is described by a weak-coupling mean-field theory (MFT) for a generalised multi-mode Dicke model. We show that a remarkable relation between the two theories exists in the limit of large photon bandwidth and large negative detuning, i.e., when the nature of polariton quasiparticles becomes qubit-like. In this regime, the weak coupling theory predicts the existence of a single Mott lobe with a change of the universality class of the phase transition at the tip of the lobe, in perfect agreement with the slave-boson theory. Moreover, the spectra of low energy excitations, i.e., the sound velocity of the Goldstone mode and the gap of the amplitude mode match exactly as calculated from both theories.