ShantanuT01/DACTYL-Pretraining huggingface dataset:
We show that lattice polytopes cut out by root systems of classical type are normal and Koszul, generalizing a well-known result of Bruns, Gubeladze, and Trung in type A. We prove similar results for Cayley sums of collections of polytopes whose Minkowski sums are cut out by root systems. The proofs are based on a combinatorial characterization of diagonally split toric varieties.
Using analytic stability criteria, we demonstrate that, due to their low surface mass density and large dark matter content, LSB disks are quite stable against the growth of global nonaxisymmetric modes such as bars. However, depending on their (poorly constrained) stellar velocity dispersions, they may be only marginally stable against local instabilities. We simulate a collision between an LSB and HSB galaxy and find that, while the HSB galaxy forms a strong bar, the response of the LSB disk is milder, manifesting weaker rings and spiral features. The lack of sufficient disk self-gravity to amplify dynamical instabilities naturally explains the rarity of bars in LSB disks. The stability of LSB disks may also inhibit interaction-driven gas inflow and starburst activity in these galaxies.
A method for the study of the ground states of lattice-gas models or equivalent spin models with extended-range interactions is developed. It is shown that effect of longer-range interactions can be studied in terms of the solution of the ground-state problem for a model with short-range interactions. The method is applied to explain the emergence of fractional magnetization plateaus in TmB4 that is regarded as a strong Ising magnet on the Shastry-Sutherland lattice.
The majority of galaxy mergers are expected to be minor mergers. The observational signatures of minor mergers are not well understood, thus there exist few constraints on the minor merger rate. This paper seeks to address this gap in our understanding by determining if and when minor mergers exhibit disturbed morphologies and how they differ from the morphology of major mergers. We simulate a series of unequal-mass moderate gas-fraction disc galaxy mergers. With the resulting g-band images, we determine how the time-scale for identifying galaxy mergers via projected separation and quantitative morphology (the Gini coefficient G, asymmetry A, and the second-order moment of the brightest 20% of the light M20) depends on the merger mass ratio, relative orientations and orbital parameters. We find that G-M20 is as sensitive to 9:1 baryonic mass ratio mergers as 1:1 mergers, with observability time-scales ~ 0.2-0.4 Gyr. In contrast, asymmetry finds mergers with baryonic mass ratios between 4:1 and 1:1 (assuming local disc galaxy gas-fractions). Asymmetry time-scales for moderate gas-fraction major disc mergers are ~ 0.2-0.4 Gyr, and less than 0.06 Gyr for moderate gas-fraction minor mergers. The relative orientations and orbits have little effect on the time-scales for morphological disturbances. Observational studies of close pairs often select major mergers by choosing paired galaxies with similar luminosities and/or stellar masses. Therefore, the various ways of finding galaxy mergers (G-M20, A, close pairs) are sensitive to galaxy mergers of different mass ratios. By comparing the frequency of mergers selected by different techniques, one may place empirical constraints on the major and minor galaxy merger rates.
We establish a replacement lemma for a variational problem, which is not based on a local argument. We then apply it to a phase transition problem and obtain pointwise estimates.
We review recent advances and results in enhancing and developing helioseismic analysis methods and in solar data assimilation. In the first part of this paper we will focus on selected developments in time-distance and global helioseismology. In the second part, we review the application of data assimilation methods on solar data. Relating solar surface observations as well as helioseismic proxies with solar dynamo models by means of the techniques from data assimilation is a promising new approach to explore and to predict the magnetic activity cycle of the Sun.
We consider a random walk $S_{\tau}$ which is obtained from the simple random walk $S$ by a discrete time version of Bochner's subordination. We prove that under certain conditions on the subordinator $\tau$ appropriately scaled random walk $S_{\tau}$ converges in the Skorohod space to the symmetric $\alpha$-stable process $B^{\alpha}$. We also prove asymptotic formula for the transition function of $S_{\tau}$ similar to the P\'{o}lya's asymptotic formula for $B^{\alpha}$.
It is shown that flat zero-energy solutions (vacua) of the 5d Kaluza-Klein theory admit a non-trivial homotopy structure generated by certain Kaluza-Klein excitations. These vacua consist of an infinite set of homotopically different spacetimes denoted by $\mathcal{M}^{(n)}_5$, among which $\mathcal{M}^{(0)}_5$ and $\mathcal{M}^{(1)}_5$ are especially identified as $M_{4} \times S^{1}$ and $M_5$, the ground states of the 5d Kaluza-Klein theory and the 5d general relativity, respectively (where $M_k$ represents the $k$-dimensional Minkowski space).
The stellar mass-halo mass relation is a key constraint in all semi-analytic, numerical, and semi-empirical models of galaxy formation and evolution. However, its exact shape and redshift dependence remain debated. Several recent works support a relation in the local Universe steeper than previously thought. Based on the comparisons with a variety of data on massive central galaxies, we show that this steepening holds up to z~1, for stellar masses Mstar>2e11 Msun. Specifically, we find significant evidence for a high-mass end slope of \beta>0.35-0.70, instead of the usual \beta~0.20-0.30 reported by a number of previous results. When including the independent constraints from the recent BOSS clustering measurements, the data, independent of any systematic errors in stellar masses, tend to favor a model with a very small scatter (< 0.15 dex) in stellar mass at fixed halo mass, in the redshift range z < 0.8 and for Mstar>3e11 Msun, suggesting a close connection between massive galaxies and host halos even at relatively recent epochs. We discuss the implications of our results with respect to the evolution of the most massive galaxies since z~1.
We propose a framework to calculate the dynamics at the scission point of nuclear fission, based as far as possible on a discrete representation of orthogonal many-body configurations. Assuming axially symmetric scission shapes, we use the $K$ orbital quantum number to build a basis of wave functions. Pre-scission configurations are stable under mean-field dynamics while post-scission configurations evolve to separated fragments. In this first exploratory study, we analyze a typical fission trajectory through to scission in terms of these configurations. We find that there is a major rearrangement of the $K$ occupancy factors at scission. Interestingly, very different fragment shapes occur in the post-scission configurations, even starting from the same pre-scission configuration.
Statistics of the angle \Phi between orbital angular momenta in hierarchical triple systems with known inner visual or astrometric orbits are studied. Correlation between apparent revolution directions proves partial orbit alignment known from earlier works. The alignment is strong in triples with outer projected separation less than ~50 AU, where the average \Phi is about 20 degrees. In contrast, outer orbits wider than 1000 AU are not aligned with the inner orbits. It is established that the orbit alignment decreases with increasing mass of the primary component. Average eccentricity of inner orbits in well-aligned triples is smaller than in randomly aligned ones. These findings highlight the role of dissipative interactions with gas in defining the orbital architecture of low-mass triple systems. On the other hand, chaotic dynamics apparently played a role in shaping more massive hierarchies. Analysis of projected configurations and triples with known inner and outer orbits indicates that the distribution of \Phi is likely bimodal, where 80% of triples have \Phi<70 degrees and the remaining ones are randomly aligned.
The Ollivier-Poulin-Zurek definition of objectivity provides a philosophical basis for the environment as witness formulation of decoherence theory and hence for quantum Darwinism. It is shown that no account of the reference of the key terms in this definition can be given that does not render the definition either empty or circular. It is argued that this is not the fault of the language used, but of the assumption that the laws of physics are independent of Hilbert-space decomposition. All evidence suggests that this latter assumption is true. If it is, decoherence cannot explain the emergence of classicality.
We combine spectroscopic, photometric, and astrometric information from APOGEE data release 17 and $Gaia$ early data release 3 to perform a self-consistent characterization of $Gaia$-Sausage/Enceladus (GSE), the remnant of the last major merger experienced by the Milky Way, considering stars and globular clusters (GCs) altogether. Our novel set of chemodynamical criteria to select genuine stars of GSE yields a metallicity distribution function with a median [Fe/H] of $-1.22$ dex and $0.23$ dex dispersion. Stars from GSE present an excess of [Al/Fe] and [Mg/Mn] (also [Mg/Fe]) in comparison to surviving Milky Way dwarf satellites, which can be explained by differences in star-formation efficiencies and timescales between these systems. However, stars from Sequoia, another proposed accreted halo substructure, essentially overlap the GSE footprint in all analyzed chemical-abundance spaces, but present lower metallicities. Among probable GCs of GSE with APOGEE observations available, we find no evidence for atypical [Fe/H] spreads with the exception of $\omega$ Centauri ($\omega$Cen). Under the assumption that $\omega$Cen is a stripped nuclear star cluster, we estimate the stellar mass of its progenitor to be $M_\star \approx 1.3 \times 10^9 M_\odot$, well-within literature expectations for GSE. This leads us to envision GSE as the best available candidate for the original host galaxy of $\omega$Cen. We also take advantage of $Gaia$'s photometry and APOGEE metallicities as priors to determine fundamental parameters for eight high-probability ($>$70%) GC members of GSE via statistical isochrone fitting. Finally, the newly determined ages and APOGEE [Fe/H] values are utilized to model the age-metallicity relation of GSE.
We study correlations of spin currents flowing through a Coulomb blockaded quantum dot. While vanishing for elastic co-tunneling, these correlations develop as the quantum dot enters the Kondo regime. They are a manifestation of Kondo physics in quantum dots. We demonstrate that the spin current correlator is non-perturbative in the Kondo coupling.
Motivated by its potential application to earthquake statistics, we study the exactly self-similar branching process introduced recently by Vere-Jones, which extends the ETAS class of conditional branching point-processes of triggered seismicity. One of the main ingredient of Vere-Jones' model is that the power law distribution of magnitudes m' of daughters of first-generation of a mother of magnitude m has two branches m'<m with exponent beta-d and m'>m with exponent beta+d, where beta and d are two positive parameters. We predict that the distribution of magnitudes of events triggered by a mother of magnitude $m$ over all generations has also two branches m'<m with exponent beta-h and m'>m with exponent beta+h, with h= d \sqrt{1-s}, where s is the fraction of triggered events. This corresponds to a renormalization of the exponent d into h by the hierarchy of successive generations of triggered events. The empirical absence of such two-branched distributions implies, if this model is seriously considered, that the earth is close to criticality (s close to 1) so that beta - h \approx \beta + h \approx \beta. We also find that, for a significant part of the parameter space, the distribution of magnitudes over a full catalog summed over an average steady flow of spontaneous sources (immigrants) reproduces the distribution of the spontaneous sources and is blind to the exponents beta, d of the distribution of triggered events.
Recently much attention has been paid to quantum circuit design to prepare for the future "quantum computation era." Like the conventional logic synthesis, it should be important to verify and analyze the functionalities of generated quantum circuits. For that purpose, we propose an efficient verification method for quantum circuits under a practical restriction. Thanks to the restriction, we can introduce an efficient verification scheme based on decision diagrams called   Decision Diagrams for Matrix Functions (DDMFs). Then, we show analytically the advantages of our approach based on DDMFs over the previous verification techniques. In order to introduce DDMFs, we also introduce new concepts, quantum functions and matrix functions, which may also be interesting and useful on their own for designing quantum circuits.
We investigate the collective magnetoplasmon excitations in a quantum dot containing finite number of electrons in the high magnetic field limit. We consider the electrons in the lowest Landau level and neglect mixing between the higher Landau levels. The dispersion relation of these edge modes are estimated following the energy weighted sum-rule approach. In this finite size system the edge magnetoplasmon modes have different multipolarities (or angular momemtum l). Their dependence on the magnetic field and on the system size is investigated. With increasing magnetic field, energy of these collective modes decreases and in the bulk limit they become gapless. We also consider the breathing mode of a dot in the presence of a strong magnetic field, and the energy of this mode approaches the cyclotron frequency $\hbar \omega_{c}$.
[Abridged] We present a new deep 21-cm survey of the Andromeda galaxy, based on high resolution observations performed with the Synthesis Telescope and the 26-m antenna at DRAO. The HI distribution and kinematics of the disc are analyzed and basic dynamical properties are given. The rotation curve is measured out to 38 kpc, showing a nuclear peak, a dip around 4 kpc, two distinct flat parts and an increase in the outermost regions. Except for the innermost regions, the axisymmetry of the gas rotation is very good. A very strong warp of the HI disc is evidenced. The central regions appear less inclined than the average disc inclination, while the outer regions appear more inclined. Mass distribution models by LCDM NFW, Einasto or pseudo-isothermal dark matter halos with baryonic components are presented. They fail to reproduce the exact shape of the rotation curve. No significant differences are measured between the various shapes of halo. The dynamical mass of M31 enclosed within a radius of 38 kpc is (4.7 +/- 0.5) x 10^11 Msol. The dark matter component is almost 4 times more massive than the baryonic mass inside this radius. A total mass of 1.0 x 10^12 Msol is derived inside the virial radius. New HI structures are discovered in the datacube, like the detection of up to five HI components per spectrum, which is very rarely seen in other galaxies. The most remarkable new HI structures are thin HI spurs and an external arm in the disc outskirts. A relationship between these spurs and outer stellar clumps is evidenced. The external arm is 32 kpc long, lies on the far side of the galaxy and has no obvious counterpart on the other side of the galaxy. Its kinematics clearly differs from the outer adjacent disc. Both these HI perturbations could result from tidal interactions with galaxy companions.
Coexisting density-wave and superconducting states along with the large anomalous Hall effect in the absence of local magnetism remain intriguing and enigmatic features of the AV$_3$Sb$_5$ kagome metals (A = K, Rb, Cs). Here, we demonstrate via optical spectroscopy and density-functional calculations that low-energy dynamics of KV$_3$Sb$_5$ is characterized by unconventional localized carriers, which are strongly renormalized across the density-wave transition and indicative of electronic correlations. Strong phonon anomalies are prominent not only below the density-wave transition, but also at high temperatures, suggesting an intricate interplay of phonons with the underlying electronic structure. We further propose the star-of-David and tri-hexagon (inverse star-of-David) configurations for the density-wave order in KV$_3$Sb$_5$. These configurations are strongly reminiscent of $p$-wave states expected in the Hubbard model on the kagome lattice at the filling level of the van Hove singularity. The proximity to this regime should have intriguing and far-reaching implications for the physics of KV$_3$Sb$_5$ and related materials.
We analyze fermion mass-matrix structure in an asymptotically non-free model with 4 + 1bar generations. The texture at the GUT scale is uniquely determined by supposing that the masses of heavy up-type quarks (charm as well as top) are realized as their infrared fixed point values. By assuming SO(10) GUT-like relations for Yukawa couplings in this model, this texture can explain all fermion masses and quark mixing with only one small parameter, which is almost equal to the Cabibbo angle.
Unlike the classical exponential relaxation law, the widely prevailing universal law with its fractional power-law dependence of susceptibility on frequency cannot be explained in the framework of any intuitively simple physical concept. The resulting constancy of the ratio of the imaginary to the real parts of the complex susceptibility, known as the ``energy criterion'', has a pleasing simplicity but the understanding of its origins needs a special theoretical treatment. A fresh light on the stochastic nature of the dielectric relaxation has been shed by a novel stochastic approach introduced in the last decade. Since the theoretical analysis involved is rather unfamiliar, the aim of this paper is to give some useful comments and suggestions which should help to follow in details the proposed stochastic scheme of relaxation leading to the well-known empirical responses. We justify the universality of the power-law macroscopic response as well as Jonscher's screening and energy criterion ideas, and we give a new basis to the research into the significance of relaxation processes.
In this talk I briefly review the recent progress in calculation of the high order corrections to the parameters of the nonrelativistic heavy quark-antiquark system in the effective theory approach.
We present the first measurement of two-mode squeezing between the twin beams produced by a doubly resonant optical parameter oscillator (OPO) in above threshold operation, based on parametric amplification by non degenerate four wave mixing with rubidium $^{85}$Rb. We demonstrate a maximum intensity difference squeezing of -2.7 dB (-3,5 dB corrected for losses) with a pump power of 285 mW and an output power of 12 mW for each beam, operating close to the D1 line of Rb atoms. The possibility to use open cavities combined with the high gain media can provide a strong level of noise compression, and the access to new operation regimes that could not be explored by crystal based OPOs. The spectral bandwidth of the squeezed light is broadened by the cavity dynamics, and the squeezing level is robust for strong pump powers. Stable operation was obtained up to four times above the threshold. Moreover, its operation close to the atomic resonances of alkali atoms allows a natural integration into quantum networks including structures such as quantum memories.
We derive necessary and sufficient conditions for the approximate correctability of a quantum code, generalizing the Knill-Laflamme conditions for exact error correction. Our measure of success of the recovery operation is the worst-case entanglement fidelity of the overall process. We show that the optimal recovery fidelity can be predicted exactly from a dual optimization problem on the environment causing the noise. We use this result to obtain an easy-to-calculate estimate of the optimal recovery fidelity as well as a way of constructing a class of near-optimal recovery channels that work within twice the minimal error. In addition to standard subspace codes, our results hold for subsystem codes and hybrid quantum-classical codes.
The potential of the LHC for investigation of anomalous top quark interactions with gluon ($tug,tcg$) through the production of $tW$-channel of single top quark is studied. In the Standard Model, the single top quarks in the $tW$-channel mode are charge symmetric meaning that $\sigma(pp\to t+W^{-}) = \sigma(pp\to \bar{t}+W^{+})$. However, the presence of anomalous FCNC couplings leads to charge asymmetry. In this paper a method is proposed in which this charge asymmetry may be used to constrain anomalous FCNC couplings. The strength of resulting constraints is estimated for the LHC for the center of mass energies of 7 and 14 TeV.
We present a dynamical description and analysis of non-equilibrium transitions in the noisy one-dimensional Ginzburg-Landau equation for an extensive system based on a weak noise canonical phase space formulation of the Freidlin-Wentzel or Martin-Siggia-Rose methods. We derive propagating nonlinear domain wall or soliton solutions of the resulting canonical field equations with superimposed diffusive modes. The transition pathways are characterized by the nucleations and subsequent propagation of domain walls. We discuss the general switching scenario in terms of a dilute gas of propagating domain walls and evaluate the Arrhenius factor in terms of the associated action. We find excellent agreement with recent numerical optimization studies.
We present an analysis of the Lyman alpha forests of five quasar spectra in the near UV. Properties of the intergalactic medium (IGM) at an intermediate redshift interval (0.9 < z < 1.9) are studied. The amount of baryons in the diffuse photoionised IGM and the warm-hot intergalactic medium (WHIM) are traced to get constraints on the redshift evolution of the different phases of the intergalactic gas. The baryon density of the diffuse IGM is determined with photoionisation calculations under the assumption of local hydrostatic equilibrium. We assume that the gas is ionised by a metagalactic background radiation with a Haardt & Madau (2001) spectrum. The WHIM is traced with broad Lyman alpha (BLA) absorption. The properties of a number of BLA detections are studied. Under the assumption of collisional ionisation equilibrium a lower limit to the baryon density could be estimated. It is found that the diffuse photoionised IGM contains at least 25% of the total baryonic matter at redshifts 1 < z < 2. For the WHIM a lower limit of 2.4% could be determined. Furthermore the data indicates that the intergalactic gas is in a state of evolution at z=1.5. We confirm that a considerable part of the WHIM is created between z=1 and z=2.