ShantanuT01/DACTYL-Pretraining huggingface dataset:
The phase diagram of the XXZ spin-1 quantum magnet on the kagome lattice is studied for all cases where the $J_z$ coupling is antiferromagnetic. In the zero magnetic field case, the six previously introduced phases, found using various methods, are: the nondegenerate gapped photon phase which breaks no space symmetry or spin symmetry; the six-fold degenerate phase with plaquette order, which breaks both time reversal symmetry and translational symmetry; the "superfluid" (ferromagnetic) phase with an in-plane global U(1) symmetry broken, when $J_{xy} < 0$; the $\sqrt{3}\times\sqrt{3}$ order when $J_{xy} > 0$; the nematic phase when $D < 0$ and large; and a phase with resonating dimers on each hexagon. We obtain all of these phases and partial information about their quantum phase transitions in a single framework by studying condensation of defects in the six-fold plaquette phases. The transition between nematic phase and the six-fold degenerate plaquette phase is potentially an unconventional second-order critical point. In the case of a nonzero magnetic field along $\hat{z}$, another ordered phase with translation symmetry broken is opened up in the nematic phase. Due to the breaking of time-reversal symmetry by the field, a supersolid phase emerges between the six-fold plaquette order and the superfluid phase. This phase diagram might be accessible in nickel compounds, BF$_4$ salts, or optical lattices of atoms with three degenerate states on every site.
We give a necessary and sufficient condition for a type of generalized power series to be algebraic over the ring of power series with coefficients in a finite field. This result extend a classical theorem of Huang-Stefanescu.
In this paper, we present a result similar to the shift-coupling result of Thorisson (1996) in the context of random graphs and networks. The result is that a given random rooted network can be obtained by changing the root of another given one if and only if the distributions of the two agree on the invariant sigma-field. Several applications of the result are presented for the case of unimodular networks. In particular, it is shown that the distribution of a unimodular network is uniquely determined by its restriction to the invariant sigma-filed. Also, the theorem is applied to the existence of an invariant transport kernel that balances between two given (discrete) measures on the vertices. An application is the existence of a so called extra head scheme for the Bernoulli process on an infinite unimodular graph. Moreover, a construction is presented for balancing transport kernels that is a generalization of the Gale-Shapley stable matching algorithm in bipartite graphs. Another application is on a general method that covers the situations where some vertices and edges are added to a unimodular network and then, to make it unimodular, the probability measure is biased and then a new root is selected. It is proved that this method provides all possible unimodularizations in these situations. Finally, analogous existing results for stationary point processes and unimodular networks are discussed in detail.
We use the transverse-momentum dependence of the cross section for diffractive dissociation of high energy pions to two jets to study some non-perturbative Light-Cone wave functions of the pion. We compare the predictions for this distribution by Gaussian and Coulomb wave functions as well as the wave function derived from solution of the Light-Cone Hamiltonian in the Singlet Model. We conclude that this experimentally measured information provides a powerful tool for these studies.
We present $\texttt{NPointFunctions}$, a package to incorporate desired amplitudes and observables for an arbitrary BSM model in $\texttt{FlexibleSUSY}$. The package relies on the $\texttt{SARAH}$-generated output used with $\texttt{FeynArts}/\texttt{FormCalc}$, embedded in an appropriate way, thus allowing calculations up to one-loop level. The resulting tool is an extension to $\texttt{FlexibleSUSY}$, a generator of spectrum generator programs. $\texttt{NPointFunctions}$ was designed to be customizable, modular and extensible with additional process- or amplitude- dependent contributions. We explain, how these goals are achieved, and discuss modifications to the default $\texttt{FlexibleSUSY}$ workflow.
Connes' gauge theory on $M_4\times Z_2$ is reformulated in the Lagrangian level. It is pointed out that the field strength in Connes' gauge theory is not unique. We explicitly construct a field strength different from Connes' one and prove that our definition leads to the generation-number independent Higgs potential. It is also shown that the nonuniqueness is related to the assumption that two different extensions of the differential geometry are possible when the extra one-form basis $\chi$ is introduced to define the differential geometry on $M_4\times Z_2$. Our reformulation is applied to the standard model based on Connes' color-flavor algebra. A connection between the unimodularity condition and the electric charge quantization is then discussed in the presence or absence of $\nu_R$.
Answering problems of Manin, we use the critical $L$-values of even weight $k\geq 4$ newforms $f\in S_k(\Gamma_0(N))$ to define zeta-polynomials $Z_f(s)$ which satisfy the functional equation $Z_f(s)=\pm Z_f(1-s)$, and which obey the Riemann Hypothesis: if $Z_f(\rho)=0$, then $\operatorname{Re}(\rho)=1/2$. The zeros of the $Z_f(s)$ on the critical line in $t$-aspect are distributed in a manner which is somewhat analogous to those of classical zeta-functions. These polynomials are assembled using (signed) Stirling numbers and "weighted moments" of critical values $L$-values. In analogy with Ehrhart polynomials which keep track of integer points in polytopes, the $Z_f(s)$ keep track of arithmetic information. Assuming the Bloch--Kato Tamagawa Number Conjecture, they encode the arithmetic of a combinatorial arithmetic-geometric object which we call the "Bloch-Kato complex" for $f$. Loosely speaking, these are graded sums of weighted moments of orders of \v{S}afarevi\v{c}-Tate groups associated to the Tate twists of the modular motives.
Recently a novel concise representation of the probability distribution of heat conducting nonequilibrium steady states was derived. The representation is valid to the second order in the ``degree of nonequilibrium'', and has a very suggestive form where the effective Hamiltonian is determined by the excess entropy production. Here we extend the representation to a wide class of nonequilibrium steady states realized in classical mechanical systems where baths (reservoirs) are also defined in terms of deterministic mechanics. The present extension covers such nonequilibrium steady states with a heat conduction, with particle flow (maintained either by external field or by particle reservoirs), and under an oscillating external field. We also simplify the derivation and discuss the corresponding representation to the full order.
It is conjectured that for fixed $A$, $r \ge 1$, and $d \ge 1$, there is a uniform bound on the size of the torsion submodule of a Drinfeld $A$-module of rank $r$ over a degree $d$ extension $L$ of the fraction field $K$ of $A$. We verify the conjecture for $r=1$, and more generally for Drinfeld modules having potential good reduction at some prime above a specified prime of $K$. Moreover, we show that within an $\Lbar$-isomorphism class, there are only finitely many Drinfeld modules up to isomorphism over $L$ which have nonzero torsion. For the case $A=\Fq[T]$, $r=1$, and $L=\Fq(T)$, we give an explicit description of the possible torsion submodules. We present three methods for proving these cases of the conjecture, and explain why they fail to prove the conjecture in general. Finally, an application of the Mordell conjecture for characteristic $p$ function fields proves the uniform boundedness for the $\pp$-primary part of the torsion for rank~2 Drinfeld $\Fq[T]$-modules over a fixed function field.
Side-channel attacks currently constitute the main challenge for quantum key distribution (QKD) to bridge theory with practice. So far two main approaches have been introduced to address this problem, (full) device-independent QKD and measurement-device-independent QKD. Here we present a third solution that might exceed the performance and practicality of the previous two in circumventing detector side-channel attacks, which arguably is the most hazardous part of QKD implementations. Our proposal has, however, one main requirement: the legitimate users of the system need to ensure that their labs do not leak any unwanted information to the outside. The security in the low-loss regime is guaranteed, while in the high-loss regime we already prove its robustness against some eavesdropping strategies.
We dynamically construct the interaction network in a granular gas, using the sequence of collisions collected in an MD event driven simulation of inelastic hard disks from time 0 till time t. The network is decomposed into its k-core structure: particles in a core of index k have collided at least k times with other particles in the same core. The difference between cores k+1 and k is the so-called k-shell, and the set of all shells is a complete and on-overlapping decomposition of the system. Because of energy dissipation, the gas cools down: its initial spatially homogeneous dynamics, characterized by the Haff law, i.e. a t^{-2} energy decay, is unstable towards a strongly inhomogeneous phase with clusters and vortices, where energy decays as t^{-1}. The clear transition between those two phases appears in the evolution of the k-shells structure in the collision network. In the homogeneous regime the k-shell structure evolves as in a growing network with fixed number of vertices and randomly added links: the shell distribution is strongly peaked around the most populated shell, which has an index k_{max} ~ 0.9 <d> with <d> the average number of collisions experienced by a particle. During the final non-homogeneous regime a growing fraction of collisions is concentrated in small, almost closed, 'communities' of particles: k_{max} is no more linear in <d> and the distribution of shells becomes extremely large developing a power-law tail ~ k^{-3} for high shell indexes. We propose the k-shell decomposition as a quantitative characterization of Molecular Chaos violation.
We consider the spatially inhomogeneous Landau equation with hard potentials (i.e. with $\gamma \in [0,1]$) on the whole space $\mathbb{R}^3$. We prove existence and uniquenss of solutions for a small time, assuming that the initial data is in a weighted tenth-order Sobolev space and has exponential decay in the velocity variable. In constrast to the soft potential case, local existence for the hard potentials case has been missing from the literature. This is because the moment loss issue is the most severe for these potentials. To get over this issue, our proof relies on a weighted hierarchy of norms that depends on the number of spatial and velocity derivatives in an asymmetric way. This hierarchy lets us take care of the terms that are affected by the moment loss issue the most. These terms do not give in to methods applied to study existence of solutions to Landau equation with soft potentials and are a major reason why the local existence problem was not known for the case of hard potentials.
We give a small data global well-posedness result for an incompressible Oldroyd-B model with wave number dissipation in the equation of stress tensor. The result is uniform in solvent Reynolds numbers, and requires only fractional wave-number dependent dissipation $(-\Delta)^{\beta}$, $\beta \ge \frac{1}{2}$ in the added stress.
A new class of bootstrap percolation models in which particle culling occurs only for certain numbers of nearest neighbours is introduced and studied on a Bethe lattice. Upon increasing the density of initial configuration they undergo multiple hybrid (or mixed-order) phase transitions, showing that such intriguing phase behaviours may also appear in fully homogeneous situations/environments, provided that culling is selective rather than cumulative. The idea immediately extends to facilitation dynamics, suggesting a simple way to construct one-component models of multiple glasses and glass-glass transitions as well as more general coarse-grained models of complex cooperative dynamics.
We review the main features of the generalized Chaplygin gas (GCG) proposal for unification of dark energy and dark matter and discuss how it admits an unique decomposition into dark energy and dark matter components once phantom-like dark energy is excluded. In the context of this approach we consider structure formation and show that unphysical oscillations or blow-up in the matter power spectrum are not present. Moreover, we demonstrate that the dominance of dark energy occurs about the time when energy density fluctuations start evolving away from the linear regime.
Graphene in spintronics has so far primarily meant spin current leads of high performance because the intrinsic spin-orbit coupling of its pi-electrons is very weak. If a large spin-orbit coupling could be created by a proximity effect, the material could also form active elements of a spintronic device such as the Das-Datta spin field-effect transistor, however, metal interfaces often compromise the band dispersion of massless Dirac fermions. Our measurements show that Au intercalation at the graphene-Ni interface creates a giant spin-orbit splitting (~100 meV) in the graphene Dirac cone up to the Fermi energy. Photoelectron spectroscopy reveals hybridization with Au-5d states as the source for the giant spin-orbit splitting. An ab initio model of the system shows a Rashba-split dispersion with the analytically predicted gapless band topology around the Dirac point of graphene and indicates that a sharp graphene-Au interface at equilibrium distance will account for only ~10 meV spin-orbit splitting. The ab initio calculations suggest an enhancement due to Au atoms that get closer to the graphene and do not violate the sublattice symmetry.
We present a fully consistent catalog of local and global properties of host galaxies of 882 Type Ia supernov\ae\ (SNIa) that were selected based on their light-curve properties, spanning the redshift range $0.01 < z < 1.\text{}$ This catalog corresponds to a preliminary version of the compilation sample and includes Supernova Legacy Survey (SNLS) 5-year data, Sloan Digital Sky Survey (SDSS), and low-redshift surveys. We measured low- and moderate-redshift host galaxy photometry in SNLS and SDSS images and used spectral energy distribution (SED) fitting techniques to derive host properties such as stellar mass and $U-V$ rest-frame colors; the latter are an indicator of the luminosity-weighted age of the stellar population in a galaxy. We also estimated the local observed fluxes at the supernova location within a proper distance radius of 3 kpc, and transposed them into local $U-V$ rest-frame colors. Selecting SNIa based on host photometry quality, we then performed cosmological fits using local color as a third standardization variable, for which we split the sample at the median value. We find a local color step as significant as the maximum mass step effect. Correcting for the maximum mass step correction, we still find a significant local color effect, which shows that additional information is provided by the close environment of SNIa. Departures from the initial choices were investigated, and we discuss the possible implications for cosmology. This will be of tremendous importance for the forthcoming SNIa surveys, and in particular for the Large Synoptic Survey Telescope (LSST), for which uncertainties on the dark energy equation of state will be comparable to the effects reported here.
Consider the set of equations describing Oldroyd-B fluids in an exterior domain. It is shown that this set of equations admits a unique, global solution in a certain function space provided the initial data, but not necessarily the coupling constant, is small enough.
We present constraints on extensions to the flat $\Lambda$CDM cosmological model by varying the spatial curvature $\Omega_K$, the sum of the neutrino masses $\sum m_\nu$, the dark energy equation of state parameter $w$, and the Hu-Sawicki $f(R)$ gravity $f_{R0}$ parameter. With the combined $3\times2$pt measurements of cosmic shear from the Kilo-Degree Survey (KiDS-1000), galaxy clustering from the Baryon Oscillation Spectroscopic Survey (BOSS), and galaxy-galaxy lensing from the overlap between KiDS-1000, BOSS, and the spectroscopic 2-degree Field Lensing Survey (2dFLenS), we find results that are fully consistent with a flat $\Lambda$CDM model with $\Omega_K=0.011^{+0.054}_{-0.057}$, $\sum m_\nu<1.76$ eV (95% CL), and $w=-0.99^{+0.11}_{-0.13}$. The $f_{R0}$ parameter is unconstrained in our fully non-linear $f(R)$ cosmic shear analysis. Considering three different model selection criteria, we find no clear preference for either the fiducial flat $\Lambda$CDM model or any of the considered extensions. Besides extensions to the flat $\Lambda$CDM parameter space, we also explore restrictions to common subsets of the flat $\Lambda$CDM parameter space by fixing the amplitude of the primordial power spectrum to the Planck best-fit value, as well as adding external data from supernovae and lensing of the CMB. Neither the beyond-$\Lambda$CDM models nor the imposed restrictions explored in this analysis are able to resolve the $\sim 3\sigma$ tension in $S_8$ between the $3\times2$pt constraints and Planck, with the exception of $w$CDM, where the $S_8$ tension is resolved. The tension in the $w$CDM case persists, however, when considering the joint $S_8$-$w$ parameter space. The joint flat $\Lambda$CDM CMB lensing and $3\times2$pt analysis is found to yield tight constraints on $\Omega_{\rm m}=0.307^{+0.008}_{-0.013}$, $\sigma_8=0.769^{+0.022}_{-0.010}$, and $S_8=0.779^{+0.013}_{-0.013}$.
The X-ray emission from the wind-wind collision in short-period massive O+O-star binaries is investigated. The emission is calculated from three-dimensional hydrodynamical models which incorporate gravity, the driving of the winds, orbital motion of the stars, and radiative cooling of the shocked plasma. Changes in the amount of stellar occultation and circumstellar attenuation introduce phase-dependent X-ray variability in systems with circular orbits, while strong variations in the intrinsic emission also occur in systems with eccentric orbits. The X-ray emission in eccentric systems can display strong hysteresis, with the emission softer after periastron than at corresponding orbital phases prior to periastron, reflecting the physical state of the shocked plasma at these times. Furthermore, the rise of the luminosity to maximum does not necessarily follow a 1/D law. Our models further demonstrate that the effective circumstellar column can be highly energy dependent.   We simulate Chandra and Suzaku observations, and fit these using standard XSPEC models. We find that the recovered temperatures from two or three-temperature mekal fits are comparable to those from fits to the emission from real systems with similar stellar and orbital parameters/nature. We also find that when the global abundance is thawed in the spectral fits, sub-solar values are exclusively returned, despite the calculations using solar values as input (abridged).
The observed hierarchy of quark and lepton masses and mixings may be obtained by adding an abelian family symmetry to the Minimal Supersymmetric Model and coupling quarks and leptons to an electroweak singlet scalar field. In a large class of such models, this symmetry suffers from anomalies which must be compensated by the Green-Schwarz mechanism; this in turn fixes the electroweak mixing angle to be $\sin^2 \theta_W = 3/8$ at the string scale, without any assumed GUT structure. The analysis is extended to two distinct generalisations of the Standard Model: neutrino masses and mixings and R-parity violating interactions.
We investigate the effects of higher order curvature corrections to Einstein's Gravity on the critical phenomenon near the black hole threshold, namely the Choptuik phenomenon. We simulate numerically a five dimensional spherically symmetric gravitational collapse of massless scalar field in Einstein-Gauss-Bonnet gravity towards a black hole formation threshold. When the curvature is sufficiently large the additional higher order terms, affect the evolution of the whole system. Since high curvature characterizes the region when the critical behavior takes place this critical behavior is destroyed. Both the self similarity and the mass scaling relation disappear. Instead we find a different behavior near the black hole threshold, which depends on the coupling constant of the higher order terms. The new features include a change of the sign of the Ricci scalar on the origin which indicates changes in the local geometry of space-time, and never occurs in classical general relativity collapse, and oscillations with a constant rather than with a diminishing length scale.
Magnetars younger than one century are expected to be hyper active. Besides winds powered by rotation they generate frequent magnetic flares, which launch powerful blast waves into the wind. These internal shocks act as masers producing fast (millisecond) radio bursts (FRBs) with the following properties. (1) GHz radio emission occurs at radii $r\sim 10^{14}$ cm and lasts $\lesssim 1$ ms in observer's time. (2) Induced scattering in the surrounding wind does not suppress the radio burst. (3) The emission has linear polarization set by the magnetar rotation axis. (4) The emission drifts to lower frequencies during the burst, and its duration broadens at lower frequencies. (5) Blast waves in inhomogeneous winds may emit variable bursts; periodicity might appear on sub-ms timescales if the magnetar rotates with $\sim 1$ s period. However, the observed FRB structure is likely changed by lensing effects during propagation through the host galaxy. (6) The FRBs from magnetars are expected to repeat, with rare strong bursts (up to $\sim 10^{43}$ erg) or more frequent weak bursts. (7) When a repeating flare strikes the wind bubble in the tail of a previous flare, the FRB turns into a bright optical flash. Its luminosity may approach that of a supernova Ia and last seconds. The rate of these optical flashes in the universe is much lower than the FRB rate, however it may exceed the supernova rate. Locations of hyper-active magnetars in their host galaxies depend on how they form: magnetars created in supernovae explosions will trace star formation regions, and magnetars formed in mergers of compact objects will be offset. The merger magnetars are expected to be most energetic and particularly hyper-active.
We extract the Glauber divergences from the spectator amplitudes for two-body hadronic decays $B \to M_1 M_2$ in the $k_T$ factorization theorem, where $M_2$ denotes the meson emitted at the weak vertex. Employing the eikonal approximation, the divergences are factorized into the corresponding Glauber phase factors associated with the $M_1$ and $M_2$ mesons. It is observed that the latter factor enhances the spectator contribution to the color-suppressed tree amplitude by modifying the interference pattern between the two involved leading-order diagrams. The first factor rotates the enhanced spectator contribution by a phase, and changes its interference with other tree diagrams. The above Glauber effects are compared with the mechanism in elastic rescattering among various $M_1 M_2$ final states, which has been widely investigated in the literature. We postulate that only the Glauber effect associated with a pion is significant, due to its special role as a $q \bar q$ bound state and as a pseudo Nambu-Goldstone boson simultaneously. Treating the Glauber phases as additional inputs in the perturbative QCD (PQCD) approach, we find a good fit to all the $B \to \pi\pi$, $\pi\rho$, $\pi\omega$, and $\pi K$ data, and resolve the long-standing $\pi\pi$ and $\pi K$ puzzles. The nontrivial success of this modified PQCD formalism is elaborated.