ShantanuT01/DACTYL-Pretraining huggingface dataset:
The muon capture on 3H leading to muonic neutrino and three neutrons in the final state is studied under full inclusion of final state interactions. Predictions for the three-body break-up of 3H are calculated with the AV18 potential, augmented by the Urbana IX three-nucleon force. Our results are based on the single nucleon weak current operator comprising the dominant relativistic corrections. This work is a natural extension of our investigations of the muon capture on 3He leading to 3H or n+d or n+n+p and muonic neutrino in the final state, presented in Phys. Rev. C90, 024001 (2014).
We present results from a BeppoSAX observation of the cooling flow cluster Abell 2029. The broad band spectrum (2-35 keV) of the cluster, when fitted with a model including a cooling flow component and a one temperature thermal component, yields a temperature of 8.3+/-0.2 keV and a metal abundance of 0.46+/-0.03 in solar units, for the latter. No evidence of a hard X-ray excess is found in the PDS spectrum. By performing a spatially resolved spectral analysis we find that the projected temperature and abundance drop with increasing radius, going from about 8 keV and 0.5 (solar units) at the cluster core to about 5 keV and 0.2 (solar units) at about 1.2 Mpc.
Observations made with the University of Durham Mark 6 atmospheric Cerenkov telescope confirm that PSR B1706-44 is a very high energy gamma-ray emitter. There is no indication from our dataset that the very high energy gamma-rays are pulsed, in contrast to the findings at < 20 GeV, which indicate that more than 80% of the flux is pulsed. The flux at E > 300 GeV is estimated to be (3.9 +/- 0.7 (statistical)) x 10^-11 cm^-2 s^-1.
Second RPA calculations with a Skyrme force are performed to describe both high- and low-lying excited states in $^{16}$O. The coupling between 1 particle-1 hole and 2 particle-2 hole as well as that between 2 particle-2 hole configurations among themselves are fully taken into account and the residual interaction is never neglected, not resorting therefore to a generally used approximate scheme where only the first kind of coupling is considered. The issue of the rearrangement terms in the matrix elements beyond standard RPA is addressed and discussed. As a general feature of second RPA results, a several-MeV shift of the strength distribution to lower energies is systematically found with respect to RPA distributions. A much more important fragmentation of the strength is also naturally provided by second RPA due to the huge number of 2 particle-2 hole configurations. A better description of the excitation energies of the low-lying 0$^+$ and 2$^+$ states is obtained with second RPA with respect to RPA.
We develop a novel method to simultaneously determine the vertical potential, force and stellar $z-v_z$ phase space distribution function (DF) in our local patch of the Galaxy. We assume that the Solar Neighborhood can be treated as a one-dimensional system in dynamical equilibrium and directly fit the number density in the $z-v_z$ plane to what we call the Rational Linear DF (RLDF) model. This model can be regarded as a continuous sum of isothermal DFs though it has only one more parameter than the isothermal model. We apply our method to a sample of giant stars from Gaia Data Release 2 and show that the RLDF provides an excellent fit to the data. The well-known phase space spiral emerges in the residual map of the $z-v_z$ plane. We use the best-fit potential to plot the residuals in terms of the frequency and angle of vertical oscillations and show that the spiral maps into a straight line. From its slope, we estimate that the phase spirals were generated by a perturbation $\sim540$ Myr years ago. We also determine the differential surface density as a function of vertical velocity dispersion, a.k.a. the vertical temperature distribution. The result is qualitatively similar to what was previously found for SDSS/SEGUE G dwarfs. Finally, we address parameter degeneracies and the validity of the 1D approximation. Particularly, the mid-plane density derived from a cold subsample, where the 1D approximation is more secure, is closer to literature values than that derived from the sample as a whole.
The recent generalizations of Boltzmann-Gibbs statistics mathematically relies on the deformed logarithmic and exponential functions defined through some deformation parameters. In the present work, we investigate whether a deformed logarithmic/exponential map is a bijection from $\mathbb{R}^+/\mathbb{R}$ (set of positive real numbers/all real numbers) to $\mathbb{R}/\mathbb{R}^+$, as their undeformed counterparts. We show that their inverse map exists only in some subsets of the aforementioned (co)domains. Furthermore, we present conditions which a generalized deformed function has to satisfy, so that the most important properties of the ordinary functions are preserved. The fulfillment of these conditions permits us to determine the validity interval of the deformation parameters. We finally apply our analysis to Tsallis, Kaniadakis, Abe and Borges-Roditi deformed functions.
Representations of primes by simple quadratic forms, such as $\pm a^2\pm qb^2$, is a subject that goes back to Fermat, Lagrange, Legendre, Euler, Gauss and many others. We are interested in a comprehensive list of such results, for $q\le 20$. Some of the results can be established with elementary methods and we put them at work on some instances. We are introducing new relationships between various representations.
Existence and stability properties are studied for Hawkes process, i.e. point process $S$ that has long-memory and intensity $r(t)=\lambda \big(g_0(t)+ \sum_{\tau<t, \tau \in S} h(t-\tau) \big)$. The approach to Hawkes process presented in this paper allows us to prove the uniqueness of invariant distribution of the process under weaker conditions. New speed of convergence results are also shown. Unlike previous results the function $\lambda$ is not required to be Lipschitz and can be even discontinuous. Some generalizations are also considered.
We present a scheme for fast environment light estimation from the RGBD appearance of individual objects and their local image areas. Conventional inverse rendering is too computationally demanding for real-time applications, and the performance of purely learning-based techniques may be limited by the meager input data available from individual objects. To address these issues, we propose an approach that takes advantage of physical principles from inverse rendering to constrain the solution, while also utilizing neural networks to expedite the more computationally expensive portions of its processing, to increase robustness to noisy input data as well as to improve temporal and spatial stability. This results in a rendering-aware system that estimates the local illumination distribution at an object with high accuracy and in real time. With the estimated lighting, virtual objects can be rendered in AR scenarios with shading that is consistent to the real scene, leading to improved realism.
We investigate a model of excitonic ordering (i.e electron-hole pair condensation) appropriate for the divalent hexaborides. We show that the inclusion of imperfectly nested electron hole Fermi surfaces can lead to the formation of an undoped excitonic metal phase. In addition, we find that weak ferromagnetism with compensated moments arises as a result of gapless excitations. We study the effect of the low lying excitations on the density of states, Fermi surface topology and optical conductivity and compare to available experimental data.
We introduce a set of high-resolution dissipationless simulations that model the Local Group (LG) in a cosmological context: Exploring the Local Volume in Simulations (ELVIS). The suite contains 48 Galaxy-size halos, each within high-resolution volumes that span 2-5 Mpc in size, and each resolving thousands of systems with masses below the atomic cooling limit. Half of the ELVIS galaxy halos are in paired configurations similar to the Milky Way (MW) and M31; the other half are isolated, mass-matched analogs. We find no difference in the abundance or kinematics of substructure within the virial radii of isolated versus paired hosts. On Mpc scales, however, LG-like pairs average almost twice as many companions and the velocity field is kinematically hotter and more complex. We present a refined abundance matching relation between stellar mass and halo mass that reproduces the observed satellite stellar mass functions of the MW and M31 down to the regime where incompleteness is an issue, $M_\star \sim 5\times 10^5 \, M_\odot$. Within a larger region spanning approximately 3 Mpc, the same relation predicts that there should be $\sim$ 1000 galaxies with $M_\star > 10^{3}\,M_\odot$ awaiting discovery. We show that up to 50% of halos within 1 Mpc of the MW or M31 could be systems that have previously been within the virial radius of either giant. By associating never-accreted halos with gas-rich dwarfs, we show that there are plausibly 50 undiscovered dwarf galaxies with HI masses $> 10^5\,M_\odot$ within the Local Volume. The radial velocity distribution of these predicted gas-rich dwarfs can be used to inform follow-up searches based on ultra-compact high-velocity clouds found in the ALFALFA survey.
We report polarized and unpolarized neutron scattering measurements of the magnetic order in single crystals of Na0.5CoO2. Our data indicate that below T_N=88 K the spins form a novel antiferromagnetic pattern within the CoO2 planes, consisting of alternating rows of ordered and non-ordered Co ions. The domains of magnetic order are closely coupled to the domains of Na ion order, consistent with such a two-fold symmetric spin arrangement. Magnetoresistance and anisotropic susceptibility measurements further support this model for the electronic ground state.
We have tested the theoretical values of critical exponents, predicted for the three--dimensional Heisenberg model, based on the published Monte Carlo (MC) simulation data for the susceptibility. Two different sets of the critical exponents have been considered - one provided by the usual (perturbative) renormalization group (RG) theory, and another predicted by grouping of Feynman diagrams in phi^4 model (our theory). The test consists of two steps. First we determine the critical coupling by fitting the MC data to the theoretical expression, including both confluent and analytical corrections to scaling, the values of critical exponents being taken from theory. Then we use the obtained value of critical coupling to test the agreement between theory and MC data at criticality. As a result, we have found that predictions of our theory (gamma=19/14, eta=1/10, omega=3/5) are consistent, whereas those of the perturbative RG theory (gamma=1.3895, eta=0.0355, omega=0.782) are inconsistent with the MC data. The seemable agreement between the RG prediction for eta and MC results at criticality, reported in literature, appears due to slightly overestimated value of the critical coupling. Estimation of critical exponents of 3D Ising model from complex zeroth of the partition function is discussed. A refined analysis yields the best estimate 1/nu=1.518. We conclude that the recent MC data can be completely explained within our theory (providing 1/nu=1.5 and omega=0.5) rather than within the conventional RG theory.
In 1957, Hans Lewy constructed a counterexample showing that very simple and natural differential equations can fail to have local solutions. A geometric interpretation and a generalization of this counterexample were given in 1960 by L.H\"ormander. In the early seventies, L.Nirenberg and F.Treves proposed a geometric condition on the principal symbol, the so-called condition $(\psi)$, and provided strong arguments suggesting that it should be equivalent to local solvability. The necessity of condition $(\psi)$ for solvability of pseudo-differential equations was proved by L.H\"ormander in 1981. In 1994, it was proved by N.L. that condition $(\psi)$ does not imply solvability with loss of one derivative for pseudo-differential equations, contradicting repeated claims by several authors. However in 1996, N.Dencker proved that these counterexamples were indeed solvable, but with a loss of two derivatives. We shall explore the structure of this phenomenon from both sides: on the one hand, there are first-order pseudo-differential equations satisfying condition $(\psi)$ such that no $L^2_{\text{loc}}$ solution can be found with some source in $L^2_{\text{loc}}$. On the other hand, we shall see that, for these examples, there exists a solution in the Sobolev space $H^{-1}_{\text{loc}}$.
Let C be a generic non-singular curve of genus g defined over a field of characteristic different from 2. We show that for every line bundle on C of degree at most g+1, the natural product map S^2(H^0(L))\to H^0(C,L^2) is injective. We also show that the bound on the degree of L is sharp.
We derive necessary and sufficient inseparability conditions imposed on the variance matrix of symmetric qubits. These constraints are identified by examining a structural parallelism between continuous variable states and two qubit states. Pairwise entangled symmetric multiqubit states are shown here to obey these constraints. We also bring out an elegant local invariant structure exhibited by our constraints.
The dynamical generation of complex correlations in quantum many-body systems is of renewed interest in the context of quantum chaos, where the out-of-time-ordered (OTO) correlation function appears as a convenient measure of scrambling. To detect the the transition from scrambling to many-body localization, the latter of which has limited dynamical complexity and is often classically simulatable, we develop both exact and approximate methods to compute OTO correlators for arbitrary universal quantum circuits. We take advantage of the mapping of quantum circuits to the dynamics of interacting fermions in one dimension, as Gaussian time evolution supplemented by quartic interaction gates. In this framework, the OTO correlator can be calculated exactly as a superposition of exponentially many Gaussian-fermionic trajectories in the number of interaction gates. We develop a variationally-optimized, Gaussian approximation to the spatial propagation of an initially-local operator by restriction to the fastest-traveling fermionic modes, in a similar spirit as light-front computational methods in quantum field theory. We demonstrate that our method can detect the many-body localization transitions of generally time-dependent dynamics without the need for perturbatively weak interactions.
We give a new expression for the inner product of two kernel functions associated to a cusp form. Among other applications, it yields an extension of a formula of Kohnen and Zagier, and another proof of Manin's Periods Theorem. Cohen's representation of these kernels as series is also generalized.
Given $d\geq 2$ and two rooted $d$-ary trees $D$ and $T$ such that $D$ has $k$ leaves, the density $\gamma(D,T)$ of $D$ in $T$ is the proportion of all $k$-element subsets of leaves of $T$ that induce a tree isomorphic to $D$, after erasing all vertices of outdegree $1$. In a recent work, it was proved that the limit inferior of this density as the size of $T$ grows to infinity is always zero unless $D$ is the $k$-leaf binary caterpillar $F^2_k$ (the binary tree with the property that a path remains upon removal of all the $k$ leaves). Our main theorem in this paper is an exact formula (involving both $d$ and $k$) for the limit inferior of $\gamma(F^2_k,T)$ as the size of $T$ tends to infinity.
While the formation of the first black holes at high redshift is reasonably well understood though debated, massive black hole formation at later cosmic epochs has not been adequately explored. We present a gas accretion driven mechanism that can build up black hole masses rapidly in dense, gas-rich nuclear star clusters (NSCs). Wind-fed supra-exponential accretion of an initially wandering black hole in NSCs can lead to extremely fast growth, scaling stellar mass remnant seed black holes up to intermediate mass black holes (IMBHs). Operating throughout cosmic time, growth via this new channel is modulated by the gas supply, and premature termination results in the formation of lower mass black holes with masses in the range of 50 - few 100 solar masses, filling in the so-called mass gap. However, in most gas-rich NSCs, growth is unimpeded, inevitably leading to the formation of IMBHs with masses ranging from 100 - 100,000 solar masses. A spate of new detection spanning the full range of the IMBH mass function - from the LIGO-VIRGO source GW190521 to the emerging population of 10^5 solar mass black holes harbored in low-mass dwarf galaxies - are revealing this elusive population. Naturally accounting for the detected presence of off-center IMBHs in low-mass dwarfs, this new pathway also predicts the existence of an extensive population of wandering non-central black holes in more massive galaxies would be detectable via tidal disruption events and as GW sources. Gas-rich NSCs serve as incubators for the continual formation of black holes over a wide range in mass throughout cosmic time.
In the G-framework, we establish existence of an optimal stochastic relaxed control for stochastic differential equations driven by a G-Brownian motion.
We investigate quasistatic evolution in finite plasticity under the assumption that the plastic strain is compatible. This assumption is well-suited to describe the special case of dislocation-free plasticity and entails that the plastic strain is the gradient of a plastic deformation map. The total deformation can be then seen as the composition of a plastic and an elastic deformation. This opens the way to an existence theory for the quasistatic evolution problem featuring both Lagrangian and Eulerian variables. A remarkable trait of the result is that it does not require second-order gradients.
Semiconducting single-walled carbon-nanotubes (SWCNTs) are an interesting material for strong-light matter coupling due to their stable excitons, narrow emission in the near infrared and high charge carrier mobilities. Furthermore, they have emerged as quantum light sources as a result of the controlled introduction of luminescent quantum defects (sp$^{3}$-defects) with red-shifted transitions that enable single-photon emission. The complex photophysics of SWCNTs and overall goal of polariton condensation pose the question of how exciton-polaritons are populated and how it might be optimized. The contributions of possible relaxation processes, i.e., scattering with acoustic phonons, vibrationally assisted scattering, and radiative pumping, are investigated using angle-resolved reflectivity and time-resolved photoluminescence measurements on microcavities with a wide range of detunings. We show that the predominant population mechanism for SWCNT exciton-polaritons in planar microcavities is radiative pumping. Consequently, the limitation of polariton population due to the low photoluminescence quantum yield of nanotubes, can be overcome by luminescent sp$^{3}$ defects. Without changing the polariton branch structure, radiative pumping through these emissive defects leads to an up to 10-fold increase of the polariton population for detunings with a large photon fraction. Thus, the controlled and tunable functionalization of SWCNTs with sp$^{3}$ defects presents a viable route towards bright and efficient polariton devices.
Recent analyses have shown that a sequential fourth generation can be consistent with precision electroweak data. We consider the possibility that the new generation could be a mirror generation with $V+A$ rather than $V-A$ interactions. Specifically we consider an extension of the minimal supersymmetric standard model with a light mirror generation (mirMSSM) . Implications of this extension are explored. One consequence is an enhancement of the tau neutrino magnetic moment by several orders of magnitude consistent with the current limits on the magnetic moment of the tau. The masses of the mirror generation arise due to electroweak symmetry breaking, and if a mirror generation exists its mass spectrum must lye below a TeV, and thus should be discovered at the LHC. Mirror particles and mirror sparticles produce many characteristic signatures which should be detectable at the LHC. Heavy higgs boson decays into mirror particles and an analysis of the forward-backward asymmetries can distinguish a mirror generation from a sequential fourth generation. The validity of the model can thus be tested at the LHC. A model of the type discussed here could arise from a more unified structure such as grand unification or strings where a mirror generation escapes the survival hypothesis, i.e., a generation and a mirror generation do not tie up to acquire a mass of size $M_{GUT}$ or $M_{string}$ due to a symmetry, and thus remain massless down to the electroweak scale.
The consequences of microreversibility for the linear and nonlinear transport properties of systems subjected to external magnetic fields are systematically investigated in Aharonov-Bohm rings connected to two, three, and four terminals. Within the independent electron approximation, the cumulant generating function, which fully specifies the statistics of the nonequilibrium currents, is expressed in terms of the scattering matrix of these circuits. The time-reversal symmetry relations up to the third responses of the currents and the fourth cumulants are analytically investigated and numerically tested as a function of the magnetic flux. The validity of such relations is thus firmly confirmed in this class of open quantum systems.
Dark sectors with strong interactions have received considerable interest. Assuming the existence of a minimally coupled dark sector which runs to strong interactions in the infrared, we address the question whether the scaling behavior of this dark sector can be observed in missing energy signatures at present and future hadron colliders. We compare these findings to the concrete case of self-interacting dark matter and demonstrate that the energy dependence of high-momentum transfer final states can in principle be used to gain information about the UV structure of hidden sectors at future hadron colliders, subject to large improvements in systematic uncertainties, which could complement proof-of-principle lattice investigations. We also comment on the case of dark Abelian $U(1)$ theories.
Cross-correlations between Cosmic Microwave Background (CMB) temperature and $y$-spectral distortions anisotropies have been previously proposed as a way to measure the local bispectrum parameter $f_{\rm NL}^{\rm loc.}$ in a range of scales inaccessible to either CMB ($T$, $E$) bispectra or $T$-$\mu$ correlations. This is useful e.g. to test scale dependence of primordial non-Gaussianity. Unfortunately, the primordial $y$-T signal is strongly contaminated by the late-time correlation between the Integrated Sachs Wolfe and Sunyaev-Zel'dovich (SZ) effects. Moreover, SZ itself generates a large noise contribution in the $y$-parameter map. We consider two original ways to address these issues. In order to remove the bias due to the SZ-CMB temperature coupling, while also adding new signal, we include in the analysis the cross-correlation between $y$-distortions and CMB {\em polarization}. In order to reduce the noise, we propose to clean the $y$-map by subtracting a SZ template, reconstructed via cross-correlation with external tracers (CMB and galaxy-lensing signals). We combine this SZ template subtraction with the previously adopted solution of directly masking detected clusters. Our final forecasts show that, using $y$-distortions, a PRISM-like survey can achieve $1\sigma(f_{\rm NL}^\text{loc.}) = 300$, while an ideal experiment will achieve $1\sigma(f_{\rm NL}^\text{loc.}) = 130$, with improvements of a factor $\sim 3$ from adding the $y$-$E$ signal, and a further $20-30 \%$ from template cleaning. These forecasts are much worse than current $f_{\rm NL}^\text{loc.}$ boundaries from {\em Planck}, but we stress again that they refer to completely different scales.