ShantanuT01/DACTYL-Pretraining huggingface dataset:
The signal strength of the $gg \to H \to \gamma \gamma$ reaction in $pp$ collisions at the LHC is studied within the context of the SM with UED. The impact of an arbitrary number $n$ of UED on both the $gg\to H$ and $H\to \gamma \gamma$ subprocesses is studied. The 1-loop contributions of Kaluza-Klein excitations to these subprocesses are proportional to discrete and continuous sums, which can diverge. By implementing dimensional regularization, it is shown that discrete regularized sums can naturally be expressed as multidimensional Epstein functions, and that divergences, if exist, emerge through the poles of these functions. It is found that continuous sums converge, but the discrete ones diverge, with the exception of the $n=1$ case, in which the 1-dimensional Epstein function converges. It is argued that divergences that arise from discrete sums for $n\geq 2$ are genuine UV divergences, since they correspond to short-distance effects in the compact manifold. Then, the amplitudes are renormalized in a modern sense by incorporating interactions of canonical dimension higher than four that allow us to generate the required counterterms, which are determined using a $\overline{\rm MS}$-like renormalization scheme. We find that the $gg\to H$ subprocess is quite sensitive to both the size and the dimension of the compact manifold, but the SM prediction for $H\to \gamma \gamma$ subprocess is practically unchanged. In the $n=1$ case, it is found that the experimental constraint on the compactification scale $R^{-1}\geq 1.5$ TeV allow us to reproduce the experimental limit on the signal strength $1.01\leq \mu^{(1)}_{\gamma \gamma}\leq 1.2$. In the $n\geq 2$ cases, it is found that the experimental limit on $\mu^{(n)}_{\gamma \gamma}$ leads to stronger lower bounds for the compactification scale given by $R^{-1}\geq 1.55, 2.45, 3.57, 5.10, 7.25$ TeVs for $n=2, 4, 6, 8, 10$, respectively.
We show that the global infinitesimal change in the multi-particle pure product state gives rise to an entangled state. This suggests that even if there is no interaction present between the subsystems, i.e., at each time instant the state is non-entangled, the tangent vector is typically entangled. Since the tangent space vectors tell the state-space vectors how to change this implies that quantum entanglement is necessary for motion or change in general. This is truly a `hidden power' of quantum entanglement. During quantum computation even though at each time instant the state is not entangled, quantum entanglement guides the process of computation. This observation applies to multi-particle pure, pseudo-pure and mixed states as well.
System size dependence of hadron production properties is discussed within the Wounded Nucleon Model and the Statistical Model in the grand canonical, canonical and micro-canonical formulations. Similarities and differences between predictions of the models related to the treatment of conservation laws are exposed. A need for models which would combine a hydrodynamical-like expansion with conservation laws obeyed in individual collisions is stressed.
We solve the 1D neutrino-heated non-relativistic MHD wind problem for conditions that range from slowly rotating (spin period P > 10 ms) protoneutron stars (PNSs) with surface field strengths typical of radio pulsars (B < 10^13 G), to "proto-magnetars" with B ~ 10^14-10^15 G in their hypothesized rapidly rotating initial states (P ~ 1 ms). We use the simulations of Bucciantini et al. (2006) to map our monopole results onto a more physical dipole geometry and to estimate the spindown of PNSs when their winds are relativistic. We then quantify the effects of rotation and magnetic fields on the mass loss, energy loss, and r-process nucleosynthesis in PNS winds. We describe the evolution of PNS winds through the Kelvin-Helmholtz cooling epoch, emphasizing the transition between (1) thermal neutrino-driven, (2) non-relativistic magnetically-dominated, and (3) relativistic magnetically-dominated outflows. We find that proto-magnetars with P ~ 1 ms and B > 10^15 G drive relativistic winds with luminosities, energies, and Lorentz factors (magnetization sigma ~ 0.1-1000) consistent with those required to produce long duration gamma-ray bursts and hyper-energetic supernovae (SNe). A significant fraction of the rotational energy may be extracted in only a few seconds, sufficiently rapidly to alter the asymptotic energy of the SN remnant, its morphology, and, potentially, its nucleosynthetic yield. Winds from PNSs with more modest rotation periods (2 - 10 ms) and with magnetar-strength fields produce conditions significantly more favorable for the r-process than winds from slowly rotating PNSs. Lastly, we show that energy and momentum deposition by convectively-excited waves further increase the likelihood of successful r-process in PNS winds.
We study in detail the trajectories, ordered and chaotic, of two entangled Bohmian qubits when their initial preparation satisfies (or not) Born's rule for various amounts of quantum entanglement. For any non zero value of entanglement ordered and chaotic trajectories coexist and the proportion of ordered trajectories increases with the decrease of the entanglement. In the extreme cases of zero and maximum entanglement we have only ordered and chaotic trajectories correspondingly. The chaotic trajectories of this model are ergodic, for any given value of entanglement, namely the limiting distribution of their points does not depend on their initial conditions. Consequently it is the ratio between ordered and chaotic trajectories which is responsible for the dynamical establishment (or not) of Born's rule.
We obtain a sufficient condition for a Fano threefold with terminal singularities to have a conic bundle structure.
Even if Einstein's General Relativity achieved a great success and overcame lots of experimental tests, it also showed some shortcomings and flaws which today advise theorists to ask if it is the definitive theory of gravity. In this proceeding paper it is shown that, if advanced projects on the detection of Gravitational Waves (GWs) will improve their sensitivity, allowing to perform a GWs astronomy, accurate angular and frequency dependent response functions of interferometers for GWs arising from various Theories of Gravity, i.e. General Relativity and Extended Theories of Gravity, will be the ultimate test for General Relativity. This proceeding paper is also a short review of the Essay which won Honorable Mention at the 2009 Gravity Research Foundation Awards.
We consider a population model where individuals behave independently from each other and whose genealogy is described by a chronological tree called splitting tree. The individuals have i.i.d. (non-exponential) lifetime durations and give birth at constant rate to clonal or mutant children in an infinitely many alleles model with neutral mutations. First, to study the allelic partition of the population, we are interested in its frequency spectrum, which, at a fixed time, describes the number of alleles carried by a given number of individuals and with a given age. We compute the expected value of this spectrum and obtain some almost sure convergence results thanks to classical properties of Crump-Mode-Jagers (CMJ) processes counted by random characteristics. Then, by using multitype CMJ-processes, we get asymptotic properties about the number of alleles that have undergone a fixed number of mutations with respect to the ancestral allele of the population.
Although the cosmological constant has primarily cosmological consequences, its smallness poses one of the basic problems in particle physics. Various attempts have been made to explain this mystery, but no satisfactory solution has been found yet. The appearance of extra dimensions in the framework of brane world systems seems to provide some new ideas to address this problem form a different point of view. We shall discuss some of these new approaches and see whether or not they lead to an improvement of the situation. We shall conclude that we are still far from a solution of the problem.
We develop the framework for augmented homotopical algebraic geometry. This is an extension of homotopical algebraic geometry, which itself is a homotopification of classical algebraic geometry. To do so, we define the notion of augmentation categories, which are a special class of generalised Reedy categories. For an augmentation category, we prove the existence of a closed Quillen model structure on the presheaf category which is compatible with the Kan-Quillen model structure on simplicial sets. Moreover, we use the concept of augmented hypercovers to define a local model structure on the category of augmented presheaves. We prove that crossed simplicial groups, and the planar rooted tree category are examples of augmentation categories. Finally, we introduce a method for generating new examples from old via a categorical pushout construction.
We have examined the deformation of a generic non-Abelian gauge theory obtained by replacing its Lie group by the corresponding quantum group. This deformed gauge theory has more degrees of freedom than the theory from which it is derived. By going over from point particles in the standard theory to solitonic particles in the deformed theory, it is proposed to interpret the new degrees of fredom as descriptive of a non-locality of the deformed theory. It also turns out that the original Lie algebra gets replaced by two dual algebras, one of which lies close to and approaches the original Lie algebra in a correspondence limit, while the second algebra is new and disappears in this same correspondence limit. The exotic field particles associated with the second algebra can be interpreted as quark-like constituents of the solitons, which are themselves described as point particles in the first algebra. These ideas are explored for q-deformed SU(2) and $GL_q(3)$.
The stellar initial mass function (IMF) seems to be variable and not universal, as argued in the literature in the last three decades. Several relations among the low-mass end of the IMF slope and other stellar population, photometric or kinematic parameters of massive early-type galaxies (ETGs) have been proposed, but a consolidated agreement on a factual cause of the observed variations has not been reached yet. We investigate the relations between the IMF and other stellar population parameters in NGC 3311, the central galaxy of the Hydra I cluster. NGC 3311 is characterized by old and metal-rich stars, like other massive ETGs, but has unusual increasing stellar velocity dispersion and [$\alpha/$Fe] profiles. We use spatially resolved MUSE observations to obtain stellar population properties using Bayesian full-spectrum fitting in the central part of NGC 3311 to compare the IMF slope against other stellar parameters with the goal of assessing their relations/dependencies. For NGC 3311, we unambiguously invalidate the previously observed direct correlation between the IMF slope and the local stellar velocity dispersion, confirming some doubts already raised in the literature. This relation may arise as a spatial coincidence only, between the region with the largest stellar velocity dispersion, with that where the oldest, $\textit{in situ}$ population is found and dominates. We also show robust evidence that the proposed IMF-metallicity relation is contaminated by the degeneracy between these two parameters. The tightest correlations we found are those between stellar age and IMF and between galactocentric radius and IMF. The variation of the IMF is not due to kinematical, dynamical, or global properties in NGC 3311. We speculate that IMF might be dwarf-dominated in the "red-nuggets" formed at high redshifts that ended up being the central cores of today's giant ellipticals. [Abridged]
A macroscopic single crystal of $\gamma_{\rm II}$-Li\(_2\)FeSiO\(_4\) has been grown by means of the high-pressure optical floating-zone technique. Static magnetic susceptibility $\chi$ implies that the tetrahedrally-coordinated Fe$^{2+}$ ions are in the high-spin, $S=2$, state. While a sharp decrease in $\chi$ implies long-range antiferromagnetic order below \tn\ = 17.0(5)~K, the presence of a broad maximum at $T_{\rm m} = 28$~K suggests quasi-low-dimensional magnetism. Applying magnetic fields along the easy magnetic $a$-axis yields additional contributions to the susceptibility $\partial M/\partial B$ and magnetostriction for $B > 7$~T, and an anomaly at $B\approx 14.8$~T.
We present a circuit model to describe the electron transport through a domain wall in a ferromagnetic nanowire. The domain wall is treated as a coherent 4-terminal device with incoming and outgoing channels of spin up and down and the spin-dependent scattering in the vicinity of the wall is modelled using classical resistances. We derive the conductance of the circuit in terms of general conductance parameters for a domain wall. We then calculate these conductance parameters for the case of ballistic transport through the domain wall, and obtain a simple formula for the domain wall magnetoresistance which gives a result consistent with recent experiments. The spin transfer torque exerted on a domain wall by a spin-polarized current is calculated using the circuit model and an estimate of the speed of the resulting wall motion is made.
Let $m$ be a square-free positive integer, $m\equiv 2,3 \; (\bmod \; 4)$. We show that the number field $K=Q(i,\sqrt[4]{m})$ is non-monogene, that is it does not admit any power integral bases of type $\{1,\alpha,\ldots,\alpha^7\}$. In this infinite parametric family of Galois octic fields we construct an integral basis and show non-monogenity using only congruence considerations.   Our method yields a new approach to consider monogenity or to prove non-monogenity in algebraic number fields. It is well applicable in parametric families of number fields. We calculate the index of elements as polynomials depending on the parameter, factor these polynomials and consider systems of congruences according to the factors.
We present a theoretical study of the anisotropy of the spin relaxation and decoherence in typical quantum wells with an arbitrary magnetic field. In such systems, the orientation of the magnetic field relative to the main crystallographic directions is crucial, owing to the lack of spin-rotation symmetry. For typical high mobility samples, relaxation anisotropies in the motional narrowing limit owing to the interplay of Rashba and Dresselhaus spin orbit coupling are calculated. We also include the effect of the cubic-in-momentum terms. Although commonly ignored in literature, the latter were experimentally evidenced by the observation of strong anisotropy in spin decoherence measurements by different experimental groups and has long remained unexplained.
The effects of Hubbard-type on-site interactions on the BHZ model is studied in this paper for model parameters appropriate for the HgTe/CdTe quantum well. Within a simple mean field theory we search for plausible magnetic instabilities in the model and find that the ground state becomes {\em ferromagnetic} when the interaction strength between electrons in hole orbital is strong enough. The result can be understood by an approximate mapping of the Hubbard-BHZ model to the one band Hubbard model. The same mapping suggests that the magnetic and/or other ordered phases are more likely to occur in large gap topological insulators whose occupations are close to 1/2 for both electron and hole orbital.
Sixteen years of observations of black hole transients with the Rossi X-ray Timing Explorer, complemented by other X-ray observatories and ground-based optical/infrared/radio telescopes have given us a clear view of the complex phenomenology associated with their bright outbursts. This has led to the definition of a small number of spectral/timing states which are separated by marked transitions in observables. The association of these states and their transitions to changes in the radio emission from relativistic radio jets completes the picture and have led to the study of the connection between accretion and ejection. A good number of fundamental questions are still unanswered, but the existing picture provides a good framework on which to base theoretical studies. We discuss the current observational standpoint, with emphasis onto the spectral and timing evolution during outbursts, as well as the prospects for future missions such as ASTROSAT (2012) and LOFT (>2020 if selected).
We lay a theoretical foundation in the observation of gravitational waves (GWs) by electromagnetic waves (EMWs) performing a full electromagnetic analysis without any optical approximation. For that, the perturbation of plane EMWs is obtained by solving the perturbed Maxwell equation with GWs in the Minkowski background spacetime. In a GW detector using the EMWs, we propose to measure the electromagnetic invariants that are independent of the motion of the EMW receiver and whose perturbations are gauge-invariant. Imposing a physical boundary condition at EMW emitters, we have analytic results for the perturbations of invariants that can be measured in the EMW receiver. Finally, we show antenna patterns of the detector with monochromatic plane GWs and EMWs.
We review some results recently obtained for the conformal field theories based on the affine Lie superalgebra osp(1|2). In particular, we study the representation theory of the osp(1|2) current algebras and their character formulas. By means of a free field representation of the conformal blocks, we obtain the structure constants and the fusion rules of the model. (Lecture delivered at the CERN-Santiago de Compostela-La Plata Meeting, "Trends in Theoretical Physics", La Plata, Argentina, April-May 1997).
We investigate the physical properties of structures seen in channel map observations of 21-cm neutral hydrogen (HI) emission. HI intensity maps display prominent linear structures that are well aligned with the ambient magnetic field in the diffuse interstellar medium (ISM). Some literature hold that these structures are "velocity caustics", fluctuations imprinted by the turbulent velocity field, and are not three-dimensional density structures in the ISM. We test this hypothesis by stacking probes of the density field -- broadband far infrared (FIR) emission and the integrated HI column density (NHI) -- at the locations of linear HI intensity structures. We find that the HI intensity features are real density structures and not velocity caustics. We generalize the investigation to all small-scale structure in HI channel maps, and analyze this correlation as a function of velocity channel width, finding no measurable contribution from velocity caustics to the HI channel map emission. Further, we find that small-scale HI channel maps structures have elevated FIR/NHI, implying that this emission originates from a colder, denser phase of the ISM than the surrounding material. The data are consistent with a multi-phase diffuse ISM in which small-scale structures in narrow HI channel maps are preferentially cold neutral medium (CNM) that is anisotropically distributed and aligned with the local magnetic field. The shallow spatial power spectrum (SPS) of narrow HI channels is often attributed to velocity caustics. We conjecture instead that the small-scale structure and narrow linewidths typical of CNM explain the observed relationship between the SPS and channel width.
By using quantitative information about the radiation diffuse-scattering intensity of the disordered f.c.c. substitutional alloy the Fourier component of mixing energies of atoms may be estimated. We have to use the measurement data of the diffuse-scattering intensities at the corresponding reciprocal-space points k of the disordered phase and then determine the parameter w(k). The statistical thermodynamics of the nonideal solid solution is determined by these energy parameters {w(k)}. Therefore, one can obtain the configuration free energy of an alloy, F = U - TS (U - internal energy, S - entropy), and then determine its fundamental thermodynamic characteristics, including not only its phase diagram, but also the concentration-dependent order-disorder transformation temperature, temperature and concentration long-range order parameter dependences, chemical activity, heat capacity etc. Some thermodynamic properties are calculated within the framework of the statistical-thermodynamic approach for f.c.c.-Ni-Fe alloy. The diffuse-scattering intensity values are taken from data in the literature.
A quantum system subject to external fields is said to be controllable if these fields can be adjusted to guide the state vector to a desired destination in the state space of the system. Fundamental results on controllability are reviewed against the background of recent ideas and advances in two seemingly disparate endeavors: (i) laser control of chemical reactions and (ii) quantum computation. Using Lie-algebraic methods, sufficient conditions have been derived for global controllability on a finite-dimensional manifold of an infinite-dimensional Hilbert space, in the case that the Hamiltonian and control operators, possibly unbounded, possess a common dense domain of analytic vectors. Some simple examples are presented. A synergism between quantum control and quantum computation is creating a host of exciting new opportunities for both activities. The impact of these developments on computational many-body theory could be profound.
We develop a continuum model for the dynamics of grain boundaries in three dimensions that incorporates the motion and reaction of the constituent dislocations. The continuum model is based on a simple representation of densities of curved dislocations on the grain boundary. Illposedness due to nonconvexity of the total energy is fixed by a numerical treatment based on a projection method that maintains the connectivity of the constituent dislocations. An efficient simulation method is developed, in which the critical but computationally expensive long-range interaction of dislocations is replaced by another projection formulation that maintains the constraint of equilibrium of the dislocation structure described by the Frank's formula. This continuum model is able to describe the grain boundary motion and grain rotation due to both coupling and sliding effects, to which the classical motion by mean curvature model does not apply. Comparisons with atomistic simulation results show that our continuum model is able to give excellent predictions of evolutions of low angle grain boundaries and their dislocation structures.
Symmetric varieties are normal equivariant open embeddings of symmetric homogeneous spaces and they are interesting examples of spherical varieties. The principal goal of this article is to study the rigidity under K\"{a}hler deformations of smooth projective symmetric varieties with Picard number one.
While predicting robot grasps with parallel jaw grippers have been well studied and widely applied in robot manipulation tasks, the study on natural human grasp generation with a multi-finger hand remains a very challenging problem. In this paper, we propose to generate human grasps given a 3D object in the world. Our key observation is that it is crucial to model the consistency between the hand contact points and object contact regions. That is, we encourage the prior hand contact points to be close to the object surface and the object common contact regions to be touched by the hand at the same time. Based on the hand-object contact consistency, we design novel objectives in training the human grasp generation model and also a new self-supervised task which allows the grasp generation network to be adjusted even during test time. Our experiments show significant improvement in human grasp generation over state-of-the-art approaches by a large margin. More interestingly, by optimizing the model during test time with the self-supervised task, it helps achieve larger gain on unseen and out-of-domain objects. Project page: https://hwjiang1510.github.io/GraspTTA/