ShantanuT01/DACTYL-Pretraining huggingface dataset:
We consider the CNOT quantum gate as a physical action, i.e. as unitary in time evolution of the two-qubit system. This points to the modeling of the interaction Hamiltonian of the two-qubit system which would correspond to the CNOT transformation; the analysis naturally generalizes to the Toffoli gate. Despite nonuniqueness of the model of the interaction Hamiltonian, the analysis distinguishes that the interaction Hamiltonian does not posses any global (rotational) symmetry. This forces us to conclude that the direct (non-mediated) interaction in the two-qubit system does not suffice for implementing the CNOT gate. I.e., so as to be able succesfully to implement the CNOT transformation, a mediator (i.e. an external physical system interacting with both of the qubits) is required.
It is well known that the study of $SU(n+1)$ Toda systems is important not only to Chern-Simons models in Physics, but also to the understanding of holomorphic curves, harmonic sequences or harmonic maps from Riemann surfaces to $\mathbb C\mathbb P^n$. One major goal in the study of $SU(n+1)$ Toda system on Riemann surfaces is to completely understand the asymptotic behavior of fully bubbling solutions. In this article we use a unified approach to study fully bubbling solutions to general $SU(n+1)$ Toda systems and we prove three major sharp estimates important for constructing bubbling solutions: the closeness of blowup solutions to entire solutions, the location of blowup points and a $\partial_z^2$ condition.
We report the dispersion measurements, using angle-resolved reflection electron-energy-loss-spectroscopy (AREELS), on two-dimensional (2D) plasmons in single and multilayer graphene which couple strongly to surface optical phonon (FK phonon) modes of silicon carbide substrate. The coupled modes show discrete dispersion behaviors in the single and bilayer graphene. With increasing graphene layers on SiC(0001), a transition from plasmon-like dispersion to phonon-like dispersion is observed. For plasmon-like modes, the dispersion is strongly damped by electron-hole pair excitations at entering single-particle continuum, while phonon-like mode is undamped. In the region free of coupling, the graphene 2D plasmon exhibits acoustic behavior with linear dispersion with slope and damping determined by the Fermi surface topology.
I illustrate the role of infrared renormalons in computing inclusive B-decay spectra. I explain the relation between the leading ambiguity in the definition of Sudakov form factor \sim \exp(N\Lambda/M) and that of the pole mass, and show how these ambiguities cancel out between the perturbative and non-perturbative components of the b-quark distribution in the meson.
In this paper, we systematically studied blue stragglers produced from primordial binary evolution via a binary population synthesis approach, and examined their contribution to the integrated spectral energy distributions of the host clusters. The mass transfer efficiency, $\beta$, is an important parameter for the final products (then blue stragglers) after mass transfer, and it is set to be 0.5 except for case A binary evolution. The study shows that primordial binary evolution may produce blue stragglers at any given times and that different evolutionary channels are corresponding for blue stragglers in different visual magnitude regions (in V band) on the colour-magnitude diagram (CMD) of clusters. The specific frequency of blue stragglers obtained from primordial binary evolution decreases with time first, and then increases again when the age is larger than 10Gyr, while that from angular momentum loss induced by magnetic braking in low-mass binaries increases with time and exceeds that of primordial binary evolution in a population older than 3 Gyr. Meanwhile, blue stragglers resulting from primordial binary evolution are dominant contributors to the ISEDs in ultraviolet and blue bands in a population between 0.3 and 2.0 Gyr. The value of $\beta$ significantly affects on the final results. For old open clusters, the assumption of $\beta =1$ when the primary is in HG at the onset of mass transfer matches the observations better than that of $\beta =0.5$ from the locations of BSs on the CMDs. Our study also shows that, for most Galactic open clusters, the specific frequency of blue stragglers obtained from our simulations is lower than that of observations, which is puzzling.
Equilibrium statistics of Hamiltonian systems is correctly described by the microcanonical ensemble. Classically this is the manifold of all points in the N-body phase space with the given total energy. Due to Boltzmann-Planck's principle, e^S=tr(\delta(E-H)), its geometrical size is related to the entropy S(E,N,V,...). This definition does not invoke any information theory, no thermodynamic limit, no extensivity, and no homogeneity assumption. Therefore, it describes the equilibrium statistics of extensive as well of non-extensive systems. Due to this fact it is the fundamental definition of any classical equilibrium statistics. It addresses nuclei and astrophysical objects as well. S(E,N,V,...) is multiply differentiable everywhere, even at phase-transitions. All kind of phase transitions can be distinguished harply and uniquely for even small systems. What is even more important, in contrast to the canonical theory, also the region of phase-space which corresponds to phase-separation is accessible, where the most interesting phenomena occur. No deformed q-entropy is needed for equilibrium. Boltzmann-Planck is the only appropriate statistics independent of whether the system is small or large, whether the system is ruled by short or long range forces.
We introduce DexYCB, a new dataset for capturing hand grasping of objects. We first compare DexYCB with a related one through cross-dataset evaluation. We then present a thorough benchmark of state-of-the-art approaches on three relevant tasks: 2D object and keypoint detection, 6D object pose estimation, and 3D hand pose estimation. Finally, we evaluate a new robotics-relevant task: generating safe robot grasps in human-to-robot object handover. Dataset and code are available at https://dex-ycb.github.io.
The ground state properties of even mass Cr and Fe isotopes are studied using the generalized hybrid derivative coupling model. The energy surface of each isotope is plotted as a function of the mass quadrupole moment. The neutron numbers N=20 and N=40 are seen to remain magic numbers but N= 28 and 50 are predicted to be non-magic. The neutron number N=70 turns out to be a magic number according to the present calculation. In all the isotopes studied the calculated binding energy values are less than those obtained from experiment while the deformation is in better agreement.
Following recent studies of Ford, we suggest -- in the framework of general relativity -- an inflationary cosmological model with the self-interacting spinning matter. A generalization of the standard fluid model is discussed and estimates of the physical parameters of the evolution are given.
Two questions are investigated by looking successively at classical mechanics, special relativity, and relativistic gravity: first, how is space related with spacetime? The proposed answer is that each given reference fluid, that is a congruence of reference trajectories, defines a physical space. The points of that space are formally defined to be the world lines of the congruence. That space can be endowed with a natural structure of 3-D differentiable manifold, thus giving rise to a simple notion of spatial tensor --- namely, a tensor on the space manifold. The second question is: does the geometric structure of the spacetime determine the physics, in particular, does it determine its relativistic or preferred-frame character? We find that it does not, for different physics (either relativistic or not) may be defined on the same spacetime structure --- and also, the same physics can be implemented on different spacetime structures.   Keywords: Affine space; classical mechanics; special relativity; relativistic gravity; reference fluid.
We explore parameterizations by radicals of low genera algebraic curves. We prove that for $q$ a prime power that is large enough and prime to $6$, a fixed positive proportion of all genus 2 curves over the field with $q$ elements can be parameterized by $3$-radicals. This results in the existence of a deterministic encoding into these curves when $q$ is congruent to $2$ modulo $3$. We extend this construction to parameterizations by $\ell$-radicals for small odd integers $\ell$, and make it explicit for $\ell=5$.
We have detected the synchronous enhancement of Ca II H & K emission with the short-period planetary orbit in HD 179949. High-resolution spectra taken on three observing runs extending more than a year show the enhancement coincides with phi ~ 0 (the sub-planetary point) of the 3.093-day orbit with the effect persisting for more than 100 orbits. The synchronous enhancement is consistent with planet-induced chromospheric heating by magnetic rather than tidal interaction. Something which can only be confirmed by further observations. Independent observations are needed to determine whether the stellar rotation is sychronous with the planet's orbit. Of the five 51 Peg-type systems monitored, HD 179949 shows the greatest chromospheric H & K activity. Three others show significant nightly variations but the lack of any phase coherence prevents us saying whether the activity is induced by the planet. Our two standards, tau Ceti and the Sun, show no such nightly variations.
The density-matrix renormalization group (DMRG) applied to transfer matrices allows it to calculate static as well as dynamical properties of one-dimensional quantum systems at finite temperature in the thermodynamic limit. To this end the quantum system is mapped onto a two-dimensional classical system by a Trotter-Suzuki decomposition. Here we discuss two different mappings: The standard mapping onto a two-dimensional lattice with checkerboard structure as well as an alternative mapping introduced by two of us. For the classical system an appropriate quantum transfer matrix is defined which is then treated using a DMRG scheme. As applications, the calculation of thermodynamic properties for a spin-1/2 Heisenberg chain in a staggered magnetic field and the calculation of boundary contributions for open spin chains are discussed. Finally, we show how to obtain real time dynamics from a classical system with complex Boltzmann weights and present results for the autocorrelation function of the XXZ-chain.
We investigate the observational signatures of quantum cosmology in the Cosmic Microwave Background data provided by Planck collaboration. We apply the warm inflationary paradigm with a tachyon scalar field to the loop quantum cosmology. In this context, we first provide the basic cosmological functions in terms of the tachyon field. We then obtain the slow-roll parameters and the power spectrum of scalar and tensor fluctuations respectively. Finally, we study the performance of various warm inflationary scenarios against the latest Planck data and we find a family of models which are in agreement with the observations.
The argument used, in a recent letter to Nature (Nature 130 vol 404, 2000) to arrive at the `quantum-no-deleting principle' is erroneous. It is pointed out here that there may not be anything like such a principle. In any case, the claims made in the letter are beyond its working premise.
Using the stochastic thermodynamics, we determine the entropy production and the dynamic heat capacity of systems subject to a sinusoidally time dependent temperature, in which case the systems are permanently out of thermodynamic equilibrium inducing a continuous generation of entropy. The systems evolve in time according to a Fokker-Planck or to a Fokker-Planck-Kramers equation. Solutions of these equations, for the case of harmonic forces, are found exactly from which the heat flux, the production of entropy and the dynamic heat capacity are obtained as functions of the frequency of the temperature modulation. These last two quantities are shown to be related to the real an imaginary parts of the complex heat capacity.
The ellipsoidal BGK model (ES-BGK) is a generalized version of the BGK model of the Boltzmann equation designed to yield the correct Prandtl number in the Navier-Stokes limit. In this paper, we make two observations on the entropy production functional of the ES-BGK model. First, we show that the Cercignani type estimate holds for the ES-BGK model in the whole range of parameter $-1/2<\nu<1$. Secondly, we observe that the ellipsoidal relaxation operator satisfies an unexpected sign-definite property. Some implications of these observations are also discussed.
We aim to obtain a measure of the curvature of time-resolved spectra that can be compared directly to theory. This tests the ability of models such as synchrotron emission to explain the peaks or breaks of GBM prompt emission spectra. We take the burst sample from the official Fermi GBM GRB time-resolved spectral catalog. We re-fit all spectra with a measured peak or break energy in the catalog best-fit models in various energy ranges, which cover the curvature around the spectral peak or break, resulting in a total of 1,113 spectra being analysed. We compute the sharpness angles under the peak or break of the triangle constructed under the model fit curves and compare to the values obtained from various representative emission models: blackbody, single-electron synchrotron, synchrotron emission from a Maxwellian or power-law electron distribution. We find that 35% of the time-resolved spectra are inconsistent with the single-electron synchrotron function, and 91% are inconsistent with the Maxwellian synchrotron function. The single temperature, single emission time and location blackbody function is found to be sharper than all the spectra. No general evolutionary trend of the sharpness angle is observed, neither per burst nor for the whole population. It is found that the limiting case, a single temperature Maxwellian synchrotron function, can only contribute up to $58^{+23}_{-18}$% of the peak flux. Our results show that even the sharpest but non-realistic case, the single-electron synchrotron function, cannot explain a large fraction of the observed GRB prompt spectra. Because of the fact that any combination of physically possible synchrotron spectra added together will always further broaden the spectrum, emission mechanisms other than optically thin synchrotron radiation are likely required in a full explanation of the spectral peaks or breaks of the GRB prompt emission phase.
The paper considers a chemostat model describing an activated sludge process in wastewater treatment. The model is assumed to be subject to environment noise in terms of both white noise and color noise. The paper fully characterizes the asymptotic behavior of the model that is a hybrid switching diffusion. We show that the long-term properties of the system can be classified using a value $\lambda$. More precisely, if $\lambda\leq 0$, the bacteria in the sewage will die out, which means that the process does not operate. If $\lambda>0$, the system has an invariant probability measure to which the transition probability of the solution process converges exponentially fast. One of the distinctive contributions of this paper is that the critical case $\lambda=0$ is considered. Numerical examples are given to illustrate our results.
Using the form factors obtained from holographic AdS/QCD and QCD sum rules, we predict the differential branching ratio and longitudinal polarization fraction for the rare $B\to K^* \nu \bar\nu$ decay. This is an interesting decay channel as it does not suffer from hadronic uncertainties beyond the form factors. We point out that the future measurement of the $B\to K^* \nu \bar\nu$ with around 30% accuracy can discriminate between the two models.
Since 2003, the Spitzer Space Telescope has provided groundbreaking views of Galactic star formation in bands from 3.6 past 24 microns. During the cryogenic mission (the first 5.5 years), variability of young stars at these bands was noted, although typically with just a few epochs of observation. The cryogen ran out in 2009, and we are now in the warm mission era where the shortest two bands (3.6 and 4.5 microns) continue to function essentially as before. The phenomenal sensitivity and stability of Spitzer at these bands has enabled several dedicated monitoring programs studying the variability of young stars at timescales from minutes to years. The largest of these programs is YSOVAR (Stauffer et al.), but there are several smaller programs as well. With at least as many as 2200 young star light curves likely to come out of this, these programs as a whole enable more detailed study of the young star-disk interaction in the infrared for a wider range of ages and masses than has ever been accomplished before. Early results suggest a wide variety of sources of variability, including dust clouds in the disk, disk warps, star spots, and accretion. This contribution will review some of the most recent results from these programs.
We assemble an unbiased sample of 29 galaxies with [O II] $\lambda 3727$ and/or [O III] $\lambda 5007$ detections at $z < 0.15$ from the Hobby-Eberly Telescope Dark Energy Experiment (HETDEX) Pilot Survey (HPS). HPS finds galaxies without pre-selection based on their detected emission lines via integral field spectroscopy. Sixteen of these objects were followed up with the second-generation, low resolution spectrograph (LRS2) on the upgraded Hobby-Eberly Telescope. Oxygen abundances were then derived via strong emission lines using a Bayesian approach. We find most of the galaxies fall along the mass-metallicity relation derived from photometrically selected star forming galaxies in the Sloan Digital Sky Survey (SDSS). However, two of these galaxies have low metallicity (similar to the very rare green pea galaxies in mass-metallicity space). The star formation rates of this sample fall in an intermediate space between the SDSS star forming main sequence and the extreme green pea galaxies. We conclude that spectroscopic selection fills part of the mass-metallicity-SFR phase space that is missed in photometric surveys with pre-selection like SDSS, i.e., we find galaxies that are actively forming stars but are faint in continuum. We use the results of this pilot investigation to make predictions for the upcoming unbiased, large spectroscopic sample of local line emitters from HETDEX. With the larger HETDEX survey we will determine if galaxies selected spectroscopically without continuum brightness pre-selection have metallicities that fall on a continuum that bridges typical star forming and rarer, more extreme systems like green peas.
In this paper, we review the current status of the phenomenological study of quarkonium production in high energy collisions. After a brief introduction of several important models and effective field theories for quarkonium production, we discuss the comparisons between theoretical predictions and experimental measurements.
The large surface-to-volume ratio in atomically thin 2D materials allows to efficiently tune their properties through modifications of their environment. Artificial stacking of two monolayers into a bilayer leads to an overlap of layer-localized wave functions giving rise to a twist angle-dependent hybridization of excitonic states. In this joint theory-experiment study, we demonstrate the impact of interlayer hybridization on bright and momentum-dark excitons in twisted WSe$_2$ bilayers. In particular, we show that the strong hybridization of electrons at the $\Lambda$ point leads to a drastic redshift of the momentum-dark K-$\Lambda$ exciton, accompanied by the emergence of flat moir\'e exciton bands at small twist angles. We directly compare theoretically predicted and experimentally measured optical spectra allowing us to identify photoluminescence signals stemming from phonon-assisted recombination of layer-hybridized dark excitons. Moreover, we predict the emergence of additional spectral features resulting from the moir\'e potential of the twisted bilayer lattice.
An observer surrounded by sufficiently small spherical light sources at a fixed distance will see a pattern of elliptical images distributed over the sky, owing to the distortion effect (shearing effect) of the spacetime geometry upon light bundles. In lowest non-trivial order with respect to the distance, this pattern is completely determined by the conformal curvature tensor (Weyl tensor) at the observation event. In this paper we derive formulas that allow to calculate these distortion patterns in terms of the Newman-Penrose formalism. Then we represent the distortion patterns graphically for all Petrov types, and we discuss their dependence on the velocity of the observer.
We give sharp conditions for the large time asymptotic simplification of aggregation-diffusion equations with linear diffusion. As soon as the interaction potential is bounded and its first and second derivatives decay fast enough at infinity, then the linear diffusion overcomes its effect, either attractive or repulsive, for large times independently of the initial data, and solutions behave like the fundamental solution of the heat equation with some rate. The potential $W(x) \sim \log |x|$ for $|x| \gg 1$ appears as the natural limiting case when the intermediate asymptotics change. In order to obtain such a result, we produce uniform-in-time estimates in a suitable rescaled change of variables for the entropy, the second moment, Sobolev norms and the $C^\alpha$ regularity with a novel approach for this family of equations using modulus of continuity techniques.
In this note I discuss some aspects of a formulation of quantum mechanics based entirely on the Jordan algebra of observables. After reviewing some facts of the formulation in the \CS -approach I present a Jordan-algebraic Hilbert space construction (inspired by the usual GNS-construction), thereby obtaining a real Hilbert space and a (Jordan-) representation of the algebra of observables on this space. Taking the usual case as a guideline I subsequently derive a Schr\"odinger equation on this Hilbert space.
Violent nuclear collisions are open systems which require a non-equilibrium description when the process should be followed from the first instants. The heated system produced in the collision, can no more be treated within an independent-particle picture and additional correlations should be taken into account: they rely to in-medium dissipation and phase-space fluctuations. Their interplay with the one-body collective behaviour activates the transport dynamics: large-amplitude fluctuations and bifurcations in a variety of mechanisms appear, from fusion to neck formation till eventually freezing out the system into several intermediate-mass clusters. Starting from fundamental concepts tested on nuclear matter, a microscopic description is built up to address violent processes occurring in heavy-ion collisions at Fermi energies and in spallation reactions, and it is applied to experimental observables.
In the presence of a D-brane a string theory develops a new subsector. We show that for curved D-branes the corresponding sector is a (partially twisted) topological field theory. We use this result to compute the degeneracy of 2-branes wrapped around $K3$ cycles as well as 3-branes wrapped around CY threefold vanishing 3-cycles. In both cases we find the degeneracy is in accord with expectation. The counting of BPS states of a gas of 0-branes in the presence of a 4-brane in $K3$ is considered and it is noted that the effective 0-brane charge is shifted by 1, due to a quantum correction. This is in accord with string duality and the fact that left-moving ground state energy of heterotic string starts at $-1$. We also show that all the three different topological twistings of four dimensional $N=4$ Yang-Mills theory do arise from curved three-branes embedded in different spaces (Calabi-Yau manifolds and manifolds with exceptional holonomy groups).