Both, the dilemma to find a quantum field theory consistent with Einstein’s law of relativity and the problem to describe existing particles as bound states of matter has been solved by calculating bound state matrix elements from a dual fermion-boson Lagrangian. In this formalism, the fermion binding energies are compensated by boson energies, indicating that particles can be generated out of the vacuum. This yields quantitative solutions for various mesons ω (0.78 GeV) - Υ (9.46 GeV) and all leptons e, μ and τ, with uncertainties in the extracted properties of less than 1‰. For transparency, a Web-page with the address htpps://h2909473.stratoserver.net has been constructed, where all calculations can be run on line and also the underlying fortran source code can be inspected.
Let X=Σ_(i=1)^(n)a_(i)ξ_(i)be a Rademacher sum with Var(X)=1 and Z be a standard normal random variable.This paper concerns the upper bound of|P(X≤x)−P(Z≤x)|for any x∈R.Using the symmetric properties and R software,this paper gets the following improved Berry-Esseen type bound under some conditions,|P(X≤x)−P(Z≤x)|≤P(Z∈(0,a1)),∀x∈R,which is one of the modified conjecture proposed by Nathan K.and Ohad K.
The bound states around a vortex in anisotropic superconductors is a longstanding yet important issue.In this work,we develop a variational theory on the basis of the Andreev approximation to obtain the energy levels and wave functions of the low-energy quantized bound states in superconductors with anisotropic pairing on arbitrary Fermi surface.In the case of circular Fermi surface,the effective Schr¨odinger equation yielding the bound state energies gets back to the theory proposed by Volovik and Kopnin many years ago.Our generalization here enables us to prove the equidistant energy spectrum inside a vortex in a broader class of superconductors.More importantly,we are now able to obtain the wave functions of these bound states by projecting the quasiclassical wave function on the eigenmodes of the effective Schr¨odinger equation,going beyond the quasiclassical Eilenberger results,which,as we find,are sensitive to the scattering rate.For the case of isotropic Fermi surface,the spatial profile of the low-energy local density of states is dominated near the vortex center and elongates along the gap antinode directions,in addition to the ubiquitous Friedel oscillation arising from the quantum inteference neglected in the Eilenberger theory.Moreover,as a consequence of the pairing anisotropy,the quantized wave functions develop a peculiar distribution of winding number,which reduces stepwise towards the vortex center.Our work provides a flexible way to study the vortex bound states in the future.
Optical bound states in the continuum(BICs)have recently stimulated a research boom,accompanied by demonstrations of abundant exotic phenomena and applications.With ultrahigh quality(Q)factors,optical BICs have powerful abilities to trap light in optical structures from the continuum of propagation waves in free space.Besides the high Q factors enabled by the confined properties,many hidden topological characteristics were discovered in optical BICs.Especially in periodic structures with well-defined wave vectors,optical BICs were discovered to carry topological charges in momentum space,underlying many unique physical properties.Both high Q factors and topological vortex configurations in momentum space enabled by BICs bring new degrees of freedom to modulate light.BICs have enabled many novel discoveries in light-matter interactions and spin-orbit interactions of light,and BIC applications in lasing and sensing have also been well explored with many advantages.In this paper,we review recent developments of optical BICs in periodic structures,including the physical mechanisms of BICs,explored effects enabled by BICs,and applications of BICs.In the outlook part,we provide a perspective on future developments for BICs.
Holevo bound plays an important role in quantum metrology as it sets the ultimate limit for multi-parameter estimations,which can be asymptotically achieved.Except for some trivial cases,the Holevo bound is implicitly defined and formulated with the help of weight matrices.Here we report the first instance of an intrinsic Holevo bound,namely,without any reference to weight matrices,in a nontrivial case.Specifically,we prove that the Holevo bound for estimating two parameters of a qubit is equivalent to the joint constraint imposed by two quantum Cramér–Rao bounds corresponding to symmetric and right logarithmic derivatives.This weightless form of Holevo bound enables us to determine the precise range of independent entries of the mean-square error matrix,i.e.,two variances and one covariance that quantify the precisions of the estimation,as illustrated by different estimation models.Our result sheds some new light on the relations between the Holevo bound and quantum Cramer–Rao bounds.Possible generalizations are discussed.
Naked singularities form during the gravitational collapse of inhomogeneous matter clouds.The final nature of the singularity depends on the initial conditions of the matter properties and types of matter profiles.These naked singularities can also be divided into two types:null-like and timelike singularities.The spacelike singularity of the Schwarzschild black hole can be distinguished from the null and timelike naked singularity spacetimes.In light of this,we investigate the precession of timelike bound orbits in the null naked singularity spacetime,as well as tidal force effects and geodesic deviation features.As a result,we find that the orbital precession of the timelike bound orbits in null naked singularity spacetime could be distinguished from the Schwarzschild precession case.The radial component of the tidal force has an intriguing profile,whereas the angular component has a profile that is comparable to that of a Schwarzschild black hole scenario.The geodesic deviation equation is then solved numerically,yielding results that resemble Schwarzschild black holes.These characteristic features can then be used to discern among these singularities.
It was conjectured by Escobar(J Funct Anal 165:101–116,1999)that for an ndimensional(n≥3)smooth compact Riemannian manifold with boundary,which has nonnegative Ricci curvature and boundary principal curvatures bounded below by c>0,the first nonzero Steklov eigenvalue is greater than or equal to c with equality holding only on isometrically Euclidean balls with radius 1/c.In this paper,we confirm this conjecture in the case of nonnegative sectional curvature.The proof is based on a combination of Qiu-Xia’s weighted Reilly-type formula with a special choice of the weight function depending on the distance function to the boundary,as well as a generalized Pohozaev-type identity.
We propose the revised description of a baryon as a composition of bound stated sea-quarks and unbound stated sea-quarks from the previously proposed description of baryon as a meson pair. The purpose of this article is to show the following two possibilities. The first one shows the qualitative explanation to support our description of a nucleon as a pair of pions and the second one is that it gives an explanation of ALICE results that the pTdependence of Λc+/D0ratio is 0.5. Each isospin group is constructed of both baryons and antibaryons. This way of construction is consistent with that of mesons. The results obtained are listed in tables. This shows that the generalized Gell-Mann-Nishijima relation equation holds under the condition that the baryon number is 0.
Quinoa is a good source of phenolics,which both exist as free and bound forms.In order to mark clear the characteristic free and bound phenolics in different quinoa samples,in this study,characteristic free and bound phenolics in three colored quinoas including WQ(white quinoa),RQ(red quinoa)and BQ(black quinoa)were investigated.Result showed a total of 14 phenolics both acted as free and bound form were analyzed in three colored quinoas(WQ,RQ and BQ).Gallic acid,vanillic acid,epicatechin,p-coumaric acid and quercetin existed both as free and bound forms were common phenolics in quinoas.The highest total free phenolics(238.10 mg/kg)and bound phenolics(3377.75 mg/kg)were presented in WQ and RQ,respectively.It indicated WQ and RQ were respectively good source of free and bound phenolics.Moreover,characteristic free and bound phenolics in three colored quinoas could be well analyzed by principal component analysis(PCA),indicating it was an effective and reliable method in distinguishing three colored quinoas based on their characteristic free and bound phenolics,respectively.
