The Effective Gluon Propagator in the Global Color Symmetry Model

It is shown that the effective gluon propagator in the global color symmetry model can be calculated in the instanton dilute liquid approximation. The calculated effective gluon propagator is consistent with the general command on the qualitative features of the gluon propagator, i.e., (i) the gluon propagator is significantly enhanced at small space-like k², and (ii) for k² > 1.5 GeV² the perturbative results are quantitatively reliable.     

Quantum corrections from nonresonant WW scattering

An estimate is presented of the leading radiative corrections to low energy electroweak precision measurements from strong nonresonant WW scattering at the TeV energy scale. The estimate is based on a novel representation of nonresonant scattering in terms of the exchange of an effective scalar propagator with simple poles in the complex energy plane. The resulting corrections have the form of the corrections from the standard model Higgs boson with the mass set to the unitarity scale for strong WW scattering.     

Instantaneous Bethe-Salpeter Equation and Its Exact Solution

We present an approach to solve Bethe-Salpeter (BS) equations exactly without any approximation if the kernel of the BS equations exactly is instantaneous, and take positronium as an example to illustrate the general features of the exact solutions. The key step for the approach is from the BS equations to derive a set of coupled and well-determined integration equations in linear eigenvalue for the components of the BS wave functions equivalently, which may be solvable numerically under a controlled accuracy, even though there is no analytic solution. For positronium, the exact solutions precisely present corrections to those of the corresponding Schrödinger equation in order v¹ (v is the relative velocity) for eigenfunctions, in order v² for eigenvalues, and the mixing between S and D components in J^PC=1^-- states etc., quantitatively. Moreover, we also point out that there is a questionable step in some existent derivations for the instantaneous BS equations if one is pursuing the exact solutions. Finally, we emphasize that one should take the O(v) corrections emerging in the exact solutions into account accordingly if one is interested in the relativistic corrections for relevant problems to the bound states.     

Ab initio study of structural,electronic, and elastic properties of M<Subscript>2</Subscript>SbP (M = Ti,Zr, and Hf)

This study predicts the structural behaviour of selected M₂SbP compounds with the same structure as MAX phases. Zero pressure results of the lattice parameters, equilibrium volume, and the internal parameter Z_M are calculated with an error less than 3%. Band structure, total and partial density of states were calculated and show the metallic character of these phases. Moreover we observed strong hybridising states; M d–P p, and M d–Sb p. The pressure dependence of the volume, and the lattice parameters were studied. The stiffness of M–P, and M–Sb bonds was discussed in term of relative length change under hydrostatic pressure. Hf₂SbP present the highest bulk modulus and the unidirectional elastic modulus C₃₃ is slightly greater than C₁₁.     

双组分玻色-爱因斯坦凝聚体中亚稳态存在条件及其寿命

本文对双势阱中凝聚的冷原子通过约瑟夫森结隧穿时所形成的亚稳态进行研究.通过介观自旋算符建立了体系的精确量子相位模型,利用对量子自旋的势场描述给出了在两阱中振荡的原子之间相位差为时,即亚稳态时所要满足的物理条件,并用瞬子方法计算了该亚稳态存在的寿命.     

Matone's Relation ofN =2 Super Yang-Mills and Spectrum of Toda Chain

InN=2 super Yang-Mills theory, the Matone's relation relates instanton corrections of the prepotential to instanton corrections of scalar field condensation <
Trφ²>. This relation has been proved to hold for Omega deformed theories too, using localization method. In this paper, we first give a case study supporting the relation, which does not rely on the localization technique. Especially, we show that the magnetic expansion also satisfies a relation of Matone's type. Then we discuss implication of the relation for the spectrum of periodic Toda chain, in the context of recently proposed Nekrasov-Shatashvili scheme.     

Study of the stability of the fermionic instanton solutions by the scale index method

In the last years, there has been great interest to the formulation and application of wavelet transformation in variety of fields to investigate the characteristics of dynamical systems. Recently, a method based on the scalogram analysis of the continuous wavelet transform, the scale index has been proposed to measure aperiodicity and determine the transitions from aperiodic behaviour to periodic behaviour in nonlinear dynamical systems. In this work we test the scale index method by performing the analysis of the deterministic behaviour of the fermion-like two-dimensional Akdeniz–Smailagic instanton solution in Thirring Model. We show that the scale index method can also be considered to detect the periodic behaviours of the fermion-like instanton solutions.     

A conservative,thermodynamically consistent numerical approach for low Mach number combustion. Part I: Single-level integration

We present a numerical approach for low Mach number combustion that conserves both mass and energy while remaining on the equation of state to a desired tolerance. We present both unconfined and confined cases, where in the latter the ambient pressure changes over time. Our overall scheme is a projection method for the velocity coupled to a multi-implicit spectral deferred corrections (SDC) approach to integrate the mass and energy equations. The iterative nature of SDC methods allows us to incorporate a series of pressure discrepancy corrections naturally that lead to additional mass and energy influx/outflux in each finite volume cell in order to satisfy the equation of state. The method is second order, and satisfies the equation of state to a desired tolerance with increasing iterations. Motivated by experimental results, we test our algorithm on hydrogen flames with detailed kinetics. We examine the morphology of thermodiffusively unstable cylindrical premixed flames in high-pressure environments for confined and unconfined cases. We also demonstrate that our algorithm maintains the equation of state for premixed methane flames and non-premixed dimethyl ether jet flames.     

A New Treatment for Some Periodic Schr?dinger Operators Ⅱ: The Wave Function

Following the approach of our previous paper we continue to study the asymptotic solution of periodic Schrödinger operators. Using the eigenvalues obtained earlier the corresponding asymptotic wave functions are derived. This gives further evidence in favor of the monodromy relations for the Floquet exponent proposed in the previous paper. In particular, the large energy asymptotic wave functions are related to the instanton partition function of N=2 supersymmetric gauge theory with surface operator. A relevant number theoretic dessert is appended.