安培环路定理的拓扑学描述

近年来拓扑学在量子力学中得到了广泛的运用.本文将安培环路定理积分式重新表达为一矢量场在轮胎参数面上的第一类陈数积分.数值模拟展示了该积分值为一整数即第一陈数,其代表矢量场的整体性质:当经历连续变换时,矢量场的局部数值发生改变但整体积分值即陈数仍保持不变;若陈数发生改变,则表明矢量场变换的连续性条件发生破坏,矢量场出现奇点.进一步通过高斯映射将该矢量场从参数轮胎面映射到单位球面上,并给出了第一陈数的直观几何意义.理论和数值结果揭示了安培环路定理的拓扑学本质,表明拓扑概念在经典物理学中也会有广泛应用.     

Kernel polynomial representation for imaginary-time Green's functions in continuous-time quantum Monte Carlo impurity solver

Inspired by the recently proposed Legendre orthogonal polynomial representation for imaginary-time Green s functions G(τ),we develop an alternate and superior representation for G(τ) and implement it in the hybridization expansion continuous-time quantum Monte Carlo impurity solver.This representation is based on the kernel polynomial method,which introduces some integral kernel functions to filter the numerical fluctuations caused by the explicit truncations of polynomial expansion series and can improve the computational precision significantly.As an illustration of the new representation,we re-examine the imaginary-time Green's functions of the single-band Hubbard model in the framework of dynamical mean-field theory.The calculated results suggest that with carefully chosen integral kernel functions,whether the system is metallic or insulating,the Gibbs oscillations found in the previous Legendre orthogonal polynomial representation have been vastly suppressed and remarkable corrections to the measured Green's functions have been obtained.     

The collagen type I segment long spacing (SLS) and fibrillar forms: Formation by ATP and sulphonated diazo dyes

The collagen type I segment long spacing (SLS) crystallite is a well-ordered rod-like molecular aggregate, ∼300 nm in length, which is produced in vitro under mildly acidic conditions (pH 2.5–3.5) in the presence of 1 mM ATP. The formation of the SLS crystallite amplifies the inherent linear structural features of individual collagen heterotrimers, due to the punctate linear distribution and summation of the bulkier amino acid side chains along the length of individual collagen heterotrimers. This can be correlated structurally with the 67 nm D-banded collagen fibril that is found in vivo, and formed in vitro. Although first described many years ago, the range of conditions required for ATP-induced SLS crystallite formation from acid-soluble collagen have not been explored extensively. Consequently, we have addressed biochemical parameters such as the ATP concentration, pH, speed of formation and stability so as to provide a more complete structural understanding of the SLS crystallite. Treatment of collagen type I with 1 mM ATP at neutral and higher pH (6.0–9.0) also induced the formation of D-banded fibrils. Contrary to previous studies, we have shown that the polysulphonated diazo dyes Direct red (Sirius red) and Evans blue, but not Congo red and Methyl blue, can also induce the formation of SLS-like aggregates of collagen, but under markedly different ionic conditions to those employed in the presence of ATP. Specifically, pre-formed D-banded collagen fibrils, prepared in a higher than the usual physiological NaCl concentration (e.g. 500 mM NaCl, 20 mM Tris-HCl pH7.4 or x3 PBS), readily form SLS aggregates when treated with 0.1 mM Direct red and Evans blue, but this did not occur at lower NaCl concentrations. These new data are discussed in relation to the anion (Cl⁻) and polyanion (phosphate and sulphonate) binding by the collagen heterotrimer and their likely role in collagen fibrillogenesis and SLS formation.     

Implementation of Kohn's theorem for the ellipsoidal quantum dot in the presence of external magnetic field

An electron gas in a strongly oblated ellipsoidal quantum dot with impenetrable walls in the presence of external magnetic field is considered. Influence of the walls of the quantum dot is assumed to be so strong in the direction of the minor axis (the OZ axis) that the Coulomb interaction between electrons in this direction can be neglected and considered as two-dimensional. On the basis of geometric adiabaticity we show that in the case of a few-particle gas a powerful repulsive potential of the quantum dot walls has a parabolic form and localizes the gas in the geometric center of the structure. Due to this fact, conditions occur to implement the generalized Kohn theorem for this system. The parabolic confinement potential depends on the geometry of the ellipsoid, which allows, together with the magnetic field to control resonance frequencies of transitions by changing the geometric dimensions of the QD.     

Gauge functions and Galilean invariance of Lagrangians

A novel method to make Lagrangians Galilean invariant is developed. The method, based on null Lagrangians and their gauge functions, is used to demonstrate the Galilean invariance of the Lagrangian for Newton's law of inertia. It is suggested that this new solution of an old physics problem may have implications and potential applications to all gauge-based theories of physics.     

Comparative study of optical analysis methods for thin films

Three popular optical analysis methods (the transfer-matrix method, the Tinkham formula, and Beer's law) have been used for analyzing the optical spectra of thin films. While the transfer-matrix method is an accurate method, the Tinkham formula and Beer's law are approximate methods. Here we investigated the three methods using measured transmittance spectra of insulating transition-metal dichalcogenide (TMD) thin films on a quartz substrate. Three different semiconducting 2H-TMD systems (MoS₂, MoSe₂, and MoTe₂) were measured and analyzed. The optical conductivities obtained from the measured transmittance spectra using the transfer-matrix method and Tinkham formula and the absorption coefficients obtained using the transfer-matrix method and Beer's law were compared. The comparisons show some discrepancies. The reasons for the discrepancies between the results obtained via the two different methods were examined and the application limitations of the Tinkham formula and Beer's law were discussed.     

Gate-induced drain leakage (GIDL) in MFMIS and MFIS negative capacitance FinFETs

The gate induced drain leakage (GIDL) effect in negative capacitance (NC) FinFET is investigated. A Landau–Ginzburg–Devonshire equation (which considers the polarization gradient in ferroelectric material) is used to estimate the characteristics of the NC FinFET. Specifically, metal-ferroelectric-metal-insulator-semiconductor (MFMIS) and metal-ferroelectric-insulator-semiconductor (MFIS) NC FinFETs are compared, in order to figure out the effect of the internal metal layer on the GIDL effect. To analyze the impact of the polarization gradient on the GIDL effect in NC FinFET, a polarization gradient coefficient is varied. For MFMIS, the polarization gradient doesn't significantly affect the device performance. The subthreshold swing improves but the GIDL effect deteriorates because of the “uniform” NC effect in channel region. For MFIS, the device performance is explicitly affected by the polarization gradient. Smaller polarization gradients result in non-uniform NC effect in channel region, resulting in severe GIDL effects. On the other hand, higher polarization gradients alleviate GIDL effects.     

Estimation of the Reliability of a Stress–Strength System from Poisson Half Logistic Distribution

This paper discussed the estimation of stress-strength reliability parameter R=P(Y<X) based on complete samples when the stress-strength are two independent Poisson half logistic random variables (PHLD). We have addressed the estimation of R in the general case and when the scale parameter is common. The classical and Bayesian estimation (BE) techniques of R are studied. The maximum likelihood estimator (MLE) and its asymptotic distributions are obtained; an approximate asymptotic confidence interval of R is computed using the asymptotic distribution. The non-parametric percentile bootstrap and student’s bootstrap confidence interval of R are discussed. The Bayes estimators of R are computed using a gamma prior and discussed under various loss functions such as the square error loss function (SEL), absolute error loss function (AEL), linear exponential error loss function (LINEX), generalized entropy error loss function (GEL) and maximum a posteriori (MAP). The Metropolis–Hastings algorithm is used to estimate the posterior distributions of the estimators of R. The highest posterior density (HPD) credible interval is constructed based on the SEL. Monte Carlo simulations are used to numerically analyze the performance of the MLE and Bayes estimators, the results were quite satisfactory based on their mean square error (MSE) and confidence interval. Finally, we used two real data studies to demonstrate the performance of the proposed estimation techniques in practice and to illustrate how PHLD is a good candidate in reliability studies.