Dynamical first-order phase transition in kinetically constrained models of glasses

We show that the dynamics of kinetically constrained models of glass formers takes place at a first-order coexistence line between active and inactive dynamical phases. We prove this by computing the large-deviation functions of suitable space-time observables, such as the number of configuration changes in a trajectory. We present analytic results for dynamic facilitated models in a mean-field approximation, and numerical results for the Fredrickson-Andersen model, the East model, and constrained lattice gases, in various dimensions. This dynamical first-order transition is generic in kinetically constrained models, and we expect it to be present in systems with fully jammed states.     

First-order transitions and thermodynamic properties in the 2D Blume-Capel model: the transfer-matrix method revisited

We investigate the first-order transition in the spin-1 two-dimensional Blume-Capel model in square lattices by revisiting the transfer-matrix method. With large strip widths increased up to the size of 18 sites, we construct the detailed phase coexistence curve which shows excellent quantitative agreement with the recent advanced Monte Carlo results. In the deep first-order area, we observe the exponential system-size scaling of the spectral gap of the transfer matrix from which linearly increasing interfacial tension is deduced with decreasing temperature. We find that the first-order signature at low temperatures is strongly pronounced with much suppressed finite-size influence in the examined thermodynamic properties of entropy, non-zero spin population, and specific heat. It turns out that the jump at the transition becomes increasingly sharp as it goes deep into the first-order area, which is in contrast to the Wang–Landau results where finite-size smoothing gets more severe at lower temperatures.     

Coherence migration in high-dimensional bipartite systems

The conservation law for first-order coherence and mutual correlation of a bipartite qubit state was firstly proposed by Svozilík et al., and their theories laid the foundation for the study of coherence migration under unitary transformations. In this paper, we generalize the framework of first-order coherence and mutual correlation to an arbitrary (m $\otimes$ n)-dimensional bipartite composite state by introducing an extended Bloch decomposition form of the state. We also generalize two kinds of unitary operators in high-dimensional systems, which can bring about coherence migration and help to obtain the maximum or minimum first-order coherence. Meanwhile, the coherence migration in open quantum systems is investigated. We take depolarizing channels as examples and establish that the reduced first-order coherence of the principal system over time is completely transformed into mutual correlation of the (2 $\otimes$ 4)-dimensional system-environment bipartite composite state. It is expected that our results may provide a valuable idea or method for controlling the quantum resource such as coherence and quantum correlations.     

Fast prediction of scattered sound field based on Fourier diffraction theory under second-order born approximation

The directional pattern of sound waves scattered from an object insonified by a plane wave can be efficiently predicted using the Fourier diffraction theorem (FDT). This is achieved by sampling a circle in the discrete Fourier transform of the object/medium distribution. However, the FDT-based approach under the first-order Born approximation is only applicable to weak scattering. To improve the prediction accuracy and expand the method’s scope of applications, we introduce a second-order correction term to the solution, which is obtained by taking the first-order scattered waves as secondary incident sources, and calculate the “scattering” in the same way as in the first-order FDT-based approach. Adding the resulting correction term to the directional pattern based on the first-order Born approximation, the second-order prediction is obtained. Numerical results show that the proposed method can provide improved directional patterns of the scattered waves, and the range of applicability is significantly expanded.     

Higher-order radiative perturbation theory

As a computationally effective tool, the first-order term of the radiative perturbation theory has been computed successfully, and has been applied in a number of areas. In this article, we develop the computational expressions for the higher-order terms of the perturbation expansion in a plane parallel atmosphere. These expressions are then implemented, and numerical results for some typical cases are presented. These results indicate that the computation is successful and that the higher-order terms are essential in cases where the first-order term alone cannot predict the perturbation with sufficient accuracy.     

Rounding by disorder of first-order quantum phase transitions: emergence of quantum critical points

We give a heuristic argument for disorder rounding of a first-order quantum phase transition into a continuous phase transition. From both weak and strong disorder analysis of the N-color quantum Ashkin-Teller model in one spatial dimension, we find that, for N > or =3, the first-order transition is rounded to a continuous transition and the physical picture is the same as the random transverse field Ising model for a limited parameter regime. The results are strikingly different from the corresponding classical problem in two dimensions where the fate of the renormalization group flows is a fixed point corresponding to N-decoupled pure Ising models.     

Monte Carlo study of very weakly first-order transitions in the three-dimensional Ashkin-Teller model

We propose numerical simulations of the Ashkin-Teller model as a foil for theoretical techniques for studying very weakly first-order phase transitions in three dimensions. The Ashkin-Teller model is a simple two-spin model whose parameters can be adjusted so that it has an arbitrarily weakly first-order phase transition. In this limit, there are quantities characterizing the first-order transition which are universal: we measure the relative discontinuity of the specific heat, the correlation length, and the susceptibility across the transition by Monte Carlo simulation.     

Localized waves in three-component coupled nonlinear Schrdinger equation

We study the generalized Darboux transformation to the three-component coupled nonlinear Schr ¨odinger equation.First-and second-order localized waves are obtained by this technique.In first-order localized wave,we get the interactional solutions between first-order rogue wave and one-dark,one-bright soliton respectively.Meanwhile,the interactional solutions between one-breather and first-order rogue wave are also given.In second-order localized wave,one-dark-one-bright soliton together with second-order rogue wave is presented in the first component,and two-bright soliton together with second-order rogue wave are gained respectively in the other two components.Besides,we observe second-order rogue wave together with one-breather in three components.Moreover,by increasing the absolute values of two free parameters,the nonlinear waves merge with each other distinctly.These results further reveal the interesting dynamic structures of localized waves in the three-component coupled system.     

Axiomatization of Special Relativity in First Order Logic

The axiomatization of physical theories is a fundamental issue of science. The first-order axiomatic system SpecRel for special relativity proposed recently by Andréka et al. is not enough to explain all the main results in the theory, including the twin paradox and energy-mass relation. In this paper, from a four-dimensional space-time perspective, we introduce the concepts of world-line, proper time and four-momentum to our axiomatic system SpecRel⁺. Then we introduce an axiom of mass (AxMass) and take four-momentum conservation as an axiom (AxCFM) in SpecRel⁺. It turns out that the twin paradox and energy-mass relation can be derived from SpecRel⁺ logically. Hence, as an extension of SpecRel, SpecRel⁺ is a suitable first-order axiomatic system to describe the kinematics and dynamics of special relativity.     

First-order operators and boundary triples

The aim of the present paper is to introduce a first-order approach to the abstract concept of boundary triples for Laplace operators. Our main application is the Laplace operator on a manifold with boundary; a case in which the ordinary concept of boundary triples does not apply directly. In our first-order approach, we show that we can use the usual boundary operators in abstract Green’s formula as well. Another motivation for the first-order approach is to give an intrinsic definition of the Dirichlet-to-Neumann map and intrinsic norms on the corresponding boundary spaces. We also show how the first-order boundary triples can be used to define a usual boundary triple leading to a Dirac operator. In memoriam Vladimir A. Geyler (1943–2007)     

Phase-integral calculation of quantal matrix elements between unbound states,without the use of wavefunctions

The paper deals with the calculation of diagonal as well as off-diagonal matrix elements between unbound states pertaining to a radial Schrödinger equation. For the case that the effective potential, i.e. the potential with the centrifugal barrier included, is real and that only a single generalized classical turning point exists, we derive, on the basis of a phase-integral method, a new, general formula for the calculation of such matrix elements without the use of wavefunctions. The formula applies to an arbitrary order of the phase-integral approximations used. While conventional methods may present difficulties when the radial wavefunctions oscillate rapidly in space, this formula, in which the wavefunctions do not appear, is expected to be more accurate the more rapidly the wavefunctions oscillate. The formula is tested numerically for a Lennard-Jones potential and is found to yield extremely accurate results.

When specialized to the first-order approximation, our formula goes over into a formula derived previously by other authors. They derived the formula by introducing the first-order JWKB approximation for the wave-functions in the integral defining the matrix element and simplifying the resulting expression by using simple qualitative arguments. The remarkably good accuracy of this first-order formula has puzzled previous authors. So has also the fact that attempts to improve it, by including quantities neglected on the basis of the simple qualitative arguments, and by using Airy functions or uniform approximations for the wavefunctions through the turning points, have failed. Our derivation throws light on the question of the accuracy to be expected, and it explains why already the first-order formula is remarkably accurate and why no improvement is gained in the attempts mentioned.     

Osher Flux with Entropy Fix for Two-Dimensional Euler Equations

We compare in this paper the properties of Osher flux with O-variant and P-variant (Osher-O flux and Osher-P flux) in finite volume methods for the two-dimensional Euler equations and propose an entropy fix technique to improve their robustness. We consider both first-order and second-order reconstructions. For inviscid hypersonic flow past a circular cylinder, we observe different problems for different schemes: a first-order Osher-O scheme on quadrangular grids yields a carbuncle shock, while a first-order Osher-P scheme results in a dislocation shock for high Mach number cases. In addition, a second-order Osher scheme can also yield a carbuncle shock or be unstable. To improve the robustness of these schemes we propose an entropy fix technique, and then present numerical results to show the effectiveness of the proposed method. In addition, the influence of grid aspects ratio, relative shock position to the grid and Mach number on shock stability are tested. Viscous heating problem and double Mach reflection problem are simulated to test the influence of the entropy fix on contact resolution and boundary layer resolution.     

Quantum adiabatic algorithm and scaling of gaps at first-order quantum phase transitions

Motivated by the quantum adiabatic algorithm (QAA), we consider the scaling of the Hamiltonian gap at quantum first-order transitions, generally expected to be exponentially small in the size of the system. However, we show that a quantum antiferromagnetic Ising chain in a staggered field can exhibit a first-order transition with only an algebraically small gap. In addition, we construct a simple classical translationally invariant one-dimensional Hamiltonian containing nearest-neighbor interactions only, which exhibits an exponential gap at a thermodynamic quantum first-order transition of essentially topological origin. This establishes that (i)?the QAA can be successful even across first-order transitions but also that (ii)?it can fail on exceedingly simple problems readily solved by inspection, or by classical annealing.     

Shape invariance for the bent brane with two scalar fields

In this paper, we study the braneworld scenarios in the presence of two real scalar fields coupled by gravity. The first-order formalism for the bent brane (for both de Sitter and anti-de Sitter geometry), leads us to discuss the shape invariance method in the bent brane systems. So, by using the fluctuations of metric and fields we obtain the Schrödinger equation. Then we factorize the corresponding Hamiltonian in terms of multiplication of the first-order differential operators. These first-order operators lead us to obtain the energy spectrum with the help of shape invariance method.     

Shape invariance method for quintom model in the bent brane background

In the present Letter, we study the braneworld scenarios in the presence of quintom dark energy coupled by gravity. The first-order formalism for the bent brane (for both de Sitter and anti-de Sitter geometry), leads us to discuss the shape invariance method in the bent brane systems. So, by using the fluctuations of metric and quintom fields we obtain the Schrödinger equation. Then we factorize the corresponding Hamiltonian in terms of multiplication of the first-order differential operators. These first-order operators lead us to obtain the energy spectrum with the help of shape invariance method.     

一阶光学系统分数傅里叶变换的相空间分析

在维格纳相空间中,通过将一阶光学系统的传输矩阵分解为坐标旋转、比例缩放和啁啾矩阵的组合,得到了一阶光学系统在空域的分数傅里叶表示.结果表明:任意一阶光学系统均可表示为经过比例缩放和二次相位调制的分数傅里叶变换.通过将输入输出光场在相空间中作π/2角旋转,得到了一阶光学系统在频域的传输矩阵和衍射积分公式,进而得到了一阶光学系统在频域的分数傅里叶表示.比较空域和频域一阶光学系统的相空间变换矩阵,说明2个系统本质上属同一变换在不同基坐标下的表示,并推导出了光学系统在空域和频域具有相同分数傅里叶变换的条件.     

The prediction of airborne sound transmission between two rooms using first-order flanking paths

Airborne sound transmission between adjacent rooms can be predicted using the Standard EN 12354-1 (ISO 15712-1), which is equivalent to a first-order approximation of statistical energy analysis (SEA). This paper analyses airborne sound transmission between adjacent rooms in a masonry building, by comparing results obtained from EN 12354-1 to SEA predictions and measurements. It is shown that the restriction of the Standard to first-order flanking paths can lead to large errors in predictions when compared to measurements and SEA results taking into account all transmission paths. This is observed both for individual flanking paths and overall transmission between rooms, for which the Standard provides results similar to those obtained by the first-order approximation of SEA. The paper also looks at possible reasons why previous studies using the approach in EN 12354 have generally shown good agreement with measurements.     

凹型钝头体超音速粘性流场的数值模拟

本文首先从单个方程出发,根据TVD思想,比较自然地给出了二阶带通量限制器的CSCM^[1]差分方法,然后推广到方程组情形。为了验证方法和程序,将球头绕流计算结果同文献[2]作了比较,然后运用此方法模拟了轴对称凹型钝体的粘性超音速分离绕流流场,对一阶与二阶、粘性与无粘性数值结果作了比较。计算网格采用了简单、快速易行的拟正交代数生成方法。     

Influence of Spectral Filtering and Nonlinear Gain on an Optical Soliton

Using the direct soliton perturbation theory, we investigate the evolution of soliton parameters and the firstorder correction of bright soliton in a system with linear and nonlinear gain （or loss） and spectral filtering in a comprehensive way. The results obtained by means of our analytic method are consistent with numerical simulations. It is also found that the stable soliton propagation which has been investigated in a previous report by others is the limit case of our results.