Extended Einstein–Cartan theory à la Diakonov: The field equations

Diakonov formulated a model of a primordial Dirac spinor field interacting gravitationally within the geometric framework of the Poincaré gauge theory (PGT). Thus, the gravitational field variables are the orthonormal coframe (tetrad) and the Lorentz connection. A simple gravitational gauge Lagrangian is the Einstein–Cartan choice proportional to the curvature scalar plus a cosmological term. In Diakonov?s model the coframe is eliminated by expressing it in terms of the primordial spinor. We derive the corresponding field equations for the first time. We extend the Diakonov model by additionally eliminating the Lorentz connection, but keeping local Lorentz covariance intact. Then, if we drop the Einstein–Cartan term in the Lagrangian, a nonlinear Heisenberg type spinor equation is recovered in the lowest approximation.     

Accuracy of semiclassical dynamics in the presence of chaos

We review some of the issues facing semiclassical methods in classically chaotic systems, then demonstrate the long-time accuracy of semiclassical propagation of a nonstationary wave packet using the quantum baker's map of Balazs and Voros. We show why some of the standard arguments against the efficacy of semiclassical dynamics for long-time chaotic motion are incorrect.     

受迫振动非线性特性的教学拓展

受迫振动在大学物理和大学物理实验中均是重点教学内容,为了使学生更加深入理解受迫振动的非线性特性,本文基于波耳共振仪所涉及的非线性因素和实验数据,对受迫振动方程进行非线性修正,利用数值分析探讨其非线性特性.通过引入硬弹簧型杜芬方程,探讨系统由周期性运动进入混沌状态的演化,将受迫振动中相对稳定的平衡点与奇异吸引子进行类比,...     

利用阵发混沌现象测定未知信号参数

利用Duffing方程对频率的极端敏感性产生阵发混沌现象,研究了一种利用该现象定量检测未知的微弱周期信号的各项参数的新方法,通过理论分析和实例仿真证明了该方法的可行性,并针对仿真结果提出了改进措施,提高了检测精度.     

Mean-Field Theory for Percolation Models of the Ising Type

The q=2 random cluster model is studied in the context of two mean-field models: the Bethe lattice and the complete graph. For these systems, the critical exponents that are defined in terms of finite clusters have some anomalous values as the critical point is approached from the high-density side, which vindicates the results of earlier studies. In particular, the exponent ~ which characterizes the divergence of the average size of finite clusters is 1/2, and ~, the exponent associated with the length scale of finite clusters, is 1/4. The full collection of exponents indicates an upper critical dimension of 6. The standard mean field exponents of the Ising system are also present in this model (=1/2, =1), which implies, in particular, the presence of two diverging length-scales. Furthermore, the finite cluster exponents are stable to the addition of disorder, which, near the upper critical dimension, may have interesting implications concerning the generality of the disordered system/correlation length bounds.     

时域耦合模理论引入“理论力学”教学中的可行性的探究

被广泛地用于力学、光学、电学等相关学科中的时域耦合模理论,在前沿科学研究中扮演着越来越重要的角色.在教学和科研相结合的本科教学理念下,将时域耦合模理论引入“理论力学”中已刻不容缓.本文结合拉格朗日方程和久期微扰理论,将振子耦合的二阶微分方程退化为一阶微分方程,即时域耦合模理论的主方程.该探究为本科生顺利接受时域耦合模理论提供了一种方案,并且在本科生素质培养方面有一定的意义.     

Radius studies of 8Li and 8B using the optical-limit Glauber model in conjunction with relativistic mean-field theory

We study the reaction cross sections(σR) and root-mean-square(RMS) radii of 8Li and 8B,the halo-like nuclei,with stable target 12C,27Al and 9Be within the standard optical-limit Glauber model,using densities obtained from relativistic mean-field(RMF) formalisms and other types of distributions.It is found that the experimental σR can be reproduced well at high energy.The RMS radius and △r extracted by RMFtheory and harmonic oscillator distribution are compared.We find that the RMS radius and △r of 8B are larger than those of 8Li.In addition,we analyze in detail the relationship between σR and density distribution.     

用光学极限的Glauber模型结合相对论平均场对8Li和8B的半径的研究

We study the reaction cross sections （σR） and root-mean-square （RMS） radii of ^8Li and ^8B, the halo-like nuclei, with stable target ^12C, ^27Al and ^9Be within the standard optical-limit Glauber model, using densities obtained from relativistic mean-field （RMF） formalisms and other types of distributions. It is found that the experimental σR can be reproduced well at high energy. The RMS radius and Ar extracted by RMF- theory and harmonic oscillator distribution are compared. larger than those of SLi. In addition, we analyze in detail the We find that the RMS radius and Ar of SB are relationship between σR and density distribution.     

On the dynamics and ergodic properties of theXY model

The return to equilibrium is investigated for one-dimensional (one-sided) chain of theXY model. The initial state is taken to be the Gibbs state for the sum of the Hamiltonian for theXY model of lengthN and a perturbation by a uniform magnetic field acting on the firstn sites. The time evolution under the unperturbedXY model Hamiltonian is studied for the expectation value of the average magnetization of the same firstn sites in the infinitely extended system (i.e., after taking the limitN). It is found that the return to equilibrium occurs for a finite-size perturbation (i.e., for a fixedn), while it does not occur for an infinite-size perturbation (i.e., the limit n is taken simultaneously as N). A certain twisted asymptotic Abelian property of theXY model is shown and used as a technical tool.     

物质结构在夸克-轻子层次上的动力学规律和研究发展趋势

文章综述了粒子物理中标准模型理论的历史发展、面临挑战以及未来的发展趋势.目前阶段物质结构最小组成单元是夸克和轻子,量子色动力学是描述夸克-胶子之间强相互作用的基本理论,它具有渐近自由和夸克禁闭的特点.量子色动力学和电弱统一理论一起构成粒子物理中标准模型理论.标准模型理论成功同时也面临两大挑战：对称性破缺的本质和夸克禁闭难题,这意味着标准模型理论需要发展和突破.人们期望粒子物理学、天文学和宇宙学交叉发展联手解决物质结构和早期宇宙研究中面临的难题,最终揭示超出标准模型的新物理规律.     

物质结构在夸克-轻子层次上的动力学规律和研究发展趋势

文章综述了粒子物理中标准模型理论的历史发展、面临挑战以及未来的发展趋势.目前阶段物质结构最小组成单元是夸克和轻子,量子色动力学是描述夸克-胶子之间强相互作用的基本理论,它具有渐近自由和夸克禁闭的特点.量子色动力学和电弱统一理论一起构成粒子物理中标准模型理论.标准模型理论成功同时也面临两大挑战:对称性破缺的本质和夸克禁闭难题,这意味着标准模型理论需要发展和突破.人们期望粒子物理学、天文学和宇宙学交叉发展联手解决物质结构和早期宇宙研究中面临的难题,最终揭示超出标准模型的新物理规律.     

Ergodic Properties of the Non-Markovian Langevin Equation

We discuss the dissipative dynamics of a classical particle coupled to an infinitely extended heat reservoir. We announce a number of results concerning the ergodic properties of this model. The novelty of our approach is that it extends beyond Markovian dynamics to the case where the Langevin equation is driven by colored noise. Our method works in arbitrary space dimension, and for fully nonlinear systems.     

反应窗理论的适用性研究

基于低能离子与原子碰撞的分子库仑过垒模型，简要描述了与入射离子速度相关的反应窗理论.根据这一理论，计算了不同碰撞速度时O⁸⁺-H，Ar⁸⁺-H，Ar⁸⁺-He，Ne¹⁰⁺-He及Ar¹⁸⁺-He等碰撞体系单电子俘获过程的微分截面，还计算了碰撞速度为0.53 a.u.时¹⁵N⁷⁺-Ne碰撞体系单电子、双电子及三电子俘获过程的微分截面，并与他人的实验结果作了比较.研究发现，反应窗理论预言的末态电子分布与实验结果符合较好.理论和实验研究表明，随着碰撞速度的增加反应窗变宽；反应窗理论所预言的微分截面，当Q值较小时比实验结果偏大，当Q值较大时比实验结果偏小. 关键词： 反应窗理论 态选择微分截面 分子库仑过垒模型 离子与原子碰撞     

On the stochastic dynamics of Ising models

With the help of recent results in the mathematical theory of master equations, we present a rigorous derivation of the stochastic Glauber dynamics of Ising models from Hamiltonian quantum mechanics. A thermal bath is explicitly constructed and, as an illustration, the dynamics of the Ising-Weiss model is analyzed in the thermodynamic limit. We thus obtain an example of a nonequilibrium statistical mechanical system for which a link without mathematical gap can be established from microscopic quantum mechanics to a macroscopic irreversible thermodynamic process.     

A New Method for the Solution of Models of Biological Evolution: Derivation of Exact Steady-State Distributions

We investigate well-known models of biological evolution and address the open problem of how construct a correct continuous analog of mutations in discrete sequence space. We deal with models where the fitness is a function of a Hamming distance from the reference sequence. The mutation-selection master equation in the discrete sequence space is replaced by a Hamilton-Jacobi equation for the logarithm of relative frequencies of different sequences. The steady-state distribution, mean fitness and the variance of fitness are derived. All our results are asymptotic in the large genome limit. A variety of important biological and biochemical models can be solved by this new approach. PACS numbers: 87.10.+e, 87.15.Aa, 87.23.Kg, 02.50.-r     

A new formalism for the statistical dynamics of vector spin systems

The relaxational dynamics of a classical vector Heisenberg spin system is studied using the Fokker-Planck equation. To calculate the eigenvalues of the Fokker-Planck operator, a new approach is introduced. In this connection, a number space repesentation is introduced, which enables us to visualize the eigenvalue structure of the Fokker-Planck operator. The mean field approximation is derived and a systematic method to improve the mean field approximation is presented.     

Schwinger Boson Formulation and Solution of the Crow-Kimura and Eigen Models of Quasispecies Theory

We express the Crow-Kimura and Eigen models of quasispecies theory in a functional integral representation. We formulate the spin coherent state functional integrals using the Schwinger Boson method. In this formulation, we are able to deduce the long-time behavior of these models for arbitrary replication and degradation functions. We discuss the phase transitions that occur in these models as a function of mutation rate. We derive for these models the leading order corrections to the infinite genome length limit.     

A new formalism for the statistical dynamics of planar spin systems

The relaxational dynamics of a classical planar Heisenberg spin system is studied using the Fokker-Planck equation. A new approach is introduced in which we attempt to directly calculate the eigenvalues of the Fokker-Planck operator. In this connection a number space representation is introduced, which enables us to visualize the eigenvalue structure of the Fokker-Planck operator. The mean field approximation is derived and a systematic method to improve the mean field approximation is presented.     

Ergodic theory of the mixmaster universe in higher space-time dimensions. II

The topological dynamics of the mixmaster models in space-time dimension d+1 are investigated. We use a new parametrization to reduce the mixmaster map to a translation combined with an appropriate isometry or a dilating inversion. For d9, we show that the mixmaster map is ergodic and topologically mixing. For d10, the mixmaster map reduces to the identity after a finite number of iterations, except for a set of initial data with zero Lebesgue measure.Chargé de recherches au Fonds National de la Recherche Scientifique.