在非线性系统中的微观粒子的特性和非线性量子力学理论(下)

在非线性系统中由于存在着与粒子状态相关的非线性相互作用，微观粒子的状态和特征相对于线性系统而发生了很大变化。原有的线性型的量子力学理论不能很好地描述这些微观粒子的状态和特征。至此，必然要发展新的理论。本文研究了微观粒子在非线性作用下的运动特性和本性的变化，说明了在线性作用和非线性场中微观粒子的性质是明显不同的，启示我们必须建立微观粒子在非线性场中运动的新理论。接着我们研究了与微观量子效应迥然不同的宏观量子效应与非线性作用的孤立子运动的紧密关系，结合现代孤立子理论和超导与超流理论，我们首先提出了非线性量子力学的基本原理及在此基础上建立了系统、完整的非线性量子力学理论体系，并得到的一些新结论。最后我们还论证了这个理论的正确性和自洽性，它的运用范围以及它的重大意义。     

在非线性系统中的微观粒子的特性和非线性量子力学理论(上)

在非线性系统中由于存在着与粒子状态相关的非线性相互作用，微观粒子的状态和特征相对于线性系统而发生了很大变化。原有的线性型的量子力学理论不能很好地描述这些微观粒子的状态和特征。至此，必然要发展新的理论。本文研究了微观粒子在非线性作用下的运动特性和本性的变化，说明了在线性作用和非线性场中微观粒子的性质是明显不同的，启示我们必须建立微观粒子在非线性场中运动的新理论。接着我们研究了与微观量子效应迥然不同的宏观量子效应与非线性作用的孤立子运动的紧密关系，结合现代孤立子理论和超导与超流理论，我们首先提出了非线性量子力学的基本原理及在此基础上建立了系统、完整的非线性量子力学理论体系，并得到的一些新结论。最后我们还论证了这个理论的正确性和自洽性，它的运用范围以及它的重大意义。     

非线性薄膜方程的差分迭代求解

对类似于非线性薄膜一类的非线性偏微分方程提出一种新的算法.该法首先略去非线性部分的影响,或给予非线性部分莱一初值,使非线性部分成为已知,从而将原非线性方程转化为线性方程,并按差分法或其它方法求得其线性解.再将所得线性解代入非线性部分使其成为已知,再次求得其解.这样反复迭代直至收敛,进而求得原非线性方程的非线性解.     

港口非线性波浪三维耦合计算模型研究

建立了外域用差分求解高阶Boussinesq方程、内域用有限元求解Laplace方程的三维非线性波浪对船作用的时域计算耦合模型.研究了该类三维耦合模型的匹配条件,耦合求解过程和内域、外域公共区域长度的确定,探讨了内域有限元网格的剖分方法.把该耦合模型的计算结果与实验结果、内域用Euler方程的耦合模型计算结果进行了对比,结果表明该耦合模型具有满意的精度,适用于模拟较大区域内波浪对三维船等固定物体的作用,为今后近海岸大区域非线性波浪对三维非规则物体作用的时域计算和三维分区计算提供了参考.     

二阶非线性与色散性的Boussinesq类方程

从Euler方程出发 ,通过适当的无量纲变换 ,假设底面对水平坐标一阶导数的平方及二阶导数的量阶均为O(α ,β2 ) (其中 :O(α) =O( β2 ) ,α =A/h0 ,β =h0 /L ,A为特征波高、L为特征波长、h0 为特征水深 ) ,没有无旋假定 ,经严格的数学推导 ,得到量阶为O(αβ3 ,β5 )的二阶非线性与色散性的Boussinesq类方程 ,其线性色散关系及变浅作用系数的精度均为O( β4) .     

三维曲井内钻柱非线性屈曲分析平衡方程

随着钻井技术的不断进步, 油气井已由早期的铅直井发展成了当今的斜直井, 水平井, 平面曲井, 甚至三维空间曲线形状曲井. 井内钻柱屈曲性能的研究对钻井工程的成败尤为重要, 迫切需要建立分析三维曲井内钻柱屈曲性能的平衡方程. 本文基于Love的空间弯扭杆平衡方程, 考虑到井壁的径向约束条件, 导出了一套用于三维曲井内钻柱非线性屈曲分析的平衡方程. 公式引入了三维曲井的井眼轴线曲率和挠率所带来的影响. 对于径向受井壁约束的钻柱, 上端同时作用有轴向压力和扭矩, 并计及自重, 给出了非线性屈曲分析平衡方程的详细推导过程. 值得注意的是, 现有文献中用于分析直井和平面曲井内钻柱屈曲性能的平衡方程, 可由三维空间曲井内钻柱非线性屈曲分析平衡方程退化得到. 期望本文导出的平衡方程能为工程上三维曲井内钻柱的非线性屈曲分析提供理论基础.     

广义非线性强度理论及其变换应力空间

基于摩擦材料的试验规律和在前人研究成果的基础, 提出了广义非线性强度理论, 它用一个表达式统一描述π 平面及子午面上各种材料的非线性强度特性, 包含或逼近了现有的非线性单一强度理论. 在主应力空间中, 广义非线性强度理论在π 平面上的破坏函数为介于SMP准则和Mises准则之间的光滑曲线;在子午面上的破坏函数为幂函数曲线. 在基于广义非线性强度理论的变换应力空间内, 广义非线性强度理论可以合理地与各种以p和q为应力参量的本构模型相结合, 使模型简单地实现三维化.     

混凝土材料非线性多轴动态强度准则

将广义非线性强度理论的4个材料参数转化为混凝土材料的基本强度参数,通过混凝土材料的基本强度特性,分析了4个材料参数的变化规律与取值范围.基于S准则建立了混凝土材料4个基本强度参数的率效应表达式,建立了混凝土材料的非线性多轴动态强度准则,分析了动态强度参数的率效应规律,结果表明,混凝土材料的强度特性随着应变率的提高,逐渐向金属材料的强度特性过渡,在应变率从-3~3,应变率对混凝土动态强度的影响较大,并且动强度不是随着应变率的提高无限增大的,而是存在动强度峰值.通过与3组双轴压-压和2组双轴拉-压动态加载时混凝土材料试验结果的比较,表明非线性多轴动态强度准则可较好地描述混凝土材料双轴动强度规律.在同一应变率下,可较好地描述强度的非线性特性;不同应变率下,动强度面互不相交,即应变率效应与多轴应力状态对强度规律不存在耦合影响.     

推移质运动过程的非线性动力学特性

天然沙质海岸及河床上存在着不同形式的床面形态, 其运动变化受床面附近推移质泥沙的运动特性所决定. 从床面层内推移质集体运动出发, 探讨了推移质运动过程的非线性动力学特性, 发现泥沙起动、推移质平衡输沙以及床面形态由平整到沙纹及沙垄等不同发展阶段, 受推移质运动过程的非线性动力特征所决定, 它们分别对应于推移运动过程中的不同非线性状态. 通过与法国夏都水利实验室床面形态试验比较, 进一步证明: “床面形态从平整到沙垄的演化与否”由推移质泥沙运动过程的突变特性所决定, “突变分界线”是平整床面与沙纹及沙垄床面的分界曲线.     

具有相关失效模式的多自由度非线性结构随机振动系统的可靠性分析

在一般随机有限元法的基础上, 给出了在随机参数的联合概率密度函数未知的情况下, 具有相关失效模式的非线性动态随机结构系统可靠性分析的方法. 应用四阶矩技术、最大熵理论、边缘概率分布函数的概念和不完全概率信息理论, 解决了多自由度非线性随机结构振动系统的首次超限破坏问题.     

Quantum jumps,superpositions, and the continuous evolution of quantum states

The apparent dichotomy between quantum jumps on the one hand, and continuous time evolution according to wave equations on the other hand, provided a challenge to Bohr's proposal of quantum jumps in atoms. Furthermore, Schrödinger's time-dependent equation also seemed to require a modification of the explanation for the origin of line spectra due to the apparent possibility of superpositions of energy eigenstates for different energy levels. Indeed, Schrödinger himself proposed a quantum beat mechanism for the generation of discrete line spectra from superpositions of eigenstates with different energies.However, these issues between old quantum theory and Schrödinger's wave mechanics were correctly resolved only after the development and full implementation of photon quantization. The second quantized scattering matrix formalism reconciles quantum jumps with continuous time evolution through the identification of quantum jumps with transitions between different sectors of Fock space. The continuous evolution of quantum states is then recognized as a sum over continually evolving jump amplitudes between different sectors in Fock space.In today's terminology, this suggests that linear combinations of scattering matrix elements are epistemic sums over ontic states. Insights from the resolution of the dichotomy between quantum jumps and continuous time evolution therefore hold important lessons for modern research both on interpretations of quantum mechanics and on the foundations of quantum computing. They demonstrate that discussions of interpretations of quantum theory necessarily need to take into account field quantization. They also demonstrate the limitations of the role of wave equations in quantum theory, and caution us that superpositions of quantum states for the formation of qubits may be more limited than usually expected.     

The physics and metaphysics of Tychistic Bohmian Mechanics

The paper takes up Bell's (1987) “Everett (?) theory” and develops it further. The resulting theory is about the system of all particles in the universe, each located in ordinary, 3-dimensional space. This many-particle system as a whole performs random jumps through 3N-dimensional configuration space – hence “Tychistic Bohmian Mechanics” (TBM). The distribution of its spontaneous localisations in configuration space is given by the Born Rule probability measure for the universal wavefunction. Contra Bell, the theory is argued to satisfy the minimal desiderata for a Bohmian theory within the Primitive Ontology framework (for which we offer a metaphysically more perspicuous formulation than is customary). TBM's formalism is that of ordinary Bohmian Mechanics (BM), without the postulate of continuous particle trajectories and their deterministic dynamics. This “rump formalism” receives, however, a different interpretation. We defend TBM as an empirically adequate and coherent quantum theory. Objections voiced by Bell and Maudlin are rebutted. The “for all practical purposes”-classical, Everettian worlds (i.e. quasi-classical histories) exist sequentially in TBM (rather than simultaneously, as in the Everett interpretation). In a temporally coarse-grained sense, they quasi-persist. By contrast, the individual particles themselves cease to persist.     

Localization and the interface between quantum mechanics, quantum field theory and quantum gravity II: The search of the interface between QFT and QG

The main topics of this second part of a two-part essay are some consequences of the phenomenon of vacuum polarization as the most important physical manifestation of modular localization. Besides philosophically unexpected consequences, it has led to a new constructive “outside-inwards approach” in which the pointlike fields and the compactly localized operator algebras which they generate only appear from intersecting much simpler algebras localized in noncompact wedge regions whose generators have extremely mild almost free field behavior.Another consequence of vacuum polarization presented in this essay is the localization entropy near a causal horizon which follows a logarithmically modified area law in which a dimensionless area (the area divided by the square of dR where dR is the thickness of a light-sheet) appears. There are arguments that this logarithmically modified area law corresponds to the volume law of the standard heat bath thermal behavior. We also explain the symmetry enhancing effect of holographic projections onto the causal horizon of a region and show that the resulting infinite dimensional symmetry groups contain the Bondi–Metzner–Sachs group. This essay is the second part of a partitioned longer paper.     

States of ignorance and ignorance of states: Examining the Quantum Principal Principle

Earman (2018) has recently argued that the Principal Principle, a principle of rationality connecting objective chance and credence, is a theorem of quantum probability theory. This paper critiques Earman's argument, while also offering a positive proposal for how to understand the status of the Principal Principle in quantum probability theory.     

Interpretation neutrality in the classical domain of quantum theory

I show explicitly how concerns about wave function collapse and ontology can be decoupled from the bulk of technical analysis necessary to recover localized, approximately Newtonian trajectories from quantum theory. In doing so, I demonstrate that the account of classical behavior provided by decoherence theory can be straightforwardly tailored to give accounts of classical behavior on multiple interpretations of quantum theory, including the Everett, de Broglie–Bohm and GRW interpretations. I further show that this interpretation-neutral, decoherence-based account conforms to a general view of inter-theoretic reduction in physics that I have elaborated elsewhere, which differs from the oversimplified picture that treats reduction as a matter of simply taking limits. This interpretation-neutral account rests on a general three-pronged strategy for reduction between quantum and classical theories that combines decoherence, an appropriate form of Ehrenfest׳s Theorem, and a decoherence-compatible mechanism for collapse. It also incorporates a novel argument as to why branch-relative trajectories should be approximately Newtonian, which is based on a little-discussed extension of Ehrenfest׳s Theorem to open systems, rather than on the more commonly cited but less germane closed-systems version. In the Conclusion, I briefly suggest how the strategy for quantum-classical reduction described here might be extended to reduction between other classical and quantum theories, including classical and quantum field theory and classical and quantum gravity.