Quantum fractionalism: The Born rule as a consequence of the complex Pythagorean theorem

Everettian Quantum Mechanics, or the Many Worlds Interpretation, lacks an explanation for quantum probabilities. We show that the values given by the Born rule equal projection factors, describing the contraction of Lebesgue measures in orthogonal projections from the complex line of a quantum state to eigenspaces of an observable. Unit total probability corresponds to a complex Pythagorean theorem: the measure of a subset of the complex line is the sum of the measures of its projections on all eigenspaces.Postulating the existence of a continuum infinity of identical quantum universes, all with the same quasi-classical worlds, we show that projection factors give relative amounts of worlds. These appear as relative frequencies of results in quantum experiments, and play the role of probabilities in decisions and inference. This solves the probability problem of Everett's theory, allowing its preferred basis problem to be solved as well, and may help settle questions about the nature of probability.     

复杂势场量子弹球中疤痕态的量子化条件

量子疤痕是波函数在经典不稳定周期轨道周围反常凝聚的一种量子或波动现象.人们对疤痕态的量子化条件进行了大量研究,对深入理解半经典量子化起到了一定的促进作用.之前大部分研究工作主要集中在硬墙量子弹球上,即给定边界形状的无穷深量子势阱系统.本文研究具有光滑复杂势场的二维量子弹球系统,考察疤痕态的量子化条件及其重复出现的规律,得到了与硬墙弹球不一样的结果,对理解这类现象是一个有益的补充.这些结果将有助于理解具有无规长程杂质分布的二维电子系统的态密度谱和输运行为.     

Study of semileptonic decay of ${\bar{B}}_{s}^{0} \rightarrow \phi {l}^{+}{l}^{-}$ in QCD sum rule

In this work we study the semileptonic decay of ${\bar{B}}_{s}^{0}\to \phi {l}^{+}{l}^{-}$ (l=e, μ, τ) with the QCD sum rule method. We calculate the ${\bar{B}}_{s}^{0}\to \phi $ translation form factors relevant to this semileptonic decay, then the branching ratios of ${\bar{B}}_{s}^{0}\to \phi {l}^{+}{l}^{-}$ (l=e, μ, τ) decays are calculated with the form factors obtained here. Our result for the branching ratio of ${\bar{B}}_{s}^{0}\to \phi {\mu }^{+}{\mu }^{-}$ agree very well with the recent experimental data. For the unmeasured decay modes such as ${\bar{B}}_{s}^{0}\to \phi {e}^{+}{e}^{-}$ and ${\bar{B}}_{s}^{0}\to \phi {\tau }^{+}{\tau }^{-}$, we give theoretical predictions.     

Seawater—A test of multicomponent electrolyte solution theories. I. The apparent equivalent volume,expansibility, and compressibility of artificial seawater

The apparent equivalent volume _V, expansibility _E, and compressibility _K of an artificial seawater solution containing10 ionic components (Na⁺, Mg²⁺, Ca²⁺, K⁺, Sr²⁺, Cl^–, SO ₄ ^2– , HCO ₃ ^– , Br^–, and F^–) and one nonionic component (H₃BO₃) has been determined from0 to40°C (in5° intervals) and from0.1 to0.8 m ionic strength at1 atm. The concentration dependence (I_v=volume ionic strength) of the _V's, _E's, and _K's have been examined by using a Masson-type equation, = ^° +S'I _V ^1/2, and a Redlich-type equation, = ^° +SI _V ^1/2 +BI _V, where ^° is the infinite-dilution value, S is the empirical Masson slope, S is the theoretical Debye-Hückel slope, and B is an empirical deviation constant. By using Young's rule, = E_i(i), the apparent equivalent volumes, expansibilities, and compressibilities for sea salt have been estimated from the ionic and nonionic components making up the mixture. The estimated apparent molal quantities agree very well with the directly measured values providing the concentration terms, S _i and B_i, are weighted according to the methods of Wood and Reilly.Contribution Number 1599 from the University of Miami.     

Tafel slopes from first principles

Tafel slopes for multistep electrochemical reactions are derived from first principles. The derivation takes place in two stages. First, Dirac’s perturbation theory is used to solve the Schrödinger equation. Second, current–voltage curves are obtained by integrating the single-state results over the full density of states in electrolyte solutions. Thermal equilibrium is assumed throughout. Somewhat surprisingly, it is found that the symmetry factor that appears in the Butler–Volmer equation is different from the symmetry factor that appears in electron transfer theory, and a conversion formula is given. Finally, the Tafel slopes are compiled in a convenient look-up table.     

非线性光学研究水及电解质水溶液界面——空气/电解质水溶液界面特定阴阳离子效应

水及电解质溶液界面在物理、化学、环境及生物等各种过程中扮演着至关重要的角色。百年来科学家用各种实验及理论方法研究水及电解质溶液界面,试图理解其界面的结构及动力学。最近的实验和理论研究表明离子能够影响电解质水溶液界面结构,可极化性大的阴离子甚至会在界面富集。本文综述了我们研究组近年来利用二阶非线性光学方法--非共振的二次谐波与和频振动光谱研究水及电解质溶液界面的进展。首先我们研究了空气/纯水界面非共振二次谐波信号的来源,研究结果证明了空气/纯水界面非共振二次谐波信号完全可以归结为电偶极贡献,为此方法在电解质溶液界面的研究奠定了基础。同时,用偏振及对称性分析对空气/纯水界面和频振动光谱峰进行了归属,提供了纯水/空气界面结构新的物理图像。在此基础上,我们对几种电解质水溶液界面进行了深入研究,结果证明不仅可极化性大的离子会在水界面富集,并使界面层增厚,可极化性小的阴离子对界面层厚度也有影响,甚至阳离子也会在一定程度上影响界面水分子结构。     

电喷雾质谱在寡糖序列分析中的应用

选取具有不同结构特征的N-糖链、硫酸软骨素寡糖、人乳寡糖以及海洋来源的壳寡糖、褐藻胶寡糖、卡拉胶寡糖和硫酸岩藻寡糖等,对电喷雾质谱在寡糖的主链序列、分支位点、硫酸基取代位置确定、单糖组成和聚合度分析等方面的应用技术及碎片离子的断裂规律进行了总结.根据相邻同类碎片离子之间的质荷比差值可初步判断寡糖的单糖组成类型;通过与色谱分离技术联用或衍生化方法可提高寡糖的分辨率和离子化效率,并测得寡糖的分子量及聚合度;借助串联质谱及对寡糖还原端的特异性标记,可获得寡糖的还原端残基和部分序列信息;根据寡糖产生的特征碎片离子及其丰度大小可判断残基的特定位置和类型.另外,寡糖的分支通常作为一个整体发生糖苷键断裂或产生D离子,据此可判断分支点的位置;根据硫酸寡糖产生的特异性跨环断裂碎片,可以确定硫酸基的连接位置.这些规律和方法的总结为未知寡糖的结构和序列的分析提供了启发和指导.     

土壤淋溶柱色谱中同系物、氯代苯保留值与流动相组成、沸点的交点规律

基于土壤淋溶柱色谱符合logk'-ψ的线性保留方程,在同系物（正构烷基苯、甲基苯）和氯代苯中,同类溶质与固定相（土壤）和淋洗剂（甲醇-水）有相似的作用方式,所以溶质保留值（logk'）与淋洗剂有机调节剂浓度间存在浓度交点,与沸点间存在沸点交点规律,并用实验进行了验证。     

Quantum Attacks on Sum of Even–Mansour Construction with Linear Key Schedules

Shinagawa and Iwata are considered quantum security for the sum of Even–Mansour (SoEM) construction and provided quantum key recovery attacks by Simon’s algorithm and Grover’s algorithm. Furthermore, quantum key recovery attacks are also presented for natural generalizations of SoEM. For some variants of SoEM, they found that their quantum attacks are not obvious and left it as an open problem to discuss the security of such constructions. This paper focuses on this open problem and presents a positive response. We provide quantum key recovery attacks against such constructions by quantum algorithms. For natural generalizations of SoEM with linear key schedules, we also present similar quantum key recovery attacks by quantum algorithms (Simon’s algorithm, Grover’s algorithm, and Grover-meet-Simon algorithm).