Some mathematical aspects of the scaling limit of critical two-dimensional systems

It has been observed long ago that many systems from statistical physics behave randomly on macroscopic level at their critical temperature. In two dimensions, these phenomena have been classified by theoretical physicists thanks to conformal field theory, that led to the derivation of the exact value of various critical exponents that describe their behavior near the critical temperature. In the last couple of years, combining ideas of complex analysis and probability theory, mathematicians have constructed and studied a family of random fractals (called ‘Schramm-Loewner evolutions’ or SLE) that describe the only possible conformally invariant limits of the interfaces for these models. This gives a concrete construction of these random systems, puts various predictions on a rigorous footing, and leads to further understanding of their behavior. The goal of this paper is to survey some of these recent mathematical developments, and to describe a couple of basic underlying ideas. We will also briefly describe some very recent and ongoing developments relating SLE, Brownian loop soups and conformal field theory.     

Introduction to biology and chromosomal instabilities in cancer

The recent decade has witnessed a surge of physicists to biology. Some of the activities of the participating groups focus on bona fide physics questions, posed on biological systems (such as the physics of molecular motors, for example). Another kind of research in which physicists take part alongside computer scientists and applied mathematicians, deals with questions that are of direct interest to biologists; they come under the umbrella of computational and systems biology. The topic of these lectures lies at the most biological end of this spectrum, addressing problems of clinical relevance which were posed and initiated by biologists.The objective of these lectures is to help the curious physicist to learn and to understand more about this emerging, highly interdisciplinary field of research, by providing brief introductions to molecular biology and cancer research. This is followed by a cursory review of some recent research done by the “Domany group” and its collaborations with biological and clinical labs. Furthermore, we mention (mainly in footnotes) a small subset of studies in which physicists have contributed to this field during the past years. A more detailed review of recent contributions by physicists is beyond the scope of this introductory text.The introductory nature of these lecture notes naturally induces a strong bias regarding publications cited; consequently, these lecture notes do not provide a fair, historically correct and updated review of relevant literature.     

A unified model for price return distributions used in econophysics

For a decade, a new theoretical movement called “econophysics” has been initiated by some physicists who began to publish articles devoted to the study of economic and financial phenomena. Since then, econophysicists have written a very prolific literature about the way of characterizing the evolution of financial prices. Today, there is an “extreme diversity” of models recently developed by econophysicists whose research is sometimes presented as an ill-defined field. The objective of this paper is precisely to provide a unified framework in order to contribute to unify econophysics and to base this new field on shared scientific standards.     

复杂网络研究概述

近年来，真实网络中小世界效应和无标度特性的发现激起了物理学界对复杂网路的研究热潮．复杂网络区别于以前广泛研究的规则网络和随机网络最重要的统计特征是什么?物理学家研究复杂网络的终极问题是什么?物理过程以及相关的物理现象对拓扑结构是否敏感?物理学家进入这一研究领域的原因和意义何在?复杂网络研究领域将来可能会向着什么方向发展?文章围绕上述问题，从整体上概述了复杂网络的研究进展．     

正电子偶素(o-Ps)寿命困惑及其最终解决

正电子偶素o-Ps是由电子和正电子组成的纯轻子束缚系统，o-Ps在真空中的寿命可由量子电动力学进行精确的理论计算，但长期以来理论值和实验测量值之间存在较大的偏差，为了解决这一问题，理论和实验物理学经过长期共同努力，最终于近年解决了o-Ps寿命困惑．文章简要介绍了正电子偶素o-Ps寿命理论值和实验值之间不一致的历史状况和最近的实验技术的改进以及该问题的最终解决情况，并重点介绍了Tokyo实验组和Michigan实验组的最新结果．     

A further link(s) with inequivalent representations in quantum field theory

In recent years it has become more apparent how useful inequivalent representations of the CCR and CAR in quantum field theory may be in describing and explaining physical phenomena, and several properties and concepts have been stated, referred to, and/or developed in the literature on these ideas. In this paper, some of these are reviewed, and some further properties and concepts are developed as further links in understanding these inequivalent representations in quantum field theory. One of these is a statement as to what actually breaks down in some field theories in the transformation between representations which are unitarily inequivalent. This is developed using the language and ideas of point quantum mechanical invariance, since this should be more familiar to a much larger number of physicists. Also, a statement on state expectation values is developed which can be used as a criterion for the occurrence of inequivalent representations of the CCR and CAR in field theories.     

Interrogating the Legend of Einstein's “Biggest Blunder”

It is well known that, following the emergence of the first evidence for an expanding universe, Albert Einstein banished the cosmological constant term from his cosmology. Indeed, he is reputed to have labelled the term, originally introduced to the field equations of general relativity in 1917 in order to predict a static universe, his “biggest blunder.” However, serious doubts about this reported statement have been raised in recent years. We interrogate the legend of Einstein’s “biggest blunder” statement in the context of our recent studies of Einstein’s cosmology in his later years. We find that the remark is highly compatible with Einstein’s cosmic models of the 1930s, with his later writings on cosmology, and with independent reports by at least three physicists. We conclude that there is little doubt that Einstein came to view the introduction of the cosmological constant term as a serious error and that he very likely labelled the term his “biggest blunder” on at least one occasion. This finding may be of some relevance for those theoreticians today who seek to describe the recently discovered acceleration in cosmic expansion without the use of a cosmological constant term.     

Local ζ-Function Techniques vs. Point-Splitting Procedure: A Few Rigorous Results

Some general properties of local ‘-function procedures to renormalize some quantities in D-dimensional (Euclidean) Quantum Field Theory in curved background are rigorously discussed for positive scalar operators mj + V(x) in general closed D-manifolds, and a few comments are given for nonclosed manifolds too. A general comparison is carried out with respect to the more known point-splitting procedure concerning the effective Lagrangian and the field fluctuations. It is proven that, for D>1, the local ‘-function and point-splitting approaches lead essentially to the same results apart from some differences in the subtraction procedure of the Hadamard divergences. It is found that the ‘ function procedure picks out a particular term w₀(w,y) in the Hadamard expansion. The presence of an untrivial kernel of the operator mj + V(x) may produce some differences between the two analyzed approaches. Finally, a formal identity concerning the field fluctuations, used by physicists, is discussed and proven within the local ‘-function approach. This is done also to reply to recent criticism against ‘ function techniques.     

高迁移率二维电子系统中微波辐射引起的磁阻振荡和零电阻

一年以前 ,人们惊奇地发现 :在相当弱的磁场中 ,并不太强的微波辐照就可以使二维半导体的磁阻产生强烈的振荡 ,振幅的最大值可超过无辐照磁阻值的十几倍 ,最小值可以一直降到零 .全世界众多的凝聚态物理学家争相聚焦到这个领域 ,进行了许多实验和理论研究 ,企图弄清这一意外发现的机理 .经过一年多的努力 ,人们已经掌握了这个现象更多的细节 ,对其物理机制也有了初步了解 .但深入的实验和理论探索可能还要继续相当一段时间 .文章将对这个物理现象及相关的理论模型 ,尤其是目前得到较多赞同的光子辅助磁输运模型 ,作一简单的介绍 .     

Physics of particulate flows: From sand avalanche to active suspensions in plants

Flows of granular media in air or in a liquid have been a research field for physicists for several decades. Sometimes solid, sometimes liquid, these particulate materials exhibit peculiar behaviors, which have motivated many studies at the frontiers between nonlinear physics, soft matter physics and fluid mechanics. This paper presents a summary of the recent advances in the field, with a focus on the development of continuous approaches, which make it possible to treat granular media as a complex fluid and to develop a granular hydrodynamics. We also discuss how the better understanding of granular flows we have today may help to address more complex materials, such as colloidal suspensions or some biological systems.     

半导体量子点中极化子的跃迁能量

研究了半导体量子点中极化子的激发态性质。采用Huybrechts线性组合算符和幺正变换方法,计算了量子点中极化子的振动频率、基态能量、第一激发态能量、由第一激发态向基态的跃迁能量和跃迁频率。分别讨论了电子-LO声子在强弱两种耦合情况下极化子的跃迁能量和跃迁频率。数值计算结果表明,跃迁能量ΔE和跃迁频率ω均随量子点有效受限长度l₀的增加而减少,且随电子-声子耦合强度α的增加而减少。     

Sloppy-model universality class and the Vandermonde matrix

In a variety of contexts, physicists study complex, nonlinear models with many unknown or tunable parameters to explain experimental data. We explain why such systems so often are sloppy: the system behavior depends only on a few "stiff" combinations of the parameters and is unchanged as other "sloppy" parameter combinations vary by orders of magnitude. We observe that the eigenvalue spectra for the sensitivity of sloppy models have a striking, characteristic form with a density of logarithms of eigenvalues which is roughly constant over a large range. We suggest that the common features of sloppy models indicate that they may belong to a common universality class. In particular, we motivate focusing on a Vandermonde ensemble of multiparameter nonlinear models and show in one limit that they exhibit the universal features of sloppy models.     

Growth of rough surfaces

The growth of objects with rough surfaces is a common phenomenon. We describe several models used in the study of the temporal evolution of fluctuating interfaces and then we explain the dynamical scaling in this class of growth models with self-affine surfaces. The recent progress in this field is reviewed. Much emphasis is put on roughness properties and in particular on a possible kinetic roughening transition — a nonequilibrium analog of the thermal roughening transition. Both analytical and numerical results for scaling exponents are summarized and indications of a phase transition in some models are discussed.     

A statistical physics view of financial fluctuations: Evidence for scaling and universality

The unique scaling behavior of financial time series have attracted the research interest of physicists. Variables such as stock returns, share volume, and number of trades have been found to display distributions that are consistent with a power-law tail. We present an overview of recent research joining practitioners of economic theory and statistical physics to try to understand better some puzzles regarding economic fluctuations. One of these puzzles is how to describe outliers, i.e. phenomena that lie outside of patterns of statistical regularity. We review recent research, which suggests that such outliers may not in fact exist and that the same laws seem to govern outliers as well as day-to-day fluctuations.     

The politics of physicists' social models

I give an overview of the topic of this dossier, the “applications of (statistical) physics to social sciences at large.” I discuss several examples of simple social models put forward by physicists and examine their interest. I argue that while they may be conceptually useful to correct our intuitive models of social mechanisms, their relevance for real social systems is moot. What is more, since physicists have always needed to ‘tame’ the world inside laboratories to make their models relevant, I suggest that social modeling might be linked to human taming, a smashing political project.     

Midisuperspace Models of Canonical Quantum Gravity

A midisuperspace model is a field theoryobtained by symmetry reduction of a parent gravitationaltheory. Such models have proven useful for exploring theclassical and quantum dynamics of the gravitational field. I present three recent classes ofresults pertinent to canonical quantization of vacuumgeneral relativity in the context of midisuperspacemodels. (1) I give necessary and sufficient conditions such that a given symmetry reduction can beperformed at the level of the Lagrangian or Hamiltonian.(2) I discuss the Hamiltonian formulation of modelsbased upon cylindrical and toroidal symmetry. In particular, I explain how these models can beidentified with parametrized field theories of wavemaps; thus a natural strategy for canonical quantizationis available. (3) The quantization of a parametrized field theory, such as the midisuperspace modelsconsidered in (2), requires construction of a quantumfield theory on a fixed (flat) spacetime that allows fortime evolution along arbitrary foliations of spacetime. I discuss some recent results on thepossibility of finding such a quantum fieldtheory.     

Recent mathematical developments in the Skyrme model

In this review we present a pedagogical introduction to recent, more mathematical developments in the Skyrme model. Our aim is to render these advances accessible to mainstream nuclear and particle physicists. We start with the static sector and elaborate on geometrical aspects of the definition of the model. Then we review the instanton method which yields an analytical approximation to the minimum energy configuration in any sector of fixed baryon number, as well as an approximation to the surfaces which join together all the low energy critical points. We present some explicit results for B=2. We then describe the work done on the multibaryon minima using rational maps, on the topology of the configuration space and the possible implications of Morse theory. Next we turn to recent work on the dynamics of Skyrmions. We focus exclusively on the low energy interaction, specifically the gradient flow method put forward by Manton. We illustrate the method with some expository toy models. We end this review with a presentation of our own work on the semi-classical quantization of nucleon states and low energy nucleon–nucleon scattering.     

从统计物理学看复杂网络研究

从统计物理学来看,网络是一个包含了大量个体及个体之间相互作用的系统。本文从统计物理学的角度整理与总结了复杂网络目前的主要研究结果,并对将来的研究工作做了一个展望。文章把网络分为三个层次———无向网络、有向网络与加权网络,对不同网络的静态几何量研究的现状分别做了综述,并结合网络机制模型设计与评价的需要,提出了新的有待研究的静态几何量;对网络机制模型做了总结与分析,提出了有待解决的关于双向幂律网络的机制模型的问题;部分地概括了网络演化性质,网络的结构稳定性以及网络上的动力学模型的研究。然后,以我们目前正在进行的两个方面的工作—科学家网络和产品生产关系网络—为例,粗略地介绍了网络研究在一些实际问题中的应用。最后,作为一个简单的补充和索引,我们整理了复杂网络研究中部分常用的解析与数值计算的方法。