Conference on Recent Mathematical Advances in Classical, Quantum and Statistical Mechanics

经典、量子和统计力学最新数学进展会议

• 批准号: 1301706
• 负责人: Abdelmalek Abdesselam
• 金额: $ 1.5万
• 依托单位: University of Virginia Main Campus
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2012
• 资助国家: 美国
• 起止时间: 2012-12-01 至 2014-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1301706&HistoricalAwards=false
• 关键词: Conference; Recent; Mathematical; Advances; Classical

The conference "Recent Mathematical Advances in Classical, Quantum and Statistical Mechanics" will be held at the University of Virginia on March 8-9, 2013. The goal of the conference is to present a survey of some of the major recent results in the area of mathematical analysis which studies the evolution of physical systems with large or infinite number of degrees of freedom in a variety of settings while emphasizing ideas and techniques which are common to these settings. The subject of this conference is one of the most active in contemporary mathematical physics. The conference will bring together leading world-experts in such topics as KAM theory for partial differential equations, rearrangement inequalities in functional analysis, Anderson localization, the study of polaron systems and the non-equilibrium statistical mechanics of coupled anharmonic oscillators. The conference will provide a venue for the dissemination or recent results and methods in the area and will foster further advances in these important topics. A strong component of this conference is educational and aimed at disseminating recent advances in classical, quantum and statistical mechanics. Emphasis will be placed on encouraging interactions between senior and junior researchers. Special efforts will be made to invite and support graduate students, postdocs, as well as mathematicians from underrepresented groups. The study of the evolution of systems with infinite number of degrees of freedom is ubiquitous in modern science. In the situation pertaining to classical mechanics, a typical example is that of the evolution of a fluid where a degree of freedom essentially corresponds to the velocity of the fluid at some point in space. Since there are infinitely many such points one is looking at a complex system with infinitely many degrees of freedom in interaction. These give rise to nonlinear partial differential equations which feature in a huge number of applications such as the models used for weather prediction. In the quantum case, examples of such systems are the polaron systems which describe the motion of particles in an ionic crystal (structures similar to that of ordinary salt). Another example studied under the name of Anderson localization has to do with the motion of a quantum particle in interaction with a random medium. The latter is supposed to model, e.g., the impurities in a semiconductor. Finally, a third regime where systems with infinitely many degrees of freedom are the subject of very active study is that of statistical mechanics, in particular in the non equilibrium situation. An example of mathematical challenge in the area is to understand the conduction of heat or electricity, not in an ad hoc phenomenological description, but rather through a derivation from first principles: the basic laws of classical or quantum mechanics at the microscopic level.

“经典、量子和统计力学的最新数学进展”会议将于 2013 年 3 月 8 日至 9 日在弗吉尼亚大学举行。会议的目标是对数学分析领域的一些主要最新成果进行调查，这些结果研究各种环境中具有大量或无限自由度的物理系统的演化，同时强调这些环境中常见的思想和技术。这次会议的主题是当代数学物理学中最活跃的主题之一。会议将汇集偏微分方程的KAM理论、泛函分析中的重排不等式、安德森定位、极化子系统研究以及耦合非简谐振子的非平衡统计力学等领域的世界领先专家。会议将为传播该领域的最新成果和方法提供场所，并将促进这些重要主题的进一步进展。本次会议的一个重要组成部分是教育，旨在传播经典力学、量子力学和统计力学的最新进展。重点将放在鼓励高级和初级研究人员之间的互动。我们将特别努力邀请和支持研究生、博士后以及来自代表性不足群体的数学家。对无限自由度系统演化的研究在现代科学中无处不在。在与经典力学有关的情况下，一个典型的例子是流体的演化，其中自由度本质上对应于流体在空间中某个点的速度。由于存在无限多个这样的点，我们所看到的是一个具有无限多个交互自由度的复杂系统。这些产生了非线性偏微分方程，其在大量应用中具有特征，例如用于天气预报的模型。在量子情况下，此类系统的例子是极化子系统，它描述了离子晶体（结构类似于普通盐）中粒子的运动。以安德森局域化为名研究的另一个例子与量子粒子与随机介质相互作用的运动有关。后者应该模拟半导体中的杂质等。最后，具有无限多个自由度的系统是非常活跃的研究主题的第三种机制是统计力学，特别是在非平衡情况下。该领域数学挑战的一个例子是理解热或电的传导，不是通过临时的现象学描述，而是通过第一原理的推导：微观层面的经典或量子力学的基本定律。