Semiclassical Analysis

半经典分析

• 批准号: 1201417
• 负责人: Maciej Zworski
• 金额: $ 26.5万
• 依托单位: University of California-Berkeley
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2012
• 资助国家: 美国
• 起止时间: 2012-07-01 至 2015-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1201417&HistoricalAwards=false
• 关键词: Semiclassical; Analysis

The PI studies mathematical problems motivated by quantum mechanics and wave propagation. His central interest is the study of scattering resonances. These appear in many guises: as poles of Green functions, zeros of zeta functions or modes of decay and oscillation of waves, and the setting of their study ranges from geometry and automorphic forms, to microelectromechanical systems in engineering. The PI searches unifying themes and investigates specific cases. Special recent focus has been chaotic scattering and the relation between objects in thermodynamic formalism and the distribution of quantum resonances.Waves encountered in experimental and theoretical studies have rates of oscillations and rates of decay. These two properties can be described by a single complex number with the real part corresponding to the rate of oscillations, and the imaginary part, to the rate of decay. In turn, these numbers appear as zeros of natural mathematical objects. In quantum mechanics, particles are described by wave functions, and waves with decay correspond to unstable particles. Classical/quantum correspondence suggests some subtle interplay between "classical" properties of the system and properties of waves. The PI investigates this in many settings, in particular when chaotic behaviour is present on the classical level.

PI研究了由量子力学和波传播促进的数学问题。他的核心利益是对散射共振的研究。这些出现在许多方向上：作为绿色功能的极点，Zeta功能的零，波浪的模式和波浪的振荡，其研究的设置范围从几何形状和自动形式到工程中的微电力系统。 PI搜索统一主题并调查特定案例。最近的特殊重点是混乱的散射以及热力学形式主义和量子共振的分布之间的物体之间的关系。实验和理论研究中遇到的电波具有振荡和衰减速率。这两个属性可以用一个单个复数数字描述，其实际部分与振荡速率以及虚拟部分相对应与衰减速率相对应。反过来，这些数字显示为自然数学对象的零。在量子力学中，粒子由波函数描述，具有衰减的波对应于不稳定的颗粒。经典/量子对应关系表明，系统的“经典”特性与波的特性之间存在一些微妙的相互作用。 PI在许多情况下进行了调查，特别是当经典层面存在混乱行为时。