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研究由量子力学和波传播激发的数学问题。他的主要兴趣是散射共振的研究。它们以多种形式出现：作为绿色函数的极点，zeta函数的零点或波的衰减和振荡模式，其研究范围从几何和自守形式到工程中的微机电系统。PI搜索统一的主题并调查具体案件。最近特别关注的是混沌散射和热力学形式主义中物体与量子共振分布之间的关系。在实验和理论研究中遇到的波有振荡率和衰减率。这两个性质可以用一个复数来描述，其中真实的部分对应于振荡速率，虚部对应于衰减速率。反过来，这些数字作为自然数学对象的零出现。在量子力学中，粒子由波函数描述，而具有衰变的波对应于不稳定的粒子。经典/量子对应表明系统的“经典”性质与波的性质之间存在某种微妙的相互作用。 PI在许多设置中对此进行了调查，特别是当经典水平上存在混沌行为时。