Questions in Wave Turbulence and Quantum Kinetic Theories

波湍流和量子动力学理论中的问题

基本信息

批准号：
2305523
负责人：
Minh-Binh Tran
金额：
$ 10.95万
依托单位：
Texas A&M University
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2022
资助国家：
美国
起止时间：
2022-11-01 至 2023-05-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=2305523&HistoricalAwards=false
关键词：
Questions Wave Turbulence Quantum Kinetic

项目摘要

This research is devoted to developing mathematical methods for studying two different classes of physical phenomena: wave turbulence and quantum kinetics. Wave turbulence is manifested in many physical systems, including familiar water waves, water surface gravity and capillary waves, and a great variety of waves in plasmas (in particular, in fusion devices). A Bose-Einstein condensate is a state of matter that was first predicted theoretically in 1924 and produced experimentally in 1995. While quantum phenomena are exhibited on micro-scales, and nature is well described on macro-scales by classical mechanics, for a Bose-Einstein condensate macroscopic quantum phenomena become apparent. The quantum kinetic theory that describes some physical properties of this state of matter is the second subject of this research. Although wave turbulence and quantum kinetics are dramatically different as physical phenomena, their mathematical description uses similar equations. Despite the widespread applications of these kinetic equations, little is known rigorously in this field. The aim of the project is to develop mathematical techniques and apply them to concrete physical situations, leading to a more profound understanding of both wave turbulence and quantum kinetics.The project is aimed at developing the theory of the existence, uniqueness, finite-time condensation, and relaxation to equilibrium for strong solutions of the kinetic equations. The principal investigator will address the local-in-time existence via techniques of harmonic analysis and novel Strichartz-type estimates. For important questions related to 3-wave wave turbulence, regularity theory for the kinetic equation with a particular broadening (regularization) of the resonance set will be used. This research project is informed by several sub-fields of mathematics, physics, and chemistry, and the work has potential applications in optical turbulence, oceanography and atmospheric sciences, and quantum physics.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

这项研究致力于开发数学方法来研究两种不同类别的物理现象：波湍流和量子动力学。波湍流在许多物理系统中都表现出来，包括熟悉的水波，水表面重力和毛细血管波，以及等离子体中的各种波浪（尤其是在融合设备中）。 Bose-Einstein凝结物是一种物质状态，在1924年在理论上首先预测，并于1995年在实验中产生。虽然在微尺度上展示了量子现象，并且在宏观尺度上通过经典力学很好地描述了Bose-Interical机制，但对于Bose-Interical机制，用于Bose-Eintein凝聚力量量子量量子量子。描述这种物质状态的某些物理特性的量子动力学理论是这项研究的第二个主题。尽管波湍流和量子动力学与物理现象大不相同，但它们的数学描述使用了相似的方程式。尽管这些动力学方程的广泛应用，但在这一领域中鲜为人知。该项目的目的是开发数学技术并将其应用于具体的物理情况，从而更深入地了解波湍流和量子动力学。该项目旨在发展存在，独特性，有限时间的耐期和放松的理论，以使动力学方程的强烈解决方案平衡。首席研究者将通过谐波分析技术和新颖的strichartz型估计来解决当地的存在。对于与3波波湍流相关的重要问题，将使用具有特定拓宽（正则化）的动力学方程的规律性理论。该研究项目由数学，物理和化学的几个子场所得知，这项工作在光学湍流，海洋学和大气科学和量子物理学方面具有潜在的应用。这项奖项反映了NSF的法定任务，并被认为是使用该基金会的知识功能和广泛影响的评估来审查CRITERIA的评估。