Mathematical Studies in Quantum Dynamics of Matter and Radiation

物质和辐射的量子动力学的数学研究

基本信息

  • 批准号:
    7901-2012
  • 负责人:
  • 金额:
    $ 2.19万
  • 依托单位:
  • 依托单位国家:
    加拿大
  • 项目类别:
    Discovery Grants Program - Individual
  • 财政年份:
    2015
  • 资助国家:
    加拿大
  • 起止时间:
    2015-01-01 至 2016-12-31
  • 项目状态:
    已结题

项目摘要

At energy scales common on Earth, the building blocks of matter are electrons and nuclei, with interactions mediating by quantum electro-magnetic field, as well as Coulomb force. The dynamic of the total system - particles and fields - is given by a well-defined evolution equation - the Schroedinger equation. Constructing the mathematical apparatus describing this dynamic is the main thrust of our research in the next several years. We will address a wide gamut of issues, from properties of a single electron, or more precisely the electron surrounded by an induced cloud of photons, to emission and absorption of radiation by atoms and molecules, to behaviour of large aggregates of atoms forming coherent, macroscopic structures (say, localized structures like Bose-Einstein condensates or extended ones like solid crystals), or more generally some continuous medium, with quantized collective oscillations (mechanical or elastic waves), called phonons. The processes we are interested in are "irreversible", accompanied by information loss at infinity. The issues described above underlie the structure and properties of matter as we experience it. Not surprisingly, they have garnered a disproportionate number of Nobel prizes in Physics and Chemistry. Nevertheless the mathematical apparatus dealing with them is only in the initial stages of construction, especially compared with the mathematical techniques developed in the last few centuries to tackle problems of classical physics. However the pace is quickly picking up. We expect that in the next few years, the analysis of evolution equations of the type appearing in this project and the corresponding nano-, meso- and macroscopic approximations will grow into a sizable area of pure and applied mathematics. I am confident that jointly with my collaborators (including my past and present graduate students and postodcs) I will be able to make substantial contributions to this development.
在地球上常见的能量尺度下,物质的组成部分是电子和原子核,相互作用由量子电磁场和库仑力介导。整个系统的动力学-粒子和场-由一个定义明确的演化方程-薛定谔方程给出。构建描述这种动态的数学装置是我们未来几年研究的主要方向。 我们将讨论一系列广泛的问题,从单个电子的性质,或者更准确地说,被诱导的光子云包围的电子,到原子和分子的辐射发射和吸收,再到形成相干宏观结构的原子大聚集体的行为。(比如说,像玻色-爱因斯坦凝聚体这样的局部结构,或者像固体晶体这样的扩展结构),或者更一般地说,一些连续介质,量子化的集体振荡(机械波或弹性波),称为声子。我们感兴趣的过程是“不可逆的”,伴随着信息在无穷大的损失。 上述问题是我们所经历的物质结构和性质的基础。毫不奇怪,它们获得了不成比例的诺贝尔物理学奖和化学奖。然而,处理这些问题的数学工具还只是处于初步的建设阶段,特别是与过去几个世纪中为解决经典物理学问题而发展起来的数学技术相比。 然而,步伐正在迅速加快。我们预计,在未来几年内,在这个项目中出现的类型的演化方程和相应的纳米,介观和宏观近似的分析将成长为一个相当大的纯数学和应用数学领域。 我相信,与我的合作者(包括我过去和现在的研究生和博士后)一起,我将能够为这一发展做出重大贡献。

项目成果

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Sigal, IsraelMichael其他文献

Sigal, IsraelMichael的其他文献

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{{ truncateString('Sigal, IsraelMichael', 18)}}的其他基金

Mathematical Studies of Quantum Dynamics of Matter and Radiation
物质和辐射的量子动力学的数学研究
  • 批准号:
    RGPIN-2017-06588
  • 财政年份:
    2021
  • 资助金额:
    $ 2.19万
  • 项目类别:
    Discovery Grants Program - Individual
Mathematical Studies of Quantum Dynamics of Matter and Radiation
物质和辐射的量子动力学的数学研究
  • 批准号:
    RGPIN-2017-06588
  • 财政年份:
    2020
  • 资助金额:
    $ 2.19万
  • 项目类别:
    Discovery Grants Program - Individual
Mathematical Studies of Quantum Dynamics of Matter and Radiation
物质和辐射的量子动力学的数学研究
  • 批准号:
    RGPIN-2017-06588
  • 财政年份:
    2019
  • 资助金额:
    $ 2.19万
  • 项目类别:
    Discovery Grants Program - Individual
Mathematical Studies of Quantum Dynamics of Matter and Radiation
物质和辐射的量子动力学的数学研究
  • 批准号:
    RGPIN-2017-06588
  • 财政年份:
    2018
  • 资助金额:
    $ 2.19万
  • 项目类别:
    Discovery Grants Program - Individual
Mathematical Studies of Quantum Dynamics of Matter and Radiation
物质和辐射的量子动力学的数学研究
  • 批准号:
    RGPIN-2017-06588
  • 财政年份:
    2017
  • 资助金额:
    $ 2.19万
  • 项目类别:
    Discovery Grants Program - Individual
Mathematical Studies in Quantum Dynamics of Matter and Radiation
物质和辐射的量子动力学的数学研究
  • 批准号:
    7901-2012
  • 财政年份:
    2014
  • 资助金额:
    $ 2.19万
  • 项目类别:
    Discovery Grants Program - Individual
Mathematical Studies in Quantum Dynamics of Matter and Radiation
物质和辐射的量子动力学的数学研究
  • 批准号:
    7901-2012
  • 财政年份:
    2013
  • 资助金额:
    $ 2.19万
  • 项目类别:
    Discovery Grants Program - Individual
Mathematical Studies in Quantum Dynamics of Matter and Radiation
物质和辐射的量子动力学的数学研究
  • 批准号:
    7901-2012
  • 财政年份:
    2012
  • 资助金额:
    $ 2.19万
  • 项目类别:
    Discovery Grants Program - Individual
Mathematical studies in quantum dynamics
量子动力学的数学研究
  • 批准号:
    7901-2007
  • 财政年份:
    2011
  • 资助金额:
    $ 2.19万
  • 项目类别:
    Discovery Grants Program - Individual

相似海外基金

Mathematical-Physical Studies of Quantum Many-Body Systems
量子多体系统的数理研究
  • 批准号:
    22K03474
  • 财政年份:
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    $ 2.19万
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Mathematical Studies of Quantum Dynamics of Matter and Radiation
物质和辐射的量子动力学的数学研究
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    2021
  • 资助金额:
    $ 2.19万
  • 项目类别:
    Discovery Grants Program - Individual
Mathematical Studies of Quantum Dynamics of Matter and Radiation
物质和辐射的量子动力学的数学研究
  • 批准号:
    RGPIN-2017-06588
  • 财政年份:
    2020
  • 资助金额:
    $ 2.19万
  • 项目类别:
    Discovery Grants Program - Individual
Mathematical studies in quantum nano-systems
量子纳米系统的数学研究
  • 批准号:
    540425-2019
  • 财政年份:
    2019
  • 资助金额:
    $ 2.19万
  • 项目类别:
    University Undergraduate Student Research Awards
Mathematical Studies of Quantum Dynamics of Matter and Radiation
物质和辐射的量子动力学的数学研究
  • 批准号:
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  • 财政年份:
    2019
  • 资助金额:
    $ 2.19万
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    Discovery Grants Program - Individual
Mathematical Studies of Quantum Dynamics of Matter and Radiation
物质和辐射的量子动力学的数学研究
  • 批准号:
    RGPIN-2017-06588
  • 财政年份:
    2018
  • 资助金额:
    $ 2.19万
  • 项目类别:
    Discovery Grants Program - Individual
Mathematical Studies of Quantum Dynamics of Matter and Radiation
物质和辐射的量子动力学的数学研究
  • 批准号:
    RGPIN-2017-06588
  • 财政年份:
    2017
  • 资助金额:
    $ 2.19万
  • 项目类别:
    Discovery Grants Program - Individual
Mathematical Studies of Fundamental Principles of Quantum Theory
量子理论基本原理的数学研究
  • 批准号:
    26247016
  • 财政年份:
    2014
  • 资助金额:
    $ 2.19万
  • 项目类别:
    Grant-in-Aid for Scientific Research (A)
Mathematical Studies in Quantum Dynamics of Matter and Radiation
物质和辐射的量子动力学的数学研究
  • 批准号:
    7901-2012
  • 财政年份:
    2014
  • 资助金额:
    $ 2.19万
  • 项目类别:
    Discovery Grants Program - Individual
Mathematical Studies in Quantum Dynamics of Matter and Radiation
物质和辐射的量子动力学的数学研究
  • 批准号:
    7901-2012
  • 财政年份:
    2013
  • 资助金额:
    $ 2.19万
  • 项目类别:
    Discovery Grants Program - Individual
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