Topics in Theoretical and Mathematical Physics

理论与数学物理专题

基本信息

  • 批准号:
    0555313
  • 负责人:
  • 金额:
    $ 26.4万
  • 依托单位:
  • 依托单位国家:
    美国
  • 项目类别:
    Continuing Grant
  • 财政年份:
    2006
  • 资助国家:
    美国
  • 起止时间:
    2006-07-01 至 2011-06-30
  • 项目状态:
    已结题

项目摘要

Several areas of theoretical and mathematical physics are addressed. The physical applications are broadly ranging, although the techniques are mainly those of statistical and quantum mechanics. The quantization of discrete breathers is a priority. What began some years ago as an unexplained anomaly in the decay of luminescence in doped alkali halides, has blossomed into a general study of nonlinear interactions (related to solitons) both at the classical and quantum levels. The particular quantum issue that the PI expects to explore in yet greater depth, is the stability of these breathers against quantum decay. This has been studied both through numerical diagonalization in a phonon basis and through the use of the Feynman path integral. For the latter, the PI has exploited one of the most basic techniques of the path integral, the elimination of quadratic degrees of freedom (as Feynman did for the polaron), although once that was done, particular methods needed to be developed for this application. In work on nonequilibrium statistical mechanics new results on the relation between phase transitions and the eigenvectors of the transition matrix (for a stochastic process) have been found. A particular geometric construction, based on a limited number of eigenvectors, can be used to compute the probability that an arbitrary point in the state space reaches any particular basin of attraction. It can also be used to visualize the structure of metastable phases, particularly when they bear a hierarchical relation to one another (as is believed to obtain for spin glasses). As far as is known, this construction is new. Other work on nonequilibrium systems, for example, investigating the ways that reservoirs can induce complexity in open systems, is also planned. In fundamental areas of physics the PI will continue to explore time-related issues. Some are related to his 'opposite arrows' work of a few years ago, others deal with quantum transitions and experimental tests of theories of quantum measurement. A recent result of the PI on the equilibration of wave-packet spread in an interacting system, leads to general questions of whether the von Neumann entropy maximization that lies behind that result can also be invoked to established unanticipated low levels of entanglement with respect to other degrees of freedom. Besides its scientific content, this work has broad impact in two principal ways: public education on foundational issues (emanating from the PI's recent 'arrow of time' exposure), and on another front, unique cultural experiences for the several Clarkson undergraduates who have done, and will do, research at the optical crystals laboratory of the PI's collaborators in Prague.
讨论了理论和数学物理的几个领域。尽管这些技术主要是统计和量子力学的技术,但物理应用范围很广。离散呼吸的量化是一个优先事项。几年前,最初是掺杂碱金属卤化物中发光衰变的无法解释的异常现象,现已发展成为经典和量子水平上非线性相互作用(与孤子相关)的一般研究。 PI 期望更深入地探索的特定量子问题是这些呼吸器对抗量子衰变的稳定性。通过声子基中的数值对角化和使用费曼路径积分对此进行了研究。对于后者,PI 利用了路径积分最基本的技术之一,即消除二次自由度(正如费曼对极化子所做的那样),尽管一旦完成,就需要为此应用开发特定的方法。在非平衡统计力学的工作中,已经发现了相变与转变矩阵特征向量(对于随机过程)之间关系的新结果。基于有限数量的特征向量的特定几何构造可用于计算状态空间中的任意点到达任何特定吸引力盆地的概率。它还可用于可视化亚稳态相的结构,特别是当它们彼此具有层次关系时(据信自旋玻璃可以获得这种关系)。据了解,这个建筑是新的。还计划进行非平衡系统的其他工作,例如研究水库如何在开放系统中引起复杂性。在物理学的基础领域,PI 将继续探索与时间相关的问题。有些与他几年前的“相反箭头”工作有关,其他则涉及量子跃迁和量子测量理论的实验测试。 PI 最近关于交互系统中波包传播平衡的结果引发了一个普遍的问题:该结果背后的冯·诺依曼熵最大化是否也可以被调用来建立相对于其他自由度的意外低水平纠缠。除了其科学内容之外,这项工作在两个主要方面具有广泛的影响:对基础问题的公共教育(源于 PI 最近的“时间之箭”曝光),以及在另一个方面,为几位克拉克森本科生提供了独特的文化体验,他们已经在布拉格的 PI 合作者的光学晶体实验室进行了研究,并将进行研究。

项目成果

期刊论文数量(0)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)

数据更新时间:{{ journalArticles.updateTime }}

{{ item.title }}
{{ item.translation_title }}
  • DOI:
    {{ item.doi }}
  • 发表时间:
    {{ item.publish_year }}
  • 期刊:
  • 影响因子:
    {{ item.factor }}
  • 作者:
    {{ item.authors }}
  • 通讯作者:
    {{ item.author }}

数据更新时间:{{ journalArticles.updateTime }}

{{ item.title }}
  • 作者:
    {{ item.author }}

数据更新时间:{{ monograph.updateTime }}

{{ item.title }}
  • 作者:
    {{ item.author }}

数据更新时间:{{ sciAawards.updateTime }}

{{ item.title }}
  • 作者:
    {{ item.author }}

数据更新时间:{{ conferencePapers.updateTime }}

{{ item.title }}
  • 作者:
    {{ item.author }}

数据更新时间:{{ patent.updateTime }}

Lawrence Schulman其他文献

When Things Grow Many
当事物变得很多时
  • DOI:
  • 发表时间:
    2022
  • 期刊:
  • 影响因子:
    0
  • 作者:
    Lawrence Schulman
  • 通讯作者:
    Lawrence Schulman

Lawrence Schulman的其他文献

{{ item.title }}
{{ item.translation_title }}
  • DOI:
    {{ item.doi }}
  • 发表时间:
    {{ item.publish_year }}
  • 期刊:
  • 影响因子:
    {{ item.factor }}
  • 作者:
    {{ item.authors }}
  • 通讯作者:
    {{ item.author }}

{{ truncateString('Lawrence Schulman', 18)}}的其他基金

Topics in Theoretical and Mathematical Physics
理论与数学物理专题
  • 批准号:
    0099471
  • 财政年份:
    2001
  • 资助金额:
    $ 26.4万
  • 项目类别:
    Continuing Grant
Topics in Theoretical and Mathematical Physics
理论与数学物理专题
  • 批准号:
    9721459
  • 财政年份:
    1998
  • 资助金额:
    $ 26.4万
  • 项目类别:
    Continuing Grant
Topics in Theoretical and Mathematical Physics
理论与数学物理专题
  • 批准号:
    9316681
  • 财政年份:
    1994
  • 资助金额:
    $ 26.4万
  • 项目类别:
    Continuing Grant
Topics in Theoretical and Mathematical Physics
理论与数学物理专题
  • 批准号:
    9015858
  • 财政年份:
    1991
  • 资助金额:
    $ 26.4万
  • 项目类别:
    Continuing Grant
Topics in Path Integration and Nonequilibrium Statistical Mechanics (Physics)
路径积分和非平衡统计力学(物理)主题
  • 批准号:
    8811106
  • 财政年份:
    1988
  • 资助金额:
    $ 26.4万
  • 项目类别:
    Continuing Grant
Topics in Path Integration (Physics)
路径积分主题(物理)
  • 批准号:
    8518806
  • 财政年份:
    1986
  • 资助金额:
    $ 26.4万
  • 项目类别:
    Continuing Grant

相似海外基金

Workshop on Advances in Mathematical and Theoretical Biology
数学和理论生物学进展研讨会
  • 批准号:
    2234176
  • 财政年份:
    2023
  • 资助金额:
    $ 26.4万
  • 项目类别:
    Standard Grant
Mathematical and Quantitative Approaches to Generalizing the theoretical Model of Educational Inequality
推广教育不平等理论模型的数学和定量方法
  • 批准号:
    22K02372
  • 财政年份:
    2022
  • 资助金额:
    $ 26.4万
  • 项目类别:
    Grant-in-Aid for Scientific Research (C)
Core Support of the Board on Mathematical Sciences and Analytics and the Committee on Applied and Theoretical Statistics
数学科学与分析委员会和应用与理论统计委员会的核心支持
  • 批准号:
    2133303
  • 财政年份:
    2022
  • 资助金额:
    $ 26.4万
  • 项目类别:
    Continuing Grant
Theoretical and Practical Studies on the Development of Critical Thinking Through the Mathematical Modeling Processes
通过数学建模过程发展批判性思维的理论和实践研究
  • 批准号:
    21K02470
  • 财政年份:
    2021
  • 资助金额:
    $ 26.4万
  • 项目类别:
    Grant-in-Aid for Scientific Research (C)
Mathematical model of combustion in a narrow channel and its theoretical analysis
窄通道燃烧数学模型及其理论分析
  • 批准号:
    21K03353
  • 财政年份:
    2021
  • 资助金额:
    $ 26.4万
  • 项目类别:
    Grant-in-Aid for Scientific Research (C)
Theoretical Study of Mathematics Teacher Education in Scientific Faculties Based on Mathematical Literacy and Development of its method
基于数学素养的理科数学教师教育理论研究及其方法的发展
  • 批准号:
    20K03283
  • 财政年份:
    2020
  • 资助金额:
    $ 26.4万
  • 项目类别:
    Grant-in-Aid for Scientific Research (C)
Theoretical construction and real-world application of simultaneous search of robot body and motion intelligence based on mathematical model and demonstration analysis
基于数学模型和论证分析的机器人本体与运动智能同步搜索的理论构建与实际应用
  • 批准号:
    19K20371
  • 财政年份:
    2019
  • 资助金额:
    $ 26.4万
  • 项目类别:
    Grant-in-Aid for Early-Career Scientists
Mathematical Basis of the Theoretical Works of Giuseppe Tartini and its Background
朱塞佩·塔蒂尼理论著作的数学基础及其背景
  • 批准号:
    19K00164
  • 财政年份:
    2019
  • 资助金额:
    $ 26.4万
  • 项目类别:
    Grant-in-Aid for Scientific Research (C)
Theoretical and experimental study of controlling cardiac cell system dynamics using HL-1 mouse cardiomyocytes and a mathematical model
利用HL-1小鼠心肌细胞和数学模型控制心脏细胞系统动力学的理论和实验研究
  • 批准号:
    19K07290
  • 财政年份:
    2019
  • 资助金额:
    $ 26.4万
  • 项目类别:
    Grant-in-Aid for Scientific Research (C)
REU Site: Mathematical and Theoretical Biology Institute (MTBI)
REU 站点:数学与理论生物学研究所 (MTBI)
  • 批准号:
    1757968
  • 财政年份:
    2018
  • 资助金额:
    $ 26.4万
  • 项目类别:
    Standard Grant
{{ showInfoDetail.title }}

作者:{{ showInfoDetail.author }}

知道了