ITR: Solution of Eigenvalue Problems for Multi-Scale Phenomena by Quantum Monte Carlo Methods

ITR:量子蒙特卡罗方法解决多尺度现象的特征值问题

基本信息

  • 批准号:
    0218858
  • 负责人:
  • 金额:
    $ 43万
  • 依托单位:
  • 依托单位国家:
    美国
  • 项目类别:
    Standard Grant
  • 财政年份:
    2002
  • 资助国家:
    美国
  • 起止时间:
    2002-07-15 至 2007-06-30
  • 项目状态:
    已结题

项目摘要

This is an award made in response to a (small) proposal submitted to the Information Technology Research (ITR) initiative. The award is co-funded by the Divisions of Materials Research and Chemistry. The highly computational research concerns quantum mechanical and statistical mechanical problems in which a multiplicity of length or time scales renders approximate solutions inaccurate and exact numerical methods intractable. The research focuses on problems that can be reduced to the solution of eigenvalue problems for which one can use and develop quantum Monte Carlo methods without uncontrolled approximations.In critical phenomena, a multiplicity of scales arises from the divergence of the correlation length and the relaxation time. For weakly-bound clusters, the quantum mechanical component of this research, strong anharmonicity with the attendant floppiness yields a multiplicity of length scales. Here solution of the Schroedinger equation poses the computational challenge. This research will develop novel computational methods to obtain quantum mechanical spectra of weak-bound clusters. In particular, it addresses a problem that was identified in 1997 as an important, unsolved problem in cluster physics, viz. the computation of energies of bound states of small 4He clusters. These clusters find themselves in the vicinity of continuous dissociation transitions, where ground or excited state is about to merge with the continuous part of the spectrum, and the various length scales in turn go to infinity continuously. In the statistical mechanical portion of the research, the goal is to perform high accuracy computations of dynamical critical exponents, which in particular will be used in high precision tests of extended scaling relations proposed for the two-dimensional XY model. The work is of theoretical interest for the field of dynamical critical phenomena, and has implications for the study of superconducting films, Josephson junction arrays, and 4He films.%%%This is an award made in response to a (small) proposal submitted to the Information Technology Research (ITR) initiative. The award is co-funded by the Divisions of Materials Research and Chemistry. The highly computational research concerns quantum mechanical and statistical mechanical problems in which a multiplicity of length or time scales renders approximate solutions inaccurate and exact numerical methods intractable. The research focuses on problems that can be reduced to the solution of eigenvalue problems for which one can use and develop quantum Monte Carlo methods without uncontrolled approximations.The research deals with two complementary projects. In critical phenomena, a multiplicity of scales arises from the divergence of the correlation length and the relaxation time. Here high precision calculations will be done to test scaling relations. For weakly-bound clusters, the quantum mechanical component of this research and of great interest in chemistry, strong anharmonicity with the attendant floppiness yields a multiplicity of length scales. This component of the research will be done in collaboration with the theoretical chemistry group at Berkeley.***
这是对提交给信息技术研究(ITR)倡议的(小型)提案的回应。该奖项由材料研究和化学部门共同资助。高度计算的研究涉及量子力学和统计力学问题,其中长度或时间尺度的多样性使得近似解不准确,精确的数值方法难以解决。研究重点是可以简化为特征值问题的解的问题,可以使用和发展量子蒙特卡罗方法而不需要不受控制的近似。在临界现象中,由于相关长度和弛豫时间的发散,产生了多重尺度。对于弱束缚的星系团,本研究的量子力学组成部分,强非调和性与随之而来的软性产生了多重长度尺度。在这里,薛定谔方程的解提出了计算上的挑战。本研究将发展新的计算方法来获得弱束缚团簇的量子力学谱。特别是,它解决了一个在1997年被确定为团簇物理中一个重要的、未解决的问题,即小4He团簇束缚态能量的计算。这些团簇发现自己处于连续解离跃迁的附近,在那里基态或激发态即将与光谱的连续部分合并,并且各种长度尺度依次连续地走向无穷大。在研究的统计力学部分,目标是执行动态临界指数的高精度计算,特别是将用于二维XY模型的扩展缩放关系的高精度测试。这项工作对动力学临界现象领域具有理论意义,并对超导薄膜、约瑟夫森结阵列和4He薄膜的研究具有启示意义。这是对提交给信息技术研究(ITR)倡议的(小)提案的回应。该奖项由材料研究和化学部门共同资助。高度计算的研究涉及量子力学和统计力学问题,其中长度或时间尺度的多样性使得近似解不准确,精确的数值方法难以解决。研究重点是可以简化为特征值问题的解的问题,可以使用和发展量子蒙特卡罗方法而不需要不受控制的近似。这项研究涉及两个互补的项目。在临界现象中,由于相关长度和弛豫时间的发散,产生了多重尺度。这里将进行高精度计算来测试缩放关系。对于弱束缚团簇,本研究的量子力学组成部分和化学中的极大兴趣,与随之而来的软性的强非协调性产生了多重长度尺度。这部分研究将与伯克利的理论化学小组合作完成

项目成果

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M. Peter Nightingale其他文献

M. Peter Nightingale的其他文献

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{{ truncateString('M. Peter Nightingale', 18)}}的其他基金

Eigenvalue Problems in Quantum and Statistical Mechanics
量子和统计力学中的特征值问题
  • 批准号:
    9725080
  • 财政年份:
    1997
  • 资助金额:
    $ 43万
  • 项目类别:
    Continuing Grant
Computation Methods in Statistical and Quantum Mechanics
统计和量子力学的计算方法
  • 批准号:
    9214669
  • 财政年份:
    1993
  • 资助金额:
    $ 43万
  • 项目类别:
    Continuing Grant
Low-Dimensional Critical Phenomena and Wetting
低维临界现象和润湿
  • 批准号:
    8704730
  • 财政年份:
    1987
  • 资助金额:
    $ 43万
  • 项目类别:
    Continuing Grant
Low-Dimensional Critical Phenomena, and Wetting (Materials Research)
低维临界现象和润湿(材料研究)
  • 批准号:
    8406186
  • 财政年份:
    1984
  • 资助金额:
    $ 43万
  • 项目类别:
    Continuing Grant

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Analysis of Stochastic Neuronal Models Using Eigenvalue Numerical Solution Methods that Overcome the Curse of Dimensionality
使用特征值数值求解方法分析随机神经元模型,克服维数灾难
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Sixth International Workshop on Accurate Solution of Eigenvalue Problems
第六届特征值问题精确求解国际研讨会
  • 批准号:
    0539097
  • 财政年份:
    2005
  • 资助金额:
    $ 43万
  • 项目类别:
    Standard Grant
Solution of Eigenvalue Problems for Spheroidal Wave Equation, Lame Equation, and Ellipsoidal Wave Equation
球波方程、Lame方程和椭球波方程特征值问题的解
  • 批准号:
    13640128
  • 财政年份:
    2001
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    $ 43万
  • 项目类别:
    Grant-in-Aid for Scientific Research (C)
International Workshop on accurate Solution of Eigenvalue Problems, July 20-23, l998, Penn Stater Conference Center Hotel, University Park, PA
特征值问题精确解决国际研讨会,1998 年 7 月 20 日至 23 日,宾州州立大学会议中心酒店,宾夕法尼亚州大学公园
  • 批准号:
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  • 财政年份:
    1998
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Numerical Solution of Eigenvalue and Singular Value Problems with Applications
特征值和奇异值问题的数值解及其应用
  • 批准号:
    9732081
  • 财政年份:
    1998
  • 资助金额:
    $ 43万
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Postdoc: Stability Issues in the Parallel Solution of Certain Generalized Eigenvalue and Singular Value Problems
博士后:某些广义特征值和奇异值问题并行求解的稳定性问题
  • 批准号:
    9625912
  • 财政年份:
    1996
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Numerical Solution of Eigenvalue Problems and Related Least Squares Problems
特征值问题及相关最小二乘问题的数值解
  • 批准号:
    9424435
  • 财政年份:
    1995
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    $ 43万
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Numerical Solution of Eigenvalue Problems
特征值问题的数值解
  • 批准号:
    9201612
  • 财政年份:
    1992
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    $ 43万
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最小二乘特征值问题的数值求解
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