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

这是一个响应提交给信息技术研究（ITR）倡议的（小）提案的奖项。 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处理。 该研究的重点是问题，可以减少到本征值问题的解决方案，其中一个可以使用和开发量子蒙特卡罗方法没有不受控制的approximations.In临界现象，多个尺度产生的相关长度和弛豫时间的发散。 对于弱束缚的团簇，本研究的量子力学组成部分，强非谐性与随之而来的松弛性产生了多重长度尺度。 在这里，薛定谔方程的解决方案提出了计算的挑战。本研究将发展新的计算方法，以获得弱束缚团簇的量子力学谱。 特别是，它解决了一个问题，在1997年被确定为一个重要的，未解决的问题，在集群物理，即。小4He集群的束缚态能量的计算。 这些团簇发现自己处于连续解离跃迁附近，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，目标是进行高精度计算的动态临界指数，特别是将用于高精度测试的扩展标度关系提出的二维XY模型。 这项工作是理论上的兴趣领域的动力学临界现象，并有影响的研究超导薄膜，约瑟夫森结阵列，和4He膜。这是一个响应提交给信息技术研究（ITR）倡议的（小）提案的奖项。 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处理。 研究的重点是可以减少到本征值问题的解决方案，其中一个可以使用和开发量子蒙特卡罗方法没有不受控制的近似的问题。 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以测试标度关系。 对于弱束缚的团簇，这一研究的量子力学组成部分和化学的极大兴趣，强烈的非谐性与随之而来的松软性产生了多种长度尺度。 这项研究的组成部分将与伯克利的理论化学小组合作完成。

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.***