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

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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.***