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Interference in complex quantum systems : from localization in high-dimensional lattices to surface spin echo with molecules

University of British Columbia

This thesis considers (1) novel manifestations and applications of quantum interference in complex systems and (2) development of new approaches to study complex quantum systems. First, I examine a general model of particles with long-range hopping amplitudes. For at least 30 years, it has been widely accepted that these particles do not undergo Anderson localization in 3D lattices. We show that these particles do undergo Anderson localization in 3D lattices if their hopping amplitudes are isotropic. In contrast, particles with anisotropic long-range hopping appear to follow the widely held expectations. We show these results by demonstrating that cooperative shielding extends to 3D cubic lattices with isotropic long-range hopping, but not with anisotropic long-range hopping and by computing the scaling behaviour of participation ratios and energy level statistics. Secondly, I develop a fully quantum mechanical model of molecular surface spin-echo experiments, which study surface properties and dynamics by scattering molecules off the sample surface. This model, based on the transfer matrix method, incorporates molecular hyperfine degrees of freedom, allows for the efficient calculation of the experimental signal given a molecule-surface scattering matrix, and permits us to begin addressing the inverse scattering problem. This fully quantum model is required to properly describe these experiments as the semi-classical methods used to describe experiments using helium-3 atoms do not take magnetic-field induced momentum changes into account. We apply our method to the case of ortho-hydrogen and then apply Bayesian optimization to determine the molecule-surface scattering matrix elements from a calculated signal, for a scattering matrix defined by three parameters. Our work sets the stage for Bayesian optimization to solve the inverse scattering problem for these experiments. Finally, I propose using Bayesian model calibration to improve the convergence of Monte Carlo calculations in regions where the sign problem or critical slowing down are an issue. Specifically, Bayesian model calibration would correct poorly converged Monte Carlo calculations with the information from a small number of well-converged Monte Carlo calculations. As a simple proof of principle demonstration, we apply Bayesian model calibration to a diagrammatic Monte Carlo calculation of the scattering length of a spherical potential barrier.

Text

2019-09-04

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/71600

Chemistry

University of British Columbia

UBCV

http://creativecommons.org/licenses/by-nc-nd/4.0/