Bernardo Barbiellini, Robert S. Markiewicz, Jeffrey B. Sokoloff
Date of Award
Doctor of Philosophy
Department or Academic Unit
College of Arts and Sciences. Department of Physics.
Physics, Molecular physics, Stochastic Gradient Approximation (SGA), Quantum Monte Carlo (QMC)
Parallel processing (Electronic computers), Stochastic processes, Quantum dots, Wave functions
The Stochastic Gradient Approximation (SGA) is the natural extension of Quantum Monte Carlo (QMC) methods to the variational optimization of quantum wave function parameters. While many deterministic applications impose stochasticity, the SGA fruitfully takes advantage of the natural stochasticity already present in QMC in order to utilize a small number of QMC samples and approach the minimum more quickly by averaging out the random noise in the samples. The increasing efficiency of the method for systems with larger numbers of particles, and its nearly ideal scaling when running on parallelized processors, is evidence that the SGA is well suited for the study of nanoclusters. In this thesis, I discuss the SGA algorithm in detail. I also describe its application to both quantum dots, and to the Resonating Valence Bond wave function (RVB). The RVB is a sophisticated model of electronic systems that captures electronic correlation effects directly and that improves the nodal structure of quantum wave functions. The RVB is receiving renewed attention in the study of nanoclusters due to the fact that calculations of RVB wave functions have become feasible with recent advances in computer hardware and software.
Daniel Andrew Nissenbaum
Nissenbaum, Daniel Andres, "The stochastic gradient approximation: an application to li nanoclusters" (2008). Physics Dissertations. Paper 11. http://hdl.handle.net/2047/d10016466
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