Quantum Monte Carlo With a *Stochastic Poisson Solver
Das, Dyutiman
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https://hdl.handle.net/2142/80519
Description
Title
Quantum Monte Carlo With a *Stochastic Poisson Solver
Author(s)
Das, Dyutiman
Issue Date
2005
Doctoral Committee Chair(s)
Martin, Richard M.
Department of Study
Physics
Discipline
Physics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Physics, Condensed Matter
Language
eng
Abstract
"Quantum Monte Carlo (QMC) is an extremely powerful method to treat many-body systems. Usually QMC has been applied in cases where the interaction potential has a simple analytic form, like the 1/r Coulomb potential. However, in a complicated environment as in a semiconductor heterostructure, the evaluation of the interaction itself becomes a non-trivial problem. Obtaining the potential from any grid-based finite-difference method, for every walker and every step is unfeasible. We demonstrate an alternative approach of solving the Poisson equation by a classical Monte Carlo within the overall QMC scheme. We have developed a modified ""Walk On Spheres"" (WOS) algorithm using Green's function techniques, which can efficiently account for the interaction energy of walker configurations, typical of QMC algorithms. This stochastically obtained potential can be easily incorporated within popular QMC techniques like variational Monte Carlo (VMC) or diffusion Monte Carlo(DMC). We demonstrate the validity of this method by studying a simple problem, the polarization of a helium atom in the electric field of an infinite capacitor. Then we apply this method to calculate the singlet-triplet splitting in a realistic heterostructure device. We also outline some other prospective applications for spherical quantum dots where the dielectric mismatch becomes an important issue for the addition energy spectrum."
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