Quantum monte carlo with a stochastic potential solver
Das, Dyutiman
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https://hdl.handle.net/2142/33761
Description
Title
Quantum monte carlo with a stochastic potential solver
Author(s)
Das, Dyutiman
Issue Date
2005
Director of Research (if dissertation) or Advisor (if thesis)
Martin, Richard M.
Department of Study
Physics
Discipline
Physics
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Quantum Monte Carlo (QMC)
potential
Algorithm
Language
en
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 modi ed \Walk On Spheres""(WOS) algorithm using Green's function techniques, which can effciently 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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