#### Date Thesis Awarded

5-2015

#### Document Type

Honors Thesis

#### Degree Name

Bachelors of Science (BS)

#### Department

Physics

#### Advisor

Shiwei Zhang

#### Committee Member

Gina Hoatson

#### Committee Member

George Rublein

#### Abstract

We explore the existence of a residual population bias in Diffusion Monte Carlo algorithms. We develop a model problem, which mimics the single-particle, one dimensional simple harmonic oscillator of unitary ground state energy, to study these biases. We then apply an importance sampling algorithms with a population of a single random walker to calculate the ground state energy and wavefunction of our modeled system in cases of both perfect and imperfect importance sampling. In the former case, we perfectly calculate both the ground state energy and corresponding wavefunction of our system, thus validating our calculations and assumed answer. In the latter case, we show the existence of a residual population bias for populations of small numbers of random walkers. We demonstrate the convergence of our small population calculations and show that we cannot remove this bias through a number of single walker methods. Finally, we demonstrate the overall decay of this residual population bias as the population of random walkers expands, allowing our calculations to converge to the true answer.

Key Words: Diffusion Monte Carlo, Population Dynamics, Random Walk

#### Recommended Citation

Geroski, David J., "Persistent Population Biases in Branching Random Walk Algorithms" (2015). *Undergraduate Honors Theses.* Paper 167.

https://publish.wm.edu/honorstheses/167

#### Included in

Condensed Matter Physics Commons, Statistical, Nonlinear, and Soft Matter Physics Commons