2022 Conferences for Undergraduate Women in Physics
Volume 67, Number 1
Friday–Sunday, January 21–23, 2022;
Virtual
Session A01: Poster Session
12:00 AM,
Sunday, January 23, 2022
Abstract: A01.00147 : Study of Particle Interactions in Quantum Systems
Preview Abstract
Abstract
Author:
Kya Wiggins
(Berry College)
Quantum mechanical systems are characterized by their energy
eigenvalues.~Previous~studies have shown that the distribution of spacings
between adjacent energy eigenvalues is related to the dynamics in the
classical version of the system.~Systems with regular dynamics have
eigenvalue spacings~that follow the Poisson distribution, while systems with
chaotic dynamics have spacings that~follow the Gaussian Orthogonal
Ensemble~(GOE)~distribution.~ The goal of my research was to find a very
simple quantum system that exhibits a transition from Poisson to GOE
statistics, even though the classical dynamics doesn't clearly change from
regular to chaotic.~I investigated the eigenvalue spacings in a system of~1
to 9 Dirac delta barriers placed in an infinite square well such that the
ratio of the interval lengths between the barriers was irrational. I
computed 1,000~energy eigenvalues of the sequence at three energy ranges:
low~energy (the probability~that a particle is transmitted~through a delta
barrier is close to zero), medium energy (the transmission
probability~is~close to one half), and high energy (the~transmission
probability~is~close to one).~I then unfolded the sequence, so that the
average eigenvalue spacing was one, and~found the distribution of
spacings.~For~six or more barriers~the low energy sequences followed~Poisson
statistics, the medium energy sequences followed~GOE statistics, and~high
energy sequences showed~Gaussian statistics peaked at one.~These results are
interesting because this is~a very simple~system,~but~increasing the
transmission probability shifts the statistics from Poisson to~GOE~to
Gaussian.~ ~