Stability of Doublons

Date

2020-05-22

Journal Title

Journal ISSN

Volume Title

Publisher

New York, NY. Stern College for Women. Yeshiva University.

YU Faculty Profile

Abstract

In this thesis, I discuss my research of the behavior and stability of doublons. I describe the dynamics of a one-dimensional closed chain of spins ½. I show that by analyzing the eigenstates and eigenvalues of the Hamiltonian that describes the system, I can predict its dynamics. In the presence of strong interactions between the particles in the chain, particles can bind in pairs of excitations forming what is known as doublons. These doublons are very stable and they move together as a single particle, but contrary to it, doublons move slowly. Doublons were observed experimentally by many different physicists with cold atoms. In those experiments, because of strong on-site interactions between atoms, they would see sites that were doubly occupied, which is how the term “doublon” was coined. These doublons could move to other sites, but they always moved together as a bounded pair. They were never found to be split up with one in each site, they always moved together. In my thesis, the doublons are equivalent to bounded pairs of neighboring excitations in a chain instead of pairs of atoms.

Description

Senior honors thesis. Open Access.

Keywords

Senior honors thesis, stability of doublons, eigenstates, eigenvalues, quantum mechanics, Hamiltonian matrix, quantum system prediction, mathematical models, physics

Citation

Baitner, Miriam. Stability of Doublons. Presented to the S. Daniel Abrahams Honors Program in Partial Fulfillment of the Requirements for Completion of the Program. NY: Stern College for Women. Yeshiva University May 22, 2020. Mentor: Professor Lea F. Santos, Physics