Pauli Crystals

Abstract

In this thesis, previously demonstrated results in the literature regarding Pauli Crystals have been replicated, specifically from the confinement of three and six spin-polarized non-interacting fermions in an isotropic harmonic oscillator. The crystals were visualized using the Monte Carlo algorithm as well as the Metropolis algorithm. Furthermore, the distribution of particles was examined using the pair correlation function. The thesis then demonstrated the existence of Pauli Crystals in the anisotropic harmonic oscillator for three and five non-interacting spin-polarized fermions. This included an examination of the type of snapshot processing required to break the parity symmetry of the total Slater determinant wavefunction. Finally, a Gaussian modification to the isotropic harmonic oscillator was considered to study the effects the new potential might have on the distribution of the particles and the Pauli Crystals.

Popular Abstract

Thanks to the advent of modern cooling techniques, scientists are now able to cool down gases to temperatures near absolute zero. To give an analogy, imagine a large food bowl, where placing a bunch of marbles on the rim of the bowl will cause them to slide down along the surface till they all reach the bottom where they cluster together. This description of the marbles in the food bowl is similar to the behavior of atoms in a harmonic potential. In order to achieve these very low temperatures, scientists have to place atoms in a harmonic potential which will force them to congregate in the center of the potential. After these atoms fall to the bottom of the potential, a laser beam is directed onto them from all four directions in a two dimensional plane. As a result, the atoms are now fixed in their positions, and their motion is significantly reduced.

The focus of my thesis is to study how a group of fermionic atoms behave in such a harmonic trap. In order to proceed, a brief explanation of what a fermion is must be provided. In nature, two fundamental types of particles: bosons and fermions. Bosons are the type of particles which can pile up together in clusters, whereas fermions are the type of particles which cannot occupy the same position. Thus, the analogy of a bunch of marbles in a bowl falling to the bottom holds true for bosons but not for fermions.

In the case of fermions, while each fermion on its own would like to naturally fall down to the bottom of the bowl, it will not be able to do so as other fermions are also trying to achieve the same goal. As a result, the behaviour of fermions would be analogous to social distancing. All the fermions are trying to reach the same endpoint which is the center of the bowl, however, they must keep some distance from all other fermions.

This leads to at least three interesting research topics. One interesting question is, how does changing the position of one fermion affect the expected position of the other fermions? In other words, in a room of three people who are standing at opposite corners to socially distance due to some novel virus, how does one person moving across the room force the other people provided they want to socially distance to avoid infection? An extension to this question would be, how does changing the shape of the room or the bowl, alter the natural arrangement of any number of fermions in their confined space?
While studying fermionic atoms in a harmonic potential on its own may not have direct applications on its own, studying the position correlations of other types of fermionic particles in some given confinement remains an important research field in physics till today. This applies for example to electrons, which are a type of fermions, and how they behave within the confinement of molecular bonds. Studying these correlations may help scientists infer backwards the shape of these molecules, as well as the strength of the bonds involved.

• author: Dabbous, Ahmed Mohammed
• supervisor: Stephanie Reimann
• organization: Mathematical Physics; Department of Physics
• course: FYSK02 20211
• year: 2021
• type: M2 - Bachelor Degree
• subject: Physics and Astronomy
• language: English
• id: 9063931
• date added to LUP: 2021-08-27 13:59:13
• date last changed: 2021-08-27 13:59:13