Superfluid vortices in four spatial dimensions

McCanna, Ben ORCID: 0000-0002-5341-1482 (2022). Superfluid vortices in four spatial dimensions. University of Birmingham. Ph.D.

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Quantized vortices in two and three-dimensional superfluids have been studied as an important area of physics for many decades. These are topological defects forming points in 2D and lines in 3D about which the superfluid can circulate. Recent experimental developments in ``synthetic dimensions" and other fields has led to broad interest in the quantum simulation of physical systems in higher dimensions, with a particular focus on topological phases such as quantum Hall systems. However, most theoretical works in 4D have focused on topological models without interactions. This has motivated us --- via the analogy between rotating superfluids and the quantum Hall effect --- to study the behaviour of hypothetical four-dimensional superfluids under rotation. In this thesis we begin to establish the basic phenomenology of vortices in rotating 4D superfluids, using a minimal 4D GPE model. We find that vortices in four dimensions form planes (or more generally surfaces), and that ``double rotations" which arise in 4D can stabilise stationary states with orthogonal vortex planes intersecting at a point. Investigating this behaviour further, we find more general vortex stationary states based on intersecting skew planes which have cores composed of connected smoothly curved surfaces. These results suggest that vortices in four dimensional superfluids can lose their individual character, even in the absence of dynamics, which is a fascinating departure from the physics of vortices in lower dimensions. In future this work opens up many avenues of research, including the study of more experimentally relevant models, investigation of more complex topological defects in 4D, and the possibility of closed vortex surfaces.

Type of Work: Thesis (Doctorates > Ph.D.)
Award Type: Doctorates > Ph.D.
Licence: Creative Commons: Attribution-Noncommercial 4.0
College/Faculty: Colleges (2008 onwards) > College of Engineering & Physical Sciences
School or Department: School of Physics and Astronomy
Funders: Engineering and Physical Sciences Research Council
Subjects: Q Science > QC Physics


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