Topological aspects of persistent flows in 3He-A in a toroidal container
type: Item
instance of: scholarly article
title: Topological aspects of persistent flows in 3He-A in a toroidal container
zbMATH Open document ID: 0641.76138
DOI: 10.1016/0034-4877(86)90062-5
author: Charles Nash
author: Siddhartha Sen
published in: Reports on Mathematical Physics
publication date: 1986-01-01T00:00:00Z
review text: The isotope 3He can exist in different superfluid states depending on the external conditions. In this paper the authors consider 3He in its A phase and use topological arguments to gain some insight into persistent currents which they also refer to as ``quantised flows''. The authors take as their starting point the phenomenological picture of \textit{N. D. Mermin} [J. Math. Phys. 19, 1457-1467 (1978; Zbl 0398.55015)], who has argued that the problem of persistent currents in a toroidal container is equivalent to the problem of classifying all continuous maps from the solid torus to the order parameter space of 3He-A subject to the restrictions brought about in this space by the boundary conditions. However since Mermin's arguments were incomplete it is the purpose of the present paper to give a simple but complete topological explanation of the problem. They conclude that although quantised flows on the surface can extend to flows inside the container in a continuous way the flow need no longer be quantised inside the torus. However energy considerations are ignored in this work and as is pointed out by the authors the topological deformations necessary to bring about this situation may not be energetically favourable.
Mathematics Subject Classification ID: 76Y05
Mathematics Subject Classification ID: 81V99
zbMATH DE Number: 4045421
zbMATH Keywords: topological aspects of persistent flows
zbMATH Keywords: quantised flows
zbMATH Keywords: toroidal container
zbMATH Keywords: topological deformations
MaRDI profile type: Publication
full work available at URL: 0034-4877(86)90062-5
OpenAlex ID: W2066055662
cites work: Q5530411
cites work: Q5678200
cites work: Q3261851
description: scientific article; zbMATH DE number 4045421