Quantized Vortex Rings and Loop Solitons

The vortex filament model is used to investigate the interaction of a quantized vortex ring with a straight vortex line and also the interaction of two solitons traveling in opposite directions along a vortex. When a ring reconnects with a line, we find that a likely outcome is the formation of a loop soliton. When they collide, loop solitons reconnect as they overlap each other producing either one or two vortex rings. These simulations are relevant for experiments on quantum turbulence in the zero temperature limit where small vortex rings are expected to be numerous. It seems that loop solitons might also commonly occur on vortex lines as they act as transient states between the absorption of a vortex ring before another ring is emitted when the soliton is involved in a reconnection.

Generalization of the Kutta–Joukowski theorem for the hydrodynamic forces acting on a quantized vortex

The hydrodynamic forces acting on a quantized vortex in a superfluid have long been a highly controversial issue. A new approach, originally developed in the astrophysical context of compact stars, is presented to determine these forces by considering small perturbations of the asymptotically uniform flows in the region far from the vortex in the framework of Landau–Khalatnikov two-fluid model. Focusing on the irrotational part of the flows in the Helmholtz decomposition, the classical Kutta–Joukowski theorem from ordinary hydrodynamics is thus generalized to superfluid systems. The same method is applied to predict the hydrodynamic forces acting on vortices in cold atomic condensates and superfluid mixtures.

Coulomb-quantum oscillator correspondence in two dimension, pure gauge field and half-quantized vortex

Isotropic oscillator and Coulomb problems are known to have interesting correspondence. We focus on two-dimensional (2D) quantum problems and present complete treatment on the correspondence including the Schrödinger equation, eigenfunctions and eigenvalues, and the integrals of motion. We find only partial equivalence. The wave function correspondence is examined introducing local gauge transformation and the emergence of half-quantized vortex with the associated spin-half is established. Vortex structure of the electron proposed by us and the origin of charge are discussed in this paper. Outlook on the implications for QCD and hadron spectrum is outlined.

Henry Edgar Hall. 28 September 1928—4 December 2015

Henry Edgar Hall was a leading experimental and theoretical low temperature physicist of his generation, who, working first in Cambridge and then in Manchester, made important contributions to our knowledge and understanding of superfluidity in both liquid 4 He and liquid 3 He. His work focused significantly, but not exclusively, on the role of topological defects, such as quantized vortex filaments, in superfluid behaviour. He also contributed in important ways to the development of the 3 He– 4 He dilution refrigerator, which has since played a vital role in experimental work requiring temperatures below 1 K.