Quantum vortex

Abstract: Preface 1. Background on classical vortices 2. Background on liquid helium II 3. Vortex dynamics and mutual friction 4. The structure of quantized vortices 5. Vortex arrays 6. Vortex waves 7. Quantum turbulence 8. Nucleation of quantized vortices Index.

Abstract: This paper presents a summary and evaluation of the experimental properties of superfluid $^{3}\mathrm{He}$ as they were known in the fall of 1974. Subjects having thermodynamic significance, including specific heat, static magnetism, phase equilibria, and superfluid density, are discussed first. Then known flow properties are treated. After a brief discussion of the theoretical ideas which motivated some of the later experiments, the subject of dynamic magnetism is reviewed. Closely related work in a magnetic field in the immediate temperature region of the critical temperature is discussed, as are the propagation of ultrasound, the phenomena of supercooling and superheating, precise indication of the critical temperature, and the effects of certain restrictive geometries. The article concludes with a brief discussion of some new developments which appeared after the main text was finished. Appendices on thermometry and on parameters of the normal Fermi liquid are included.

Abstract: The normal and superfluid densities are defined by the response of a liquid to sample boundary motion. The free-energy change due to uniform boundary motion can be calculated by path-integral methods from the distribution of the winding number of the paths around a periodic cell. This provides a conceptually and computationally simple way of calculating the superfluid density for any Bose system. The linear-response formulation relates the superfluid density to the momentum-density correlation function, which has a short-ranged part related to the normal density and, in the case of a superfluid, a long-ranged part whose strength is proportional to the superfluid density. These facts are discussed in the context of path-integral computations and demonstrated for liquid $^{4}\mathrm{He}$ along the saturated vapor-pressure curve. Below the experimental superfluid transition temperature the computed superfluid fractions agree with the experimental values to within the statistical uncertainties of a few percent in the computations. The computed transition is broadened by finite-sample-size effects.

Abstract: TOPOLOGICAL defects formed during a rapid symmetry-breaking phase transition in the early Universe1,2 could be responsible for seeding large-scale structure, for the anisotropy of the microwave background radiation, and for the predominance of matter over antimatter3,4. The theory describing this cosmological phase transition is formally analogous to that describing the transition to the superfluid state in liquid 3He, so that in principle the process of cosmological defect formation can be modelled in the laboratory. Here we report the results of an experiment in which the 'primordial fireball' is mimicked using a neutron-induced nuclear reaction (n + 3He → p + 3He + 0.76 MeV) to heat small regions of superfluid 3He above the superfluid transition temperature. These bubbles of normal liquid cool extremely rapidly, and we find that their transition back to the superfluid state is accompanied by the formation of a random network of vortices (the superfluid analogue of cosmic strings). We monitor the evolution of this defect state by rotating the superfluid sample, allowing vortices to escape from the network and thus be probed individually. Our results provide clear confirmation of the idea that topological defects form at a rapid second-order phase transition, and give quantitative support to the Kibble–Zurek mechanism5,6 of cosmological defect formation.