Topologically protected remanent vortices in confined superfluid He 3

Thermodynamic phase transitions typically involve a transition in the microscopic ordering between a less and a more ordered state. After transitioning into an ordered state, localized structures known as defects may remain, which disrupt the overall macroscopic order. Kibble-Zurek theory predicts that for any second-order phase transition the density of defects that form should be determined by the scaling law for the system coherence time and the phase transition quench time. We have performed measurements of sound dissipation due to vortex mutual friction in thin channels of superfluid He 3 where one spatial dimension is smaller than a characteristic length scale predicted by the Kibble-Zurek theory. In this regime, we find that the density of defects is not determined by quench time, but can be estimated by replacing the Kibble-Zurek length scale with a truncated length set by the channel size. This results in significantly higher defect densities than in a bulk system.