APS/Carin Cain

Figure 1: The “world lines” through time of quantum particles confined to two dimensions can be pictured as soft polymers fluctuating in space. This picture shows the world lines of 8 quantum mechanical particles, which are a) distinguishable boltzmannons and b) indistinguishable bosons. Indistinguishable bosons can “swap” paths with each other, as shown for the 3 blue paths and the 5 green paths. This allows the world lines to become highly entangled without much bending. Boninsegni et al. have shown that the highly entangled nature of bosonic world lines is important for explaining why a liquid of helium-$4$ atoms, which are bosons, doesn’t solidify.