The quantization of vortex lines in superfluids requires the introduction of their density L(r, t) in the description of quantum turbulence. The space homogeneous balance equation for L(t), proposed by Vinen on the basis of dimensional and physical considerations, allows a number of competing forms for the production term P. Attempts to choose the correct one on the basis of time-dependent homogeneous experiments ended inconclusively. To overcome this difficulty we announce here an approach that employs an inhomogeneous channel flow which is excellently suitable to distinguish the implications of the various possible forms of the desired equation. We demonstrate that the originally selected form which was extensively used in the literature is in strong contradiction with our data. We therefore present a new inhomogeneous equation for L(r, t) that is in agreement with our data and propose that it should be considered for further studies of superfluid turbulence.

Amorphous solids exhibit quasi-universal low-temperature thermal anomalies whose origin has been ascribed to a distribution of localized tunneling defects. Using an advanced Monte Carlo procedure, we create in silico glasses spanning from hyperquenched to vapor-deposited ultrastable glasses. Using a multidimensional path-finding protocol, we locate tunneling defects with energy splittings smaller than kBTQ, with TQ the temperature below which quantum effects are relevant (TQ ≈ 1 K in most experiments). We find that the evolution of the energy landscape with the quench rate, as well as the manner in which the landscape is explored, conspire to deplete the density of tunneling defects in well-annealed glasses, as observed in recent experiments. We systematically explore the real-space nature of tunneling defects, finding that they are mostly localized to the participation of a few atoms, but are occasionally dramatically delocalized.