Andreev scattering of thermal excitations is a powerful tool for studying quantized vortices and turbulence in superfluid 3 He-B at very low temperatures. We write Hamilton's equations for a quasiparticle in the presence of a vortex line, determine its trajectory, and find under which conditions it is Andreev reflected. To make contact with experiments, we generalize our results to the Onsager vortex gas and find values of the intervortex spacing in agreement with less rigorous estimates.

Pointing out a crucial relation with caustics of the eikonal equation we discuss the singularity formation of 2-dimensional surfaces that sweep out 3-manifolds of zero mean curvature in R 3,1 .

The vortex line density of turbulent superfluid 3 He-B at very low temperature is deduced by detecting the shadow of ballistic quasiparticles, which are Andreev reflected by quantized vortices. Until now the measured total shadow has been interpreted as the sum of shadows arising from interactions of a single quasiparticle with a single vortex. By integrating numerically the quasiclassical Hamiltonian equations of motion of ballistic quasiparticles in the presence of nontrivial but relatively simple vortex systems ͑such as vortex-vortex and vortex-antivortex pairs and small clusters of vortices͒, we show that partial screening can take place, and the total shadow is not necessarily the sum of the shadows. We have also found that it is possible that, upon impinging on complex vortex configurations, quasiparticles experience multiple reflections, which can be classical, Andreev, or both.

The B phase of superfluid 3 He can support regions of extremely long-lived coherent spin precession at ultralow temperatures, known as persistent precessing domains (PPD). The domains have been described in terms of a Bose-Einstein condensate of magnons and in terms of Q balls in field theory. The domains form in a magnetic field minimum along the vertical axis of a cylindrical cell. When far from the ends of the cell, the PPD lifetime grows exponentially on decreasing temperature. When the PPD is close to the horizontal end wall of the cell, an extra surface dissipation mechanism dominates at low temperatures. We present measurements of the PPD generated at various locations in the cell over a broad range of temperatures below 0.3 T C . We compare the measured properties with theoretical expectations for spin-wave modes. We present model calculations of different dissipation mechanisms and we compare these to the measured lifetimes.

Superfluid 3He-B in the zero-temperature limit offers a unique means of studying quantum turbulence by the Andreev reflection of quasiparticle excitations by the vortex flow fields. We validate the experimental visualization of turbulence in 3He-B by showing the relation between the vortex-line density and the Andreev reflectance of the vortex tangle in the first simulations of the Andreev reflectance by a realistic 3D vortex tangle, and comparing the results with the first experimental measurements able to probe quantum turbulence on length scales smaller than the intervortex separation.