B phase nucleation and A-B interface dynamics in superfluid helium-3

This thesis deals with the theory of the primary nucleation and subsequent expansion of the superfluid $\sp3$He-B phase in the metastable, hypercooled A phase. An overview of the theory of dynamical phenomena in Fermi superfluids is presented in Chapter 1 with an eye towards formulating a theory suitable for studying the dynamics of the first order A-B phase transition. The mechanism for the primary B phase nucleation in the metastable A is not at all understood, and in Chapter 2 various possibilities are discussed, although no resolution to the problem is reached. The focus here is on an exotic non-equilibrium, cosmic ray, which involves non-hydrodynamic heat transport in a state far from equilibrium. Chapter 3 deals with some idealized, model transport problems inspired by the physics behind the cosmic-ray mechanism, and it is shown that certain non-hydrodynamic dynamical structures similar to the ones needed in the cosmic-ray mechanism can form in these model problems. An application of superfluid kinetic equations to the nonlinear, dissipative motion of the A-B interface is discussed in Chapter 4; in particular, the mobility of the phase boundary is obtained in several different dynamical regimes (depending on temperature and pressure), including the (currently) experimentally relevant ballistic regime where the Andreev scattering of normal excitations off the moving interface strongly influences the dynamics. The theoretical prediction for the terminal velocity is too big by a factor $\sim$2, and possible reasons for this discrepancy are discussed. A study of the stability and vibrations of the interface is presented in Chapter 5, where we argue that (1) the moving planar interface is linearly stable and (2) it should be possible to observe underdamped vibrations of a pinned interface at low temperatures. Finally, in Chapter 6 we point out other possible applications of the dynamical theory formulated here and list some open problems.U of I OnlyETDs are only available to UIUC Users without author permissio