Superfluid helium-3 in confined geometries

Superfluid {dollar}sp3{dollar}He is a fermionic superfluid with a critical temperature {dollar}Tsb{lcub}c{rcub}approx1{dollar} mK. In this thesis we describe some of the experimentally observable effects of confining superfluid {dollar}sp3{dollar}He on scales of the order of the coherence length {dollar}xiapprox60{dollar} nm. The Ginzburg-Landau theory is used throughout, so the results are valid near {dollar}Tsb{lcub}c{rcub}{dollar} only.; The introduction discusses the various theoretical approaches to understanding superfluid {dollar}sp3{dollar}He and considers the position of the Ginzburg-Landau theory in the hierarchy of theories of fermionic superfluidity. Chapter 2 deals with the calculation of critical currents and the modification of the phase diagram of superfluid {dollar}sp3{dollar}He in narrow pores and thin slabs.; In chapter 3 we derive the magnetic resonance (NMR) frequencies of superfluid {dollar}sp3{dollar}He in thin slabs: we find that NMR can be a very sensitive experimental probe of the order parameter in severely confined geometries.; Finally, chapter 4 addresses the problem of the flow of superfluid {dollar}sp3{dollar}He-{dollar}B{dollar} through a constriction (a "weak link") separating two bulk regions of superfluid. We argue that the boundary conditions that describe the applied flow (specified phase gradient) at the bulk ends differ from the analogous situation in a superconducting weak link (specified phase difference).