Studies of Models of Superfluids from Nanometres to Astrophysical Scales

Abstract

In this thesis, we study various models of superfluids applicable across a broad range of systems, from laboratory flows to astrophysical scales. At zero temperature, we utilize the Gross-Pitaevskii model of superfluid 4He to investigate the dynamics of quantum vortices in laboratory settings. This model also has relevance in astrophysical contexts, such as within pulsars and in the form of dark matter surrounding galaxies. At finite temperatures, we employ the two-fluid model of liquid 4He to examine turbulence in superfluids. Specifically, we study the following problems: 1. We show that the Gross-Pitaevskii equation coupled with the wave equation for a wire (GP-W) provides a natural theoretical framework for understanding recent experiments employing a nanowire to detect a single quantum vortex in superfluid 4He. We uncover the complete spatiotemporal evolution of such wire-based vortex detection via direct numerical simulations of the GP-W system. 2. We use pseudospectral direct numerical simulations (DNSs) to solve the three-dimensional (3D) Hall-Vinen-Bekharevich-Khalatnikov (HVBK) model of superfluid Helium. We then explore the statistical properties of inertial particles, in both coflow and counterflow superfluid turbulence (ST) in the 3D HVBK system; particle motion is governed by a generalization of the Maxey-Riley-Gatignol equations. 3. We develop a theoretical framework that allows us to explore the coupled motion of neutron-superfluid vortices and proton-superconductor flux tubes in a gravitationally collapsed condensate, which describe neutron stars that form pulsars. Our framework uses the 3D Gross-Pitaevskii-Poisson-Equation (GPPE) for neutron Cooper pairs, the Real-Time-Ginzburg-Landau equation (RTGLE) for proton Cooper pairs, the Maxwell equations for the vector potential A, and Newtonian gravity and interactions, both direct and induced by the Poisson equation, between the neutron and proton subsystems. 4. We show how to use the cubic-quintic Gross-Pitaevskii-Poisson equa- tion (cq-GPPE) and the cubic-quintic Stochastic Ginzburg-Landau-Poisson equation (cq- SGLPE) to investigate the gravitational collapse of a tenuous axionic gas into a collapsed axionic condensate for both zero and finite temperature T.