Turbulence is characterised by the chaotic state of a fluid flow. Given its widespread relevance, turbulent flows have been the subject of intense research in classical fluids. Turbulence can also arise in superfluids that have no viscosity, and which are governed by the laws of quantum mechanics. Following the first realisation of Bose-Einstein condensates (BECs) in 1995, superfluidity is now routinely studied in these systems that comprise a new state of matter consisting of many atoms in a quantum degenerate state. For scalar BECs, the superfluid wavefunction that describes the matter wave and can be expressed as a single complex scalar field. This wavefunction obeys a Gross- Pitaevskii equation [1] (also known as a Nonlinear Schrödinger equation in other contexts). Nowadays, BECs can be created where the spin degrees of freedom of the atom are not frozen out giving rise to spinor BECs. For a spin-1 BEC, this means three complex scalar fields are required to describe the superfluid order parameter. Spinor BECs allow different superfluid phases to form [2,3]. In scalar BECs, the vorticity field of the vortices, that provides a measure of the amount of rotation, has a singular distribution that is concentrated along a filament. In contrast, in some superfluid phases of spinor BECs, the corresponding vorticity field is continuously distributed. This allows for a more interesting type of turbulence in a spinor BEC. Yet, very little is understood about the turbulent states in these systems [4]. The project will be aimed at numerically modelling turbulence in spinor BECs [5] in order to uncover the similarities and differences from turbulence in classical fluids and in scalar BECs. We seek someone who is competent in programming and who is interested in working on numerical simulations. A basic background of fluid mechanics and/or quantum mechanics would be advantageous.
