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Turbulence in Spinor Superfluids

   School of Mathematics

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  Dr H Salman  No more applications being accepted  Self-Funded PhD Students Only

About the Project

Turbulence is characterised by the chaotic state of a fluid flow. Turbulent flows have been the subject of intense interest in classical fluids. However, turbulence can also arise in superfluids that have no viscosity, and which are governed by the laws of quantum mechanics. Superfluidity is now routinely studied in Bose-Einstein condensates (BECs) a state of matter consisting of a large collection of atoms in a quantum degenerate state; i.e. individual atoms have lost their identity and exist as a macroscopic matter wave. For scalar BECs, the superfluid order parameter, representing the wavefunction describing the macroscopic matter wave, 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. The matter wave field must then be described by a spinor. 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 and complicated type of turbulence in a spinor BEC. Yet, very little is understood about the turbulent states that these systems can support [4]. The PhD project will be aimed at numerically modelling turbulence in spinor BECs in order to uncover the similarities and differences from turbulence in scalar BECs. We seek someone who is competent in programming. A basic background of fluid mechanics and/or quantum mechanics would be advantageous.

Funding Notes

This PhD project is offered on a self-funding basis. It is open to applicants with funding or those applying to funding sources. Details of tuition fees can be found at
A bench fee is also payable on top of the tuition fee to cover specialist equipment or laboratory costs required for the research. Applicants should contact the primary supervisor for further information about the fee associated with the project.


1. C.F. Barenghi, L. Skrbek, K.R. Sreenivasan, PNAS, 111, 4647-4652 (2014)
2. D.M. Stamper-Kurn, M. Ueda, Rev. Mod. Phys., 85, 1191-1244, (2013).
3. Y. Kawaguchi, M. Ueda, Phys. Rep., 520, 253, (2012).
4. M. Tsubota and K. Fujimoto, J. Phys: Conf. Ser. 497, 012002 (2014)
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