# Nonequilibrium superfluid flows

**Project level:** Honours, Summer

See Mason, D. J., Borunda, M. F., & Heller, E. J. (2015). Revealing the flux: Using processed Husimi maps to visualize dynamics of bound systems and mesoscopic transport. Phys. Rev. B, 91(16), 165405. http://doi.org/10.1103/PhysRevB.91.165405

The aim is to make a connection between classical mechanics and quantum mechanics - looking for the signatures of classical trajectories in the quantum wavefunctions. This is potentially interesting for superfluids, as to some extent they behave as classical fluids. This would require adding the effects of interactions - an additional nonlinear term in the Schrodinger equation.

- Learn how to find eigenstates of the Schrodinger equation for a arbitrary 1D potential. This is simply matrix diagonalisation in the end.
- Extend to 2D potentials. This is conceptually no different to (1), but requires more efficient numerical procedures to be able to do it in a reasonable amount of time.
- Be able to find eigenstates for a stadium billiards potential. At this stage it would be interesting to add interactions, and see how this modifies the solutions.
- I would also like to properly understand the "Husimi map" procedure describe in this paper, eg as applied to the solutions above.This is a way of better visualising the classical flows in the eigenstates.
- Another extension I would like to be able to do is to make figures like Fig 10 in this paper - where there is a flux of particles through the system, due to injection on one side, and absorption on the other. You could start in 1D with this.