Long range ordering of topological excitations in a two dimensional superfluid far from equilibrium

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• Hayder Salman (UEA)
• Thursday 23 February 2017, 13:45-15:00
• Theory Library.

If you have a question about this talk, please contact Mike Gunn.

We study the relaxation of a 2D ultracold Bose-gas from a nonequilibrium initial state consisting of vortices and antivortices in experimentally realizable squareand rectangular traps. In this work, we focus on how quantized vortices can form clusters of like signed vortices. Such clustering can be understood in terms of negative temperature states of a vortex gas.

Using a mean field approximation for the vortex gas, we show that, within the negative temperature regime, an order parameter emerges that is related to the formation of long range correlations between vortices. It turns out that the order parameter corresponds to the streamfunction of the 2D flow field that is governed by a Poisson-Boltzmann equation. It is, therefore, associated with the emergence of a mean rotational hydrodynamic flow with a non-zero coarse-grained vorticity field.

Solutions of the Boltzmann-Poisson equation in a square domain reveal that maximum entropy states of the vortex gas correspond to a large scale monopole flow field. A striking feature of this mean flow, is the spontaneous acquisition of angular momentum by a superfluid flow with a neutral vortex charge. These mean-field predictions are verified through direct simulations of a point vortex gas and 2D simulations of the Gross-Pitaevskii equation.

Due to the long-range nature of the Coulomb-like interactions in point vortex flows, the negative temperature states strongly depend on the shape of the geometry. By modifying the domain to a rectangular region, we identify a geometry induced phase transition of the most probable mean flow field. The resulting maximum entropy state in a rectangular region exceeding a critical aspect ratio then corresponds to a large scale mean dipole flow field with zero net angular momentum which our numerical simulations reproduce.

As a further extension of these results, we analyse the spectra of the flow in the vortex clustered regime and relate these to the theory of non-thermal fixed points and the theory of Kraichnan for inverse energy cascades in 2D hydrodynamic turbulence.

This talk is part of the Theoretical Physics Seminars series.

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