A statistical mechanical approach of self-organization of a quantised vortex gas in a two-dimensional superfluid

Maestrini, Davide (2016) A statistical mechanical approach of self-organization of a quantised vortex gas in a two-dimensional superfluid. Doctoral thesis, University of East Anglia.

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Abstract

In this work the relaxation of a two-dimensional Bose-gas from a non-equilibrium
initial condition consisting of vortices is studied. To focus on the role of the vortex
excitations on the time evolution of the system, a point vortex model is used. The
relaxation of the vortex gas is seen to lead to clustering of like-signed vortices that
can be explained in terms of negative temperature states. The nature of the Coulomb
interactions between vortices, precludes a well-defined thermodynamic limit. The large
scale
flow structures, therefore strongly depend on the shape of the geometry. These
structures can be explained in terms of a maximum entropy principle for the vortex
gas that leads to the Boltzmann-Poisson equation. For a square region the maximum
entropy configuration corresponds to a monopole. This configuration results in the
spontaneous acquisition of angular momentum by the
ow. However, by stretching
the square domain into a rectangle, the configuration which maximises the entropy
switched to a dipole where like-signed vortices tend to equally occupy the two halves
of the domain. In this case, the mean
flow has zero angular momentum. A direct qualitative
and quantitative comparison between the predictions of the mean-field theory
and dynamical simulations of a point vortex model are presented. In particular, we
show that vortex-antivortex annihilation results in evaporative heating of the vortex
gas and the subsequent migration of the system into the negative temperature regime.
Moreover, the study is extended to the dynamics of quantised vortices in the same
confined geometries in a two-dimensional Bose-Einstein condensate described by the
Gross-Pitaevskii equation. Despite the coexistence of phonons with vortex excitations
that interact together, the above predictions continue to apply in this more realistic
model of a two-dimensional superfl
uid.

Item Type: Thesis (Doctoral)
Faculty \ School: Faculty of Science > School of Mathematics
Depositing User: Jackie Webb
Date Deposited: 09 Mar 2017 10:22
Last Modified: 30 Sep 2017 00:38
URI: https://ueaeprints.uea.ac.uk/id/eprint/62927
DOI:

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