Abstract
We experimentally study emergence of microcanonical equilibrium states in the turbulent relaxation dynamics of a two-dimensional chiral vortex gas. Same-sign vortices are injected into a quasi-two-dimensional disk-shaped atomic Bose-Einstein condensate using a range of mechanical stirring protocols. The resulting long-time vortex distributions are found to be in excellent agreement with the meanfield Poisson-Boltzmann equation for the system describing the microcanonical ensemble at fixed energy $\cal{H}$ and angular momentum $\cal{M}$. The equilibrium states are characterized by the corresponding thermodynamic variables of inverse temperature $\hat{\beta}$ and rotation frequency $\hat{\omega}$. We are able to realize equilibria spanning the full phase diagram of the vortex gas, including on-axis states near zero-temperature, infinite temperature, and negative absolute temperatures. At sufficiently high energies the system exhibits a symmetry-breaking transition, resulting in an off-axis equilibrium phase at negative absolute temperature that no longer shares the symmetry of the container. We introduce a point-vortex model with phenomenological damping and noise that is able to quantitatively reproduce the equilibration dynamics.
Highlights
Turbulence continues to stand as one of the most challenging problems in physics despite several centuries of study
Before presenting our experimental results, we first provide context by briefly introducing the model of a chiral vortex gas in a disk, and we review the known equilibrium results obtained from statistical mechanics
We have experimentally studied equilibrium and nonequilibrium states of a chiral vortex gas confined within a disk-shaped atomic Bose-Einstein condensate
Summary
Turbulence continues to stand as one of the most challenging problems in physics despite several centuries of study. Provided the vortex cores are small, the vortex dynamics are governed precisely by the Hamiltonian point-vortex system originally considered by Onsager [46,47] These systems, offer the unique prospect of experimentally testing the maximum entropy approach in a system which is genuinely inviscid and contains a relatively small number of degrees of freedom (determined by the vortex number N), where simulations suggest that the ergodicity assumption may hold [48–50]. These experiments both suffer from key limitations: (i) The temperature of the vortex distributions could only be inferred from a priori assumptions of equilibrium, and (ii) the relaxation to equilibrium is not tested for a wide range of nonequilibrium initial conditions Without having tested these aspects, it cannot yet be said whether the maximum entropy approach proves useful for describing two-dimensional turbulent flows in superfluids.
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