Labouvie et al.  recently studied the dynamical behaviour of a Bose-Einstein condensate in a one-dimensional optical lattice. One site was designated as the system, whereas the remaining sites were treated as a particle reservoir. The experiment studied the dynamics and long-time steady state of the system following the introduction of controllable single particle dissipation. They discovered that there was a range of dissipation rates for which the system exhibited bistability - the steady-state at long times depended on whether the system was initially full or empty. Labouvie et al. also provided evidence of critical slowing down in the dynamics, suggesting a possible non-equilibrium phase transition. We have developed a classical field model for this system . Particles tunnel into the system at finite energy corresponding to the chemical potential of the reservoir. These subsequently undergo thermalisation which can lead to to the formation of a Bose-Einstein condensate, dependent on the rate of dissipation. We provide a theoretical basis for understanding the experimental observations, and provide an analysis of the nonequilibrium phase transition. The results can be used to inform the design of future atomtronic devices with quantum gases. I will also spend a few minutes with a brief introduction to recent experiments and theory at the University of Queensland where we have demonstrated the emergence of negative temperature states of a vortex gas in a 2D superfluid .
 R. Labouvie, B. Santra, S. Heun, and H. Ott, Physical Review Letters 116, 235302 (2016).
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 T. Simula, M. J. Davis, and K. Helmerson, Phys. Rev. Lett. 113, 165302 (2014).