Nonequilibrium steady states of Bose-Einstein condensates with a local particle loss in double potential barriers

We investigate the stability of nonequilibrium steady states of Bose-Einstein condensates with a local one-body loss in the presence of double potential barriers. We construct an exactly solvable mean-field model, in which the local loss and the potential barriers take the form of a delta function. Using the exact solutions of our model, we show that there are parameter regions in which two steady-state solutions are dynamically stable, i.e., the model exhibits bistability. We also find that unidirectional hysteresis phenomena appear when the local-loss rate is varied in some parameter region.