Dissipative quantum fluctuations-induced droplets in Bose-Einstein mixtures

We present a theoretical framework for one-dimensional open Bose-Bose mixtures by coupling a driven-dissipative Gross-Pitaevskii equation to a dynamically evolving inhomogeneous reservoir while incorporating the beyond-mean-field Lee-Huang-Yang correction. An adiabatic elimination procedure yields a complex Ginzburg-Landau equation with quadratic-cubic nonlinearity in the regime of rapid reservoir relaxation. Through linear stability analysis, we identify regimes of modulational instability via a modified Lange-Newell criterion and numerically confirm the ensuing nucleation of dissipative quantum droplets. Our findings highlight the critical role of balancing beyond-mean-field effects and dissipation in shaping nontrivial, far-from-equilibrium states of quantum fluids.