We theoretically investigate the time dependence of the first order coherence function for a one-dimensional driven dissipative non-equilibrium condensate. Simulations on the generalized Gross-Pitaevskii equation (GGPE) show that the characteristic t
ime scale of exponential decay agrees with the linearized Bogoliubov theory in the regime of large interaction energy. For very weak interactions, the temporal correlation deviates from the linear theory, and instead respects the dynamic scaling of the Kardar-Parisi-Zhang universality class. This nonlinear dynamics is found to be quantitatively captured by a noisy Kuramoto-Sivashinsky equation for the phase dynamics.
The polaronic system consisting of an impurity in a dilute Bose-Einstein condensate is considered in the presence of a narrow Feshbach resonance. For this purpose a coupled-channel model is used, which at the mean field level predicts the formation o
f quasiparticles that are a superposition of the impurity and the molecular states. The impurity-boson interactions and the coupling between the open and closed channels are then considered weak and a perturbative calculation of the corrections to the mean field results is presented. This allows to examine the properties of the quasiparticles, such as the lifetime and the effective mass. The model is applied to two physical systems: an impurity atom in a Bose-condensed atomic gas in 3D and a spin down lower polariton in a Bose-Einstein condensate of spin up lower polaritons in 2D. The model parameters are linked to the physical parameters by identifying the low energy T-matrix and applying a proper renormalization scheme.
We present a theoretical analysis of spatial correlations in a one-dimensional driven-dissipative non-equilibrium condensate. Starting from a stochastic generalized Gross-Pitaevskii equation, we derive a noisy Kuramoto-Sivashinsky equation for the ph
ase dynamics. For sufficiently strong interactions, the coherence decays exponentially in close analogy to the equilibrium Bose gas. When interactions are small on a scale set by the nonequilibrium condition, we find through numerical simulations a crossover between a Gaussian and exponential decay with peculiar scaling of the coherence length on the fluid density and noise strength.
