Mohammad MAGHREBI
Dissipative systems often exhibit wavelength-dependent loss rates. One prominent example is Rydberg polaritons where dissipation is in the form of quantum diffusion and vanishes at long wavelengths. In this talk, I describe the effect of quantum diffusion in two opposite limits of weakly and strongly interacting bosons. I show that a 1D condensate of weakly interacting bosons subject to this type of loss displays an unusual instability to long-wavelength density fluctuations. I connect this behavior to an effective equation for the nearly uniform condensate—a dispersive analog to the Kardar-Parisi-Zhang equation—which develops singularities in finite time. In the opposite limit of strongly interacting particles, I show that quantum diffusion cools down a highly disordered initial state to a condensate-like state with a rather slow algebraic decay of population. Beside a numerically exact method based on tensor networks, we can construct an exact solution for hard-core bosons --- or, an XY spin chain --- even in the presence of small, but finite dissipation.