Statistical properties of the continuum Salerno model

The statistical properties of the Salerno model are investigated. In particular, a comparison between the coherent and partially coherent wave modes is made for the case of a random-phased wave packet. It is found that the random-phased-induced spectral broadening gives rise to the damping of instabilities, but also a broadening of the instability region in quasiparticle momentum space. The results can be of significance for the condensation of magnetic-moment bosons in deep optical lattices.

Figure 1

The growth rate $\Gamma$ plotted as a function of the perturbation wave number $K$ for different parameter values. All curves have normalized the parameter $\nu$ to one and intensity $I_0=0.25$. The heavy solid curve has $\mu =\Delta =0$ and corresponds to the coherent nonlinear Schrödinger modulational instability; the thin solid curve has $\mu =0$ and $\Delta =0.1$; the heavy dotted curve has $\mu =0.5$ and $\Delta =0$, while the thin dotted curve has $\mu =0.5$ and $\Delta =0.1$; finally, the heavy dashed curve has $\mu =-0.5$ and $\Delta =0$, while the thin dashed curve has $\mu =-0.5$ and $\Delta =0.1$. Thus, all cases show damping through the broadening of the background wave-number distribution.