Coherent transport of waves in disordered systems with nonlinearity and interactions

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We want to investigate the interplay between disorder and nonlinearity or interactions in the propagation of waves through random media. We are especially interested in coherent effects due to wave interference, which, as well known from the case of linear or non-interacting systems, may modify or even completely change the character of wave transport as compared to the incoherent regime, for example turn diffusion into localization. By means of nonlinear diagrammatic scattering theory in connection with numerical simulations, we will analyze the impact of nonlinearities and interactions on those coherent effects, both for propagation of waves in classical nonlinear media and for interacting many-particle quantum systems. In particular, we want to examine whether - contrary to common belief - wave localization can be favored rather than hindered by properly chosen nonlinearities, as suggested by our previous work on nonlinear coherent backscattering.