Dynamics of the nonlinear Schrödinger equation in the presence of a constant electric field is studied. Both discrete and continuous limits of the model are considered. For the discrete limit, a probabilistic description of subdiffusion is suggested and a subdiffusive spreading of a wave packet is explained in the framework of a continuous time random walk. In the continuous limit, the biased nonlinear Schrödinger equation is shown to be integrable, and solutions in the form of the Painlevé transcendents are obtained.

The Generalized Elastic Model is a linear stochastic model which accounts for the behaviour of many physical systems in nature, ranging from polymeric chains to single-file systems. If an external perturbation is exerted only on a single point x⋆ (tagged probe), it propagates throughout the entire system. Within the fractional Langevin equation framework, we study the effect of such a perturbation, in cases of a constant force applied. We report most of the results arising from our previous analysis and, in the present work, we show that the Fox H-functions formalism provides a compact, elegant and useful tool for the study of the scaling properties of any observable. In particular we show how the generalized Kubo fluctuation relations can be expressed in terms of H-functions.