Wandering breather in coupled nonlinear chains as classical counterpart of macroscopic tunneling quantum dynamics

In our lectures we will present analytical and numerical studies of phase-coherent dynamics of intrinsically localized excitations (discrete breathers) in weakly coupled nonlinear lattices. We will discuss the possibility of the existence of two qualitatively different dynamical regimes of the coupled breathers. We will show that these two regimes of coupled phase-coherent breathers are similar and are described by a similar pair of equations to the two regimes in the nonlinear tunneling dynamics of two weakly linked interacting (non ideal) Bose-Einstein condensates. On the basis of this profound analogy, we will describe a new tunneling mode of two weakly coupled Bose-Einstein condensates with unusual dynamics of relative phase. We will also discuss other coupled systems in physics, chemistry and biology, in which similar tunneling dynamics of nonlinear objects can be revealed and studied.