Universal features of self-trapping in nonlinear tight-binding lattices

We use the discrete nonlinear Schrodinger (DNLS) equation to show that nonl inear tight-binding lattices of different geometries and dimensionalities d isplay a universal self-trapping behavior. First, we consider the problem o f a single nonlinear impurity embedded in various tight-binding lattices, a nd calculate the minimum nonlinearity strength tu form a stationary bound s tate. For all lattices, we find that this critical nonlinearity parameter ( scaled by the energy of the bound state), in terms of the nonlinearity expo nent, falls inside a narrow band, which converges to c(1/2) asymptotically. Then, we examine the self-trapping dynamics of an excitation, initially lo calized on the impurity, and compute the critical nonlinearity parameter fo r abrupt dynamical self-trapping. Fur a given nonlinearity exponent, this c ritical parameter, properly scaled, is found to be nearly the same for all lattices. Same results are obtained when generalizing to completely nonline ar lattices, suggesting an underlying self-trapping universality behavior f or all nonlinear (even disordered) tight-binding lattices described by DNLS .