Nonlinear Impurity in a Lattice: Dispersion Effects

Details Nonlinear Impurity in a Lattice: Dispersion Effects Nonlinear Impurity in a Lattice: Dispersion Effects

2002-07-05

arxiv.org/abs/cond-mat/0207160v1

Physics

Condensed Matter

Disordered Systems and Neural Networks

24 pages, 10 figures

Scientific paper

10.1103/PhysRevB.67.054202

We examine the bound state(s) associated with a single cubic nonlinear impurity, in a one-dimensional tight-binding lattice, where hopping to first--and--second nearest neighbors is allowed. The model is solved in closed form {\em v\`{\i}a} the use of the appropriate lattice Green function and a phase diagram is obtained showing the number of bound states as a function of nonlinearity strength and the ratio of second to first nearest--neighbor hopping parameters. Surprisingly, a finite amount of hopping to second nearest neighbors helps the formation of a bound state at smaller (even vanishingly small) nonlinearity values. As a consequence, the selftrapping transition can also be tuned to occur at relatively small nonlinearity strength, by this increase in the lattice dispersion.

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