Nonlinear Impurity in a Lattice: Dispersion Effects

Abstract

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\`ıa} 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.

24 pages, 10 figures

References in corpus (1)

• Self-trapping transition for nonlinear impurities embedded in a Cayley tree

Cited by in corpus (4)

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• Nonlinear surface impurity in a semi-infinite 2D square lattice
• Lattice Green's function approach to the solution of the spectrum of an array of quantum dots and its linear conductance
• Strong asymmetry for surface modes in nonlinear lattices with long-range coupling