Nonlinear Impurity in a Lattice: Dispersion Effects

M. I. Molina

doi:10.1103/physrevb.67.054202

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Nonlinear Impurity in a Lattice: Dispersion Effects

M. I. Molina

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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.

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M. I. Molina. 2002-07-05. Nonlinear Impurity in a Lattice: Dispersion Effects. https://doi.org/10.1103/physrevb.67.054202

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