A Study of The Formation of Stationary Localized States Due to Nonlinear Impurities Using The Discrete Nonlinear Schrödinger Equation

Details A Study of The Formation of Stationary Localized States Due to Nonlinear Impurities Using The Discrete Nonlinear Schrödinger Equation A Study of The Formation of Stationary Localized States Due to Nonlinear Impurities Using The Discrete Nonlinear Schrödinger Equation

1996-06-17

arxiv.org/abs/cond-mat/9606125v1

Physics

Condensed Matter

10 figures available on request

Scientific paper

10.1103/PhysRevB.55.894

The Discrete Nonlinear Schr$\ddot{o}$dinger Equation is used to study the formation of stationary localized states due to a single nonlinear impurity in a Caley tree and a dimeric nonlinear impurity in the one dimensional system. The rotational nonlinear impurity and the impurity of the form $-\chi \mid C \mid^{\sigma}$ where $\sigma$ is arbitrary and $\chi$ is the nonlinearity parameter are considered. Furthermore, $\mid C \mid$ represents the absolute value of the amplitude. Altogether four cases are studies. The usual Greens function approach and the ansatz approach are coherently blended to obtain phase diagrams showing regions of different number of states in the parameter space. Equations of critical lines separating various regions in phase diagrams are derived analytically. For the dimeric problem with the impurity $-\chi \mid C \mid^{\sigma}$, three values of $\mid \chi_{cr} \mid$, namely, $\mid \chi_{cr} \mid = 2$, at $\sigma = 0$ and $\mid \chi_{cr} \mid = 1$ and $\frac{8}{3}$ for $\sigma = 2$ are obtained. Last two values are lower than the existing values. Energy of the states as a function of parameters is also obtained. A model derivation for the impurities is presented. The implication of our results in relation to disordered systems comprising of nonlinear impurities and perfect sites is discussed.

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