SELF-TRAPPING TRANSITION FOR A NONLINEAR IMPURITY EMBEDDED IN A LATTICE

A nonlinear impurity embedded in a lattice is found to have a self-trapping transition. The system considered is a quantum-mechanical quasiparticle such as an electron or exciton moving via nearest-neighbor interactions among the sites of a chain, one particular site in the chain being such that its site energy is dependent on the occupation probability of the site by the quasiparticle. An integral equation for the quasiparticle amplitude is derived and solved numerically. The numerical results appear to show that a self-trapping transition, which tends to localize the quasiparticle, occurs when the nonlinearity exceeds a critical value relative to the intersite transfer interaction. Analytical arguments are presented to support the numerical findings and additional results are obtained in higher dimensions. The appearance of the transition is found to be more compelling in higher-dimensional lattices.