SELF-TRAPPING ON A GENERALIZED NONLINEAR TETRAHEDRON

Abstract

We analyze the dynamical self-trapping of an excitation propagating on a generalized n-sites tetrahedron, characterized by having every site at equal distance from each other. The evolution equation is given by the Discrete Nonlinear Schrödinger (DNLS) equation. For completely localized initial conditions, we find an exact solution for the critical nonlinearity strength (χ/V) c as a function of the number of sites n of the generalized tetrahedron. This critical nonlinearity, that marks the onset of the self-trapping transition, is always negative for n ≥ 3 and its magnitude increases monotonically with n, always remaining inside the sector delimited by (|χ|/V) = n and (|χ|/V) = 2n.