Transport properties of nonlinear chains with random dimer nonlinearity parameters

Abstract

By using the recursion relation of discrete Schrödinger equation we investigate the transport properties of nonlinear chains with random dimer nonlinearity parameters. It is shown that there is a resonance state, which is just the product of the nonlinearity and the square of the incident wave amplitude modulus. The transmission coefficients are calculated in two conditions. One is that the transmission wave amplitude is a certain value, the other is that the incident wave amplitude modulus is a certain value. There are obvious differences in non-resonant states between the two kinds of conditions. The transmission is a single value function of the electronic energy for the former. However, it will be multi-stability for the latter. It is pointed out that the influence of the nonlinearity parameters on the transport properties can be exactly reflected only when the modulus of incident wave is set to be a certain value.