Dynamics of one electron in a nonlinear disordered chain

Abstract

In this paper we report new numerical results on the disordered Schrödinger equation with nonlinear hopping. By using a classical harmonic Hamiltonian and the Su-Schrieffer-Heeger approximation we write an effective Schrödinger equation. This model with off-diagonal nonlinearity allows us to study the interaction of one electron and acoustical phonons. We solve the effective Schrödinger equation with nonlinear hopping for an initially localized wavepacket by using a predictor-corrector Adams-Bashforth-Moulton method. Our results indicate that the nonlinear off-diagonal term can promote a long-time subdiffusive regime similar to that observed in models with diagonal nonlinearity.