Fractional Schrodinger dynamics and decoherence

We study the dynamics of the Schrodinger equation with a fractional Laplacian (-Delta)(alpha), and the decoherence of the solution is observed. Analytically, we obtain equations of motion for the expected position and momentum in the fractional Schodinger equation, equations that are the fractional counterpart of the well-known Newtonian equations of motion for the standard (alpha = 1) Schrodinger equation. Numerically, we propose an explicit, effective numerical method for solving the time dependent fractional nonlinear Schrodinger equation-a method that has high order spatial accuracy, requires little memory, and has low computational cost. We apply our method to study the dynamics of fractional Schrodinger equation and find that the nonlocal interactions from the fractional Laplacian introduce decoherence into the solution. The local nonlinear interactions can however reduce or delay the emergence of decoherence. Moreover, we find that the solution of the standard NLS behaves more like a particle, but the solution of the fractional NLS behaves more like a wave with interference effects. (C) 2016 Elsevier B.V. All rights reserved.