Fractional Schrödinger dynamics and decoherence
نویسندگان
چکیده
Abstract. We study the dynamics of the Schrödinger equation with a fractional Laplacian (−∆), and the decoherence of the solution is observed in certain cases. Analytically, we find equations describing the dynamics of the expected position and expected momentum in the fractional Schödinger equation, equations that are the fractional counterpart of the Newtonian equations of motion for the non-fractional Schrödinger equation (α = 1). Numerically, we propose an explicit, effective numerical method for solving the timedependent fractional nonlinear Schrödinger 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 Schrödinger equation and find that the nonlocal interaction from the fractional Laplacian introduces decoherence into the solution. The local nonlinear interactions can however reduce (in 1D) or delay (in 2D) the emergence of decoherence. Our results are consistent with those reported in the literature of discrete nonlinear Schrödinger equation with long-range interactions.
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