Continuous limits of linear and nonlinear quantum walks
Masaya Maeda, Akito Suzuki · Reviews in Mathematical Physics · 2019
In this paper, we consider the continuous limit of a nonlinear quantum walk (NLQW) that incorporates a linear quantum walk as a special case. In particular, we rigorously prove that the walker (solution) of the NLQW on a lattice [Formula: see text] uniformly converges (in Sobolev space [Formula: see text]) to the solution to a nonlinear Dirac equation (NLD) on a fixed time interval as [Formula: see text]. Here, to compare the walker defined on [Formula: see text] and the solution to the NLD defined on [Formula: see text], we use Shannon interpolation.