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A nonlinear quantum walk induced by a quantum graph with nonlinear delta potentials. (English) Zbl 1417.81143

Summary: We study a nonlinear quantum walk naturally induced by a quantum graph with nonlinear delta potentials. We find a strongly ballistic spreading in the behavior of this nonlinear quantum walk with some special initial states.

MSC:

81S25 Quantum stochastic calculus
81Q35 Quantum mechanics on special spaces: manifolds, fractals, graphs, lattices
60G50 Sums of independent random variables; random walks
05C81 Random walks on graphs
47H40 Random nonlinear operators
46F10 Operations with distributions and generalized functions
82C41 Dynamics of random walks, random surfaces, lattice animals, etc. in time-dependent statistical mechanics
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