Scattering and inverse scattering for nonlinear quantum walks
Copyright policy )Scattering and inverse scattering for nonlinear quantum walks
We study large time behavior of quantum walks (QWs) with self-dependent (nonlinear) coin. In particular, we show scattering and derive the reproducing formula for inverse scattering in the weak nonlinear regime. The proof is based on space-time estimate of (linear) QWs such as dispersive estimates and Strichartz estimate. Such argument is standard in the study of nonlinear Schrödinger equations and discrete nonlinear Schrödinger equations but it seems to be the first time to be applied to QW.
18 pages, text overlap with arXiv:1711.00620
Inverse scattering problems in quantum theory, scattering theory, Sums of independent random variables; random walks, NLS equations (nonlinear Schrödinger equations), FOS: Physical sciences, Mathematical Physics (math-ph), Strichartz estimates, Mathematics - Analysis of PDEs, FOS: Mathematics, Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics, quantum walks, dispersive estimates, nonlinear scattering, Quantum stochastic calculus, Mathematical Physics, Analysis of PDEs (math.AP)
Inverse scattering problems in quantum theory, scattering theory, Sums of independent random variables; random walks, NLS equations (nonlinear Schrödinger equations), FOS: Physical sciences, Mathematical Physics (math-ph), Strichartz estimates, Mathematics - Analysis of PDEs, FOS: Mathematics, Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics, quantum walks, dispersive estimates, nonlinear scattering, Quantum stochastic calculus, Mathematical Physics, Analysis of PDEs (math.AP)
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