Asymptotic stability of small bound state of nonlinear quantum walks

Abstract

In this paper, we study the long time behavior of nonlinear quantum walks when the initial data is small in $l^2$. In particular, we study the case where the linear part of the quantum walk evolution operator has exactly two eigenvalues and show that the solution decomposed into nonlinear bound states bifurcating from the eigenvalues and scattering waves.

31 pages

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