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arXiv · 1511.06657

Attractor-repeller pair of topological zero-modes in a nonlinear quantum walk

Y. Gerasimenko·B. Tarasinski·C. W. J. Beenakker
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Abstract

The quantum-mechanical counterpart of a classical random walk offers a rich dynamics that has recently been shown to include topologically protected bound states (zero-modes) at boundaries or domain walls. Here we show that a topological zero-mode may acquire a dynamical role in the presence of nonlinearities. We consider a one-dimensional discrete-time quantum walk that combines zero-modes with a particle-conserving nonlinear relaxation mechanism. The presence of both particle-hole and chiral symmetry converts two zero-modes of opposite chirality into an attractor-repeller pair of the nonlinear dynamics. This makes it possible to steer the walker towards a domain wall and trap it there.

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Y. Gerasimenko, B. Tarasinski, C. W. J. Beenakker. 2016-02-12. Attractor-repeller pair of topological zero-modes in a nonlinear quantum walk. https://doi.org/10.1103/physreva.93.022329

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