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Quantum walk hydrodynamics
Mohamed Hatifi1, Giuseppe Di Molfetta2,3, Fabrice Debbasch4
1Aix-Marseille Université, CNRS, École Centrale de Marseille, Institut Fresnel UMR 7249, 13013, Marseille, France.
Abstract:
A simple Discrete-Time Quantum Walk (DTQW) on the line is revisited and given an hydrodynamic interpretation through a novel relativistic generalization of the Madelung transform. Numerical results show that suitable initial conditions indeed produce hydrodynamical shocks and that the coherence achieved in current experiments is robust enough to simulate quantum hydrodynamical phenomena through DTQWs. An analytical computation of the asymptotic quantum shock structure is presented. The non-relativistic limit is explored in the Supplementary Material (SM).
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