Quantum walk hydrodynamics
arXiv:1709.10417
Abstract
A simple Discrete-Time Quantum Walk on the line is revisited and given an hydrodynamic interpretation through a novel relativistic generalization of the Madelung transform. Numerical results are presented which show that suitable initial conditions indeed produce hydrodynamical shocks. An analytical computation of the asymptotic quantum shock structure is presented. The non-relativistic limit is explored in the Supplementary Material (SM).
14 Figs, any comment is welcome