TY  - JOUR
AU  - Hatifi, M.
AU  - Di Molfetta, G.
AU  - Debbasch, F.
AU  - Brachet, M.
PY  - 2019
DA  - 2019//
TI  - Quantum walk hydrodynamics
T2  - Sci Rep
JO  - Scientific Reports
SP  - 2989
EP  - 7pp
VL  - 9
PB  - Nature Publishing Group
AB  - 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).
SN  - 2045-2322
UR  - https://arxiv.org/abs/1709.10417
UR  - https://doi.org/10.1038/s41598-019-40059-x
DO  - 10.1038/s41598-019-40059-x
LA  - English
N1  - WOS:000459799800138
ID  - Hatifi_etal2019
ER  -