R. Feynman and A. Hibbs, Quantum mechanics and path integrals, International Series in Pure and Applied Physics, 1965.

Y. Aharonov, L. Davidovich, and N. Zagury, Quantum random walks, Phys. Rev. A, vol.48, pp.1687-1690, 1993.

D. A. Meyer, From quantum cellular automata to quantum lattice gases, Journal of Statistical Physics, vol.85, pp.551-574, 1996.

H. Schmitz, Quantum walk of a trapped ion in phase space, Phys. Rev. Lett, vol.103, p.90504, 2009.

F. Zähringer, Realization of a quantum walk with one and two trapped ions, Phys. Rev. Lett, vol.104, p.100503, 2010.

A. Schreiber, Photons walking the line: A quantum walk with adjustable coin operations, Phys. Rev. Lett, vol.104, p.50502, 2010.

M. Karski, Quantum walk in position space with single optically trapped atoms, Science, vol.325, pp.174-177, 2009.

L. Sansoni, Two-particle bosonic-fermionic quantum walk via integrated photonics, Phys. Rev. Lett, vol.108, p.10502, 2012.

B. Sanders, S. Bartlett, B. Tregenna, and P. Knight, Two-particle bosonic-fermionic quantum walk via 3d integrated photonics, Phys. Rev. A, vol.67, p.42305, 2003.

B. Perets, Realization of quantum walks with negligible decoherence in waveguide lattices, Phys. Rev. Lett, vol.100, p.170506, 2008.

A. Ambainis, Quantum walk algorithm for element distinctness, SIAM Journal on Computing, vol.37, pp.210-239, 2007.

F. Magniez, A. Nayak, J. R. Santha, and M. , Search via quantum walk, Proceedings of the thirty-ninth annual ACM symposium on Theory of computing, 2007.

C. Aslangul, Quantum dynamics of a particle with a spin-dependent velocity, Journal of Physics A: Mathematical and Theoretical, vol.38, pp.1-16, 2005.
URL : https://hal.archives-ouvertes.fr/hal-00011241

S. Bose, Quantum communication through an unmodulated spin chain, Phys. Rev. Lett, vol.91, p.207901, 2003.

D. Burgarth, Quantum state transfer with spin chains, 2006.

S. Bose, Quantum communication through spin chain dynamics: an introductory overview, Contemporary Physics, vol.48, pp.13-30, 2007.

E. Collini, Coherently wired light-harvesting in photosynthetic marine algae at ambient temperature, Nature, vol.644, 2010.

G. S. Engel, Evidence for wavelike energy transfer through quantum coherence in photosynthetic systems, Nature, vol.446, pp.782-786, 2007.

M. Hoefer, P. Engels, and J. Chang, Matter-wave interference in bose-einstein condensates: A dispersive hydrodynamic perspective, Nonlinear Phenomena in Degenerate Quantum Gases, vol.238, pp.1311-1320, 2009.

D. A. Uzdensky and S. Rightley, Plasma physics of extreme astrophysical environments, Reports on Progress in Physics, vol.77, p.36902, 2014.

G. D. Molfetta, M. Brachet, and F. Debbasch, Quantum walks in artificial electric and gravitational fields, Physica A: Statistical Mechanics and its Applications, vol.397, pp.157-168, 2014.

C. Nore, M. Brachet, and S. Fauve, Numerical study of hydrodynamics using the nonlinear schrödinger equation, Physica D: Nonlinear Phenomena, vol.65, issue.93, p.90011, 1993.

C. Nore, M. Abid, and M. Brachet, Decaying Kolmogorov turbulence in a model of superflow, Phys. Fluids, vol.9, pp.2644-2669, 1997.
URL : https://hal.archives-ouvertes.fr/hal-00364491

F. Dalfovo, S. Giorgini, L. P. Pitaevskii, and S. Stringari, Theory of Bose-Einstein condensation in trapped gases, Rev. Mod. Phys, vol.71, 1999.

F. Debbasch and M. Brachet, Relativistic hydrodynamics of semiclassical fluids, Physica D, vol.82, p.255, 1995.

E. Madelung, Eine anschauliche deutung der gleichung von schrödinger, Naturwissenschaften, vol.14, pp.1004-1004, 1926.

E. Madelung, Quantentheorie in hydrodynamischer form, Zeitschrift für Physik, vol.40, pp.322-326, 1927.

R. J. Donnelly, Quantized Vortices in Helium II, 1991.

M. A. Hoefer, Dispersive and classical shock waves in bose-einstein condensates and gas dynamics, Phys. Rev. A, vol.74, p.23623, 2006.

W. Wan, S. Jia, and J. W. Fleischer, Dispersive superfluid-like shock waves in nonlinear optics, Nat Phys, vol.3, pp.46-51, 2007.

J. Boutari, Large scale quantum walks by means of optical fiber cavities, Journal of Optics, vol.18, p.94007, 2016.

A. Regensburger, Photon propagation in a discrete fiber network: An interplay of coherence and losses, Physical review letters, vol.107, p.233902, 2011.

M. V. Berry and S. Klein, Colored diffraction catastrophes, Proceedings of the National Academy of Sciences, vol.93, pp.2614-2619, 1996.
DOI : 10.1073/pnas.93.6.2614
URL : http://www.pnas.org/content/93/6/2614.full.pdf

T. Pearcey and . Xxxi, the structure of an electromagnetic field in the neighbourhood of a cusp of a caustic. The London, Edinburgh, and Dublin Philosophical Magazine and, Journal of Science, vol.37, pp.311-317, 1946.

D. Kaminski, Asymptotic expansion of the pearcey integral near the caustic, SIAM Journal on Mathematical Analysis, vol.20, pp.987-1005, 1989.

J. L. López and P. J. Pagola, The pearcey integral in the highly oscillatory region, Applied Mathematics and Computation, vol.275, pp.404-410, 2016.

S. Succi, F. Fillion-gourdeau, and S. Palpacelli, Quantum lattice boltzmann is a quantum walk, EPJ Quantum Technology, vol.2, pp.1-17, 2015.

A. Mezzacapo, Quantum simulator for transport phenomena in fluid flows, Scientific Reports, vol.5, 2015.

Y. Shikano, T. Wada, and J. Horikawa, Discrete-time quantum walk with feed-forward quantum coin, Scientific reports, vol.4, p.4427, 2014.

G. Di-molfetta, F. Debbasch, and M. Brachet, Nonlinear optical galton board: Thermalization and continuous limit, Phys. Rev. E, vol.92, p.42923, 2015.

I. Vakulchyk, M. Fistul, P. Qin, and S. Flach, Nonlinear disordered discrete time quantum walks, Bulletin, 2018.

I. Márquez-martn, P. Arnault, G. Di-molfetta, and A. Pérez, Electromagnetic lattice gauge invariance in two-dimensional discretetime quantum walks, Physical Review A, vol.98, p.32333, 2018.

P. Arnault, G. Di-molfetta, M. Brachet, and F. Debbasch, Quantum walks and non-abelian discrete gauge theory, Phys. Rev. A, vol.94, p.12335, 2016.
DOI : 10.1103/physreva.94.012335
URL : https://hal.archives-ouvertes.fr/hal-01554164

P. Arnault and F. Debbasch, Quantum walks and discrete gauge theories, Phys. Rev. A, vol.93, p.52301, 2016.
DOI : 10.1103/physreva.93.052301
URL : https://hal.archives-ouvertes.fr/tel-01737873

C. Lee, P. Kurzy?ski, and H. Nha, Quantum walk as a simulator of nonlinear dynamics: Nonlinear dirac equation and solitons, Physical Review A, vol.92, p.52336, 2015.

A. Javadi, Single-photon non-linear optics with a quantum dot in a waveguide, Nature communications, vol.6, p.8655, 2015.

P. Arnault and F. Debbasch, Quantum walks and gravitational waves, Annals of Physics, vol.383, p.3, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01517371