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

E. Farhi and S. Gutmann, Quantum computation and decision trees, Phys. Rev. A, vol.58, p.915, 1998.

A. Childs, Universal computation by quantum walk, Phys. Rev. Lett, vol.102, p.180501, 2009.

J. Kempe, Quantum random walks -an introductory overview, Contemp. Phys, vol.44, p.307, 2003.

A. Ambainis, Quantum walks and their algorithmic applications, Int. J. Quantum Inf, vol.1, p.507, 2003.

S. Venegas-andraca, Quantum walks: a comprehensive review Quantum Inf. Process, vol.11, p.1015, 2012.

C. Ryan, M. Laforest, J. Boileau, and R. Laflamme, Experimental implementation of a discrete-time quantum random walk on an NMR quantum-information processor, Phys. Rev. A, vol.72, p.62317, 2005.

H. Schmitz, R. Matjeschk, C. Schneider, J. Glueckert, M. Enderlein et al., Quantum walk of a trapped ion in phase space, Phys. Rev. Lett, vol.103, p.90504, 2009.

F. Zähringer, G. Kirchmair, R. Gerritsma, E. Solano, R. Blatt et al., Phys. Rev. Lett, vol.104, p.100503, 2010.

M. Karski, L. Förster, J. Choi, A. Steffen, W. Alt et al., Quantum walk in position space with single optically trapped atoms, Science, vol.325, p.174, 2009.

A. Schreiber, K. Cassemiro, V. Poto?ek, A. Gábris, P. Mosley et al., Photons walking the line: A quantum walk with adjustable coin operations, Phys. Rev. Lett, vol.104, p.50502, 2010.

P. Knight, R. E. Sipe, and J. , Quantum walk on the line as an interference phenomenon, Phys. Rev. A, vol.68, p.20301, 2003.

H. Perets, Y. Lahini, F. Pozzi, M. Sorel, R. Morandotti et al., Realization of quantum walks with negligible decoherence in waveguide lattices, Phys. Rev. Lett, vol.100, p.170506, 2008.

M. Hillery, Quantum walks through a waveguide maze, Science, vol.329, p.1477, 2010.

A. Peruzzo, M. Lobino, J. Matthews, N. Matsuda, A. Politi et al., Science, vol.329, p.1500, 2010.

Y. Lahini, Y. Bromberg, D. Christodoulides, and Y. Silberberg, Quantum correlations in two-particle Anderson localization, Phys. Rev. Lett, vol.105, p.163905, 2010.

L. Sansoni, F. Sciarrino, G. Vallone, P. Mataloni, A. Crespi et al., Two-particle bosonic-fermionic quantum walk via integrated photonics, Phys. Rev. Lett, vol.108, p.10502, 2012.

Y. Omar, N. Paunkovic, S. L. Bose, and S. , Phys. Rev. A, vol.74, p.42304, 2006.

J. Gamble, M. Friesen, D. Zhou, J. R. Coppersmith, and S. , Two-particle quantum walks applied to the graph isomorphism problem, Phys. Rev. A, vol.81, p.52313, 2010.

M. ?tefa?ák, S. Barnett, B. Kollár, T. Kiss, and I. Jex, Directional correlations in quantum walks with two particles, New J. Phys, vol.13, p.33029, 2011.

C. Chandrashekar and T. Busch, Quantum walk on distinguishable non-interacting manyparticles and indistinguishable two-particle Quantum Inf, Process, vol.11, p.1287, 2012.

X. Qin, Y. Ke, X. Guan, Z. Li, A. N. Lee et al., Statistics-dependent quantum cowalking of two particles in one-dimensional lattices with nearest-neighbor interaction, Phys. Rev. A, vol.90, p.62301, 2014.

S. De-toro-arias and J. Luck, Anomalous dynamical scaling and bifractality in the onedimensional Anderson model, J. Phys. A: Math. Gen, vol.31, p.7699, 1998.

P. Krapivsky, J. Luck, and K. Mallick, Interacting quantum walkers: Two-body bosonic and fermionic bound states, J. Phys. A: Math. Theor, vol.48, p.475301, 2015.
URL : https://hal.archives-ouvertes.fr/cea-01307070

T. Antal, P. Krapivsky, and K. Mallick, Molecular spiders in one dimension, J. Stat. Mech, p.8027, 2007.
URL : https://hal.archives-ouvertes.fr/cea-02927237

A. Baraviera, T. Franco, and A. Neumann, Hydrodynamic limit of quantum random walks in From Particle Systems to Partial Differential Equations II Springer Proceedings in Mathematics & Statistics, p.129, 2015.

G. Grimmett, J. S. Scudo, and P. , Weak limits of quantum random walks, Phys. Rev. E, vol.69, p.26119, 2004.

A. Gottlieb, Convergence of continuous-time quantum walks on the line, Phys. Rev. E, vol.72, p.47102, 2005.

N. Konno, Limit theorem for continuous-time quantum walk on the line, Phys. Rev. E, vol.72, p.26113, 2005.

F. Strauch, Connecting the discrete-and the continuous-time quantum walk, Phys. Rev. A, vol.74, p.30301, 2006.

O. Mülken, V. Pernice, and A. Blumen, Universal behavior of quantum walks with long-range steps, Phys. Rev. E, vol.77, p.21117, 2008.

O. Mülken and A. Blumen, Continuous-time quantum walks: Models for coherent transport on complex networks, Phys. Rep, vol.502, p.37, 2011.

X. Xu, Continuous-time quantum walks on one-dimensional regular networks, Phys. Rev. E, vol.77, p.61127, 2008.

X. Xu, Coherent exciton transport and trapping on long-range interacting cycles, Phys. Rev. E, vol.79, p.11117, 2009.

A. Geim and K. Novoselov, The rise of graphene, Nature Materials, vol.6, p.183, 2007.

A. Castro-neto, F. Guinea, N. Peres, K. Novoselov, and A. Geim, The electronic properties of graphene, Rev. Mod. Phys, vol.81, p.109, 2009.

P. Krapivsky, R. S. Ben-naim, and E. , A Kinetic View of Statistical Physics, 2010.

R. Nepomechie, Bethe Ansatz solution of the open XX spin chain with non-diagonal boundary terms, J. Phys. A: Math. Gen, vol.34, p.9993, 2001.

L. ?amaj and J. Bajnok, Introduction to the Statistical Physics of Integrable Many-body Systems, 2013.

E. Lieb, T. Schultz, and D. Mattis, Two soluble models of an antiferromagnetic chain, Ann. Phys, vol.16, p.407, 1961.

H. Hinrichsen, K. Krebs, and I. Peschel, Solution of a one-dimensional diffusion-reaction model with spatial asymmetry, Z. Phys. B, vol.100, p.105, 1996.

U. Bilstein and B. Wehefritz, The XX-model with boundaries: Part I. Diagonalisation of the finite chain, J. Phys. A: Math. Gen, vol.32, p.191, 1999.

I. Gradshteyn and I. Ryzhik, Table of Integrals, Series, and Products, 1965.

R. Pei, S. Taylor, D. Stefanovic, S. Rudchenko, T. Mitchell et al., Behavior of polycatalytic assemblies in a substrate-displaying matrix, J. Am. Chem. Soc, vol.128, p.12693, 2006.

N. Inui, N. Konno, and E. Segawa, One-dimensional three-state quantum walk, Phys. Rev. E, vol.72, p.56112, 2005.

M. ?tefa?ák, I. Bezdekova, and I. Jex, Limit distributions of three-state quantum walks: The role of coin eigenstates, Phys. Rev. A, vol.90, p.12342, 2014.

P. Brouwer, C. Mudry, and B. Simons, Delocalization in coupled onedimensional chains, Phys. Rev. Lett, vol.81, p.862, 1998.

C. Mudry, P. Brouwer, and A. Furusaki, Random magnetic flux problem in a quantum wire, Phys. Rev. B, vol.59, p.13221, 1999.

C. Mudry, P. Brouwer, and A. Furusaki, Crossover from the chiral to the standard universality classes in the conductance of a quantum wire with random hopping only, Phys. Rev. B, vol.62, p.8249, 1999.

P. Brouwer, C. Mudry, and A. Furusaki, Nonuniversality in quantum wires with off-diagonal disorder: a geometric point of view, Nucl. Phys. B, vol.565, p.653, 2000.