A. Polkovnikov, K. Sengupta, A. Silva, and M. Vengalatorre, : Nonequilibrium dynamics of closed interacting quantum systems, Reviews of Modern Physics, vol.5, issue.3, p.863, 2011.
DOI : 10.1103/PhysRevLett.95.105701

L. Bertini, A. De-sole, D. Gabrielli, G. Jona-lasinio, and C. Landim, Macroscopic fluctuation theory, Reviews of Modern Physics, vol.2005, issue.2, p.593, 2015.
DOI : 10.1088/1751-8113/41/50/505001
URL : http://arxiv.org/pdf/1404.6466

H. Spohn, Large Scale Dynamics of Interacting Particles, 1991.
DOI : 10.1007/978-3-642-84371-6

M. Takahashi, Thermodynamics of One-Dimensional Solvable Models, 1999.
DOI : 10.1017/CBO9780511524332

B. Sutherland, Beautiful Models: 70 Years of Exactly Solved Quantum Many-Body Problems, 2004.
DOI : 10.1142/5552

B. Paredes, A. Widera, V. Murg, O. Mandel, S. Folling et al., Tonks???Girardeau gas of ultracold atoms in an optical lattice, Nature, vol.42, issue.6989, p.277, 2004.
DOI : 10.1103/PhysRevLett.90.150402
URL : https://hal.archives-ouvertes.fr/hal-00009247

T. Kinoshita, T. Wenger, and D. S. Weiss, A quantum Newton's cradle, Nature, vol.71, issue.7086, p.900, 2006.
DOI : 10.1103/PhysRevA.71.011602

T. Chou, K. Mallick, and R. K. Zia, Non-equilibrium statistical mechanics: from a paradigmatic model to biological transport, Reports on Progress in Physics, vol.74, issue.11, p.116601, 2011.
DOI : 10.1088/0034-4885/74/11/116601

T. Halpin-healy and Y. Zhang, Kinetic roughening phenomena, stochastic growth, directed polymers and all that. Aspects of multidisciplinary statistical mechanics, Physics Reports, vol.254, issue.4-6, p.215, 1995.
DOI : 10.1016/0370-1573(94)00087-J

B. Derrida and A. Gerschenfeld, Current Fluctuations in One Dimensional Diffusive Systems with a Step Initial Density Profile, Journal of Statistical Physics, vol.8, issue.5-6, p.978, 2009.
DOI : 10.1007/978-3-662-03752-2

I. Corwin, Random Matrices: Theory Appl, p.1130001, 2012.

B. Bertini, M. Collura, J. De-nardis, and M. Fagotti, Chains: Exact Profiles of Charges and Currents, Physical Review Letters, vol.117, issue.20, p.207201, 2016.
DOI : 10.1103/PhysRevLett.97.050401
URL : https://hal.archives-ouvertes.fr/hal-01554315

V. B. Bulchandani, R. Vasseur, C. Karrasch, and J. E. Moore, Bethe-Boltzmann hydrodynamics and spin transport in the XXZ chain, Physical Review B, vol.33, issue.4, p.45407, 2018.
DOI : 10.1017/CBO9780511524332

V. B. Bulchandani, R. Vasseur, C. Karrasch, and J. E. Moore, Solvable Hydrodynamics of Quantum Integrable Systems, Physical Review Letters, vol.270, issue.22, p.220604, 2017.
DOI : 10.1103/PhysRevB.83.035115

B. Doyon, J. Dubail, R. Konik, and T. Yoshimura, Large-Scale Description of Interacting One-Dimensional Bose Gases: Generalized Hydrodynamics Supersedes Conventional Hydrodynamics, Physical Review Letters, vol.1, issue.19, p.195301, 2017.
DOI : 10.1088/1742-5468/aa7abf
URL : https://hal.archives-ouvertes.fr/hal-01645811

E. Ilievski and J. De-nardis, Microscopic Origin of Ideal Conductivity in Integrable Quantum Models, Physical Review Letters, vol.119, issue.2, p.20602, 2017.
DOI : 10.1103/PhysRevLett.74.816

L. Piroli, J. De-nardis, M. Collura, B. Bertini, and M. Fagotti, Transport in out-of-equilibrium XXZ chains: Nonballistic behavior and correlation functions, Physical Review B, vol.96, issue.11, p.115124, 2017.
DOI : 10.1088/1742-5468/aa7df0

T. Antal, Z. Rácz, A. Rákos, and G. Schütz, chain at zero temperature: Emergence of flat magnetization profiles, Physical Review E, vol.16, issue.5, p.4912, 1999.
DOI : 10.1016/0003-4916(61)90115-4

T. Antal, P. L. Krapivsky, and A. Rákos, Logarithmic current fluctuations in nonequilibrium quantum spin chains, Physical Review E, vol.48, issue.6, p.61115, 2008.
DOI : 10.1016/S0370-1573(99)00123-4

D. Gobert, C. Kollath, U. Schollwöck, and G. Schütz, chains with adaptive time-dependent density matrix renormalization group, Physical Review E, vol.66, issue.3, p.36102, 2005.
DOI : 10.1103/PhysRevE.69.066103

T. Sabetta and G. Misguich, Nonequilibrium steady states in the quantum XXZ spin chain, Physical Review B, vol.88, issue.24, p.245114, 2013.
DOI : 10.1103/PhysRevLett.110.257203
URL : https://hal.archives-ouvertes.fr/cea-01117917

J. Mossel and J. Caux, spin-1/2 chain, New Journal of Physics, vol.12, issue.5, p.55028, 2010.
DOI : 10.1088/1367-2630/12/5/055028

J. Sirker, R. G. Pereira, and I. Affleck, Conservation laws, integrability, and transport in one-dimensional quantum systems, Physical Review B, vol.74, issue.3, p.35115, 2011.
DOI : 10.1103/PhysRevB.64.024425

I. Klich and L. Levitov, Quantum Noise as an Entanglement Meter, Physical Review Letters, vol.58, issue.10, p.100502, 2009.
DOI : 10.1103/PhysRevLett.100.086602
URL : http://arxiv.org/pdf/0804.1377

H. F. Song, S. Rachel, C. Flindt, I. Klich, N. Laflorencie et al., Bipartite fluctuations as a probe of many-body entanglement, Physical Review B, vol.58, issue.3, p.35409, 2012.
DOI : 10.1073/pnas.0703293104
URL : https://hal.archives-ouvertes.fr/hal-00703455

H. F. Song, C. Flindt, S. Rachel, I. Klich, and K. L. Hur, Entanglement entropy from charge statistics: Exact relations for noninteracting many-body systems, Physical Review B, vol.58, issue.16, p.161408, 2011.
DOI : 10.1103/PhysRevB.83.085112

V. Eisler and Z. Rácz, Full Counting Statistics in a Propagating Quantum Front and Random Matrix Spectra, Physical Review Letters, vol.16, issue.6, p.60602, 2013.
DOI : 10.1007/s00220-009-0761-0

M. Ganahl, E. Rabel, F. H. Essler, and H. G. Evertz, Chain Using Local Quantum Quenches, Physical Review Letters, vol.50, issue.7, p.77206, 2012.
DOI : 10.1103/PhysRevLett.100.210402

R. Vlijm, M. Ganahl, D. Fioretto, M. Brockmann, M. Haque et al., Quasi-soliton scattering in quantum spin chains, Physical Review B, vol.92, issue.21, p.214427, 2015.
DOI : 10.1016/0003-4916(79)90391-9

M. P. Zaletel, R. S. Mong, C. Karrasch, J. E. Moore, and F. Pollmann, Time-evolving a matrix product state with long-ranged interactions, Physical Review B, vol.91, issue.16, p.165112, 2015.
DOI : 10.1103/PhysRevLett.110.033001