P. W. Anderson, Absence of Diffusion in Certain Random Lattices, Physical Review, vol.23, issue.5, p.1492, 1958.
DOI : 10.1016/S0031-8914(57)92891-4

J. Chabé, G. Lemarié, B. Grémaud, D. Delande, P. Szriftgiser et al., Experimental Observation of the Anderson Metal-Insulator Transition with Atomic Matter Waves, Physical Review Letters, vol.8, issue.25, p.255702, 2008.
DOI : 10.1007/BF01578242

I. Manai, J. F. Clément, R. Chicireanu, C. Hainaut, J. C. Garreau et al., Experimental Observation of Two-Dimensional Anderson Localization with the Atomic Kicked Rotor, Physical Review Letters, vol.115, issue.24, p.240603, 2015.
DOI : 10.1016/0167-2789(83)90318-4
URL : https://hal.archives-ouvertes.fr/hal-01142263

J. Billy, V. Josse, Z. Zuo, A. Bernard, B. Hambrecht et al., Direct observation of Anderson localization of matter waves in a controlled disorder, Nature, vol.100, issue.7197, p.891, 2008.
DOI : 10.1038/nature07000
URL : https://hal.archives-ouvertes.fr/hal-00271681

F. Jendrzejewski, A. Bernard, K. Müller, P. Cheinet, V. Josse et al., Three-dimensional localization of ultracold atoms in an optical disordered potential, Nature Physics, vol.4, issue.5, p.398, 2012.
DOI : 10.1126/science.1209019
URL : https://hal.archives-ouvertes.fr/hal-00612680

G. Semeghini, M. Landini, P. Castilho, S. Roy, G. Spagnolli et al., Measurement of the mobility edge for 3D Anderson localization, Nature Physics, vol.86, issue.7, p.554, 2015.
DOI : 10.1103/RevModPhys.86.563

H. Hu, A. Strybulevych, J. H. Page, S. E. Skipetrov, and B. A. Van-tiggelen, Localization of ultrasound in a three-dimensional elastic network, Nature Physics, vol.84, issue.12, p.945, 2008.
DOI : 10.1103/PhysRevLett.74.2674
URL : https://hal.archives-ouvertes.fr/hal-00372952

G. Modugno, Anderson localization in Bose???Einstein condensates, Reports on Progress in Physics, vol.73, issue.10, p.102401, 2010.
DOI : 10.1088/0034-4885/73/10/102401
URL : http://arxiv.org/pdf/1009.0555

B. Shapiro, Cold atoms in the presence of disorder, Journal of Physics A: Mathematical and Theoretical, vol.45, issue.14, p.143001, 2012.
DOI : 10.1088/1751-8113/45/14/143001

W. R. Mcgehee, S. S. Kondov, W. Xu, J. J. Zirbel, and B. Demarco, Three-Dimensional Anderson Localization in Variable Scale Disorder, Physical Review Letters, vol.111, issue.14, p.145303, 2013.
DOI : 10.1038/srep00721

C. A. Müller and B. Shapiro, Comment on ???Three-Dimensional Anderson Localization in Variable Scale Disorder???, Physical Review Letters, vol.113, issue.9, p.99601, 2014.
DOI : 10.1088/1751-8113/45/14/143001

P. Lugan, D. Clement, P. Bouyer, A. Aspect, and L. Sanchez-palencia, Anderson Localization of Bogolyubov Quasiparticles in Interacting Bose-Einstein Condensates, Physical Review Letters, vol.53, issue.18, p.180402, 2007.
DOI : 10.1103/PhysRevLett.91.010405
URL : https://hal.archives-ouvertes.fr/hal-00163902

I. L. Aleiner, B. L. Altshuler, and G. V. Shlyapnikov, A finite-temperature phase transition for disordered weakly interacting bosons in one??dimension, Nature Physics, vol.6, issue.11, p.900, 2010.
DOI : 10.1103/PhysRevB.75.155111

N. Cherroret, T. Karpiuk, B. Grémaud, and C. Miniatura, Thermalization of matter waves in speckle potentials, Physical Review A, vol.92, issue.6, p.63614, 2015.
DOI : 10.1088/1367-2630/9/6/161

M. I. Trappe, D. Delande, and C. A. Müller, Semiclassical spectral function for matter waves in random potentials, Journal of Physics A: Mathematical and Theoretical, vol.48, issue.24, p.245102, 2015.
DOI : 10.1088/1751-8113/48/24/245102
URL : http://arxiv.org/pdf/1411.2412

G. M. Falco, A. A. Fedorenko, J. Giacomelli, and M. Modugno, Density of states in an optical speckle potential, Physical Review A, vol.26, issue.5, p.53405, 2010.
DOI : 10.1103/PhysRevA.80.023605
URL : https://hal.archives-ouvertes.fr/hal-00517445

S. John, M. Y. Chou, M. H. Cohen, and C. M. Soukoulis, Density of states for an electron in a correlated Gaussian random potential: Theory of the Urbach tail, Physical Review B, vol.28, issue.12, p.6963, 1988.
DOI : 10.1103/PhysRevB.28.6358

J. W. Goodman, Statistical Properties of Laser Speckle Patterns, 2008.
DOI : 10.1007/bfb0111436

R. C. Kuhn, O. Sigwarth, C. Miniatura, D. Delande, and C. A. Müller, Coherent matter wave transport in speckle potentials, New Journal of Physics, vol.9, issue.6, p.161, 2007.
DOI : 10.1088/1367-2630/9/6/161
URL : https://hal.archives-ouvertes.fr/hal-00137714

B. Grammaticos and A. Voros, Semiclassical approximations for nuclear hamiltonians. I. Spin-independent potentials, Annals of Physics, vol.123, issue.2, p.359, 1979.
DOI : 10.1016/0003-4916(79)90343-9

M. Tabor, A semiclassical quantization of area-preserving maps, Physica D: Nonlinear Phenomena, vol.6, issue.2, p.195, 1983.
DOI : 10.1016/0167-2789(83)90005-2

G. M. Falco and A. A. Fedorenko, Instanton theory for bosons in a disordered speckle potential, Physical Review A, vol.92, issue.2, p.23412, 2015.
DOI : 10.1088/0305-4470/12/8/023

A. Altland and B. Simons, Condensed Matter Field Theory, 2010.
DOI : 10.1017/cbo9780511804236
URL : http://cds.cern.ch/record/1126063/files/9780521845083_TOC.pdf

W. Research and . Inc, Mathematica, Version 10, 2015.

G. N. Watson, A Treatise on the Theory of Bessel Functions, The Mathematical Gazette, vol.18, issue.231, 1966.
DOI : 10.2307/3605513

A. Weinrib, Percolation threshold of a two-dimensional continuum system, Physical Review B, vol.53, issue.3, p.1352, 1982.
DOI : 10.1063/1.1674565

A. Weinrib and B. I. Halperin, Distribution of maxima, minima, and saddle points of the intensity of laser speckle patterns, Physical Review B, vol.50, issue.3, p.1362, 1982.
DOI : 10.1364/JOSA.50.000838

M. Pasek, Z. Zhao, D. Delande, and G. Orso, Phase diagram of the three-dimensional Anderson model for short-range speckle potentials, Physical Review A, vol.92, issue.5, p.53618, 2015.
DOI : 10.1103/PhysRev.89.1189

S. Ghosh, D. Delande, C. Miniatura, and N. Cherroret, Coherent Backscattering Reveals the Anderson Transition, Physical Review Letters, vol.115, issue.20, p.200602, 2015.
DOI : 10.1209/0295-5075/87/37007
URL : http://arxiv.org/pdf/1506.08116

W. Magnus, On the exponential solution of differential equations for a linear operator, Communications on Pure and Applied Mathematics, vol.187, issue.4, p.649, 1954.
DOI : 10.1002/cpa.3160070404

D. R. Brillinger, Time Series: Data Analysis and Theory., Biometrics, vol.37, issue.4, 2001.
DOI : 10.2307/2530198

V. P. Leonov, A. N. Shiryaev, and . Theor, On a Method of Calculation of Semi-Invariants, Theory of Probability & Its Applications, vol.4, issue.3, p.319, 1959.
DOI : 10.1137/1104031

P. W. Anderson, Absence of Diffusion in Certain Random Lattices, Physical Review, vol.23, issue.5, p.1492, 1958.
DOI : 10.1016/S0031-8914(57)92891-4

A. A. Chabanov, M. Stoytchev, and A. Z. Genack, Statistical signatures of photon localization, Nature, vol.58, issue.6780, p.850, 2000.
DOI : 10.1103/PhysRevLett.58.226
URL : http://arxiv.org/pdf/cond-mat/0108182

T. Schwartz, G. Bartal, S. Fishman, and M. Segev, Transport and Anderson localization in disordered two-dimensional photonic lattices, Nature, vol.57, issue.7131, p.52, 2007.
DOI : 10.1051/jphys:01987004804052700

M. Störzer, P. Gross, C. M. Aegerter, and G. Maret, Observation of the Critical Regime Near Anderson Localization of Light, Physical Review Letters, vol.4, issue.6, p.63904, 2006.
DOI : 10.1103/PhysRevLett.63.259

T. Sperling, L. Schertel, M. Ackermann, G. J. Aubry, C. M. Aegerter et al., Can 3D light localization be reached in ???white paint????, New Journal of Physics, vol.18, issue.1, p.13039, 2016.
DOI : 10.1088/1367-2630/18/1/013039
URL : https://hal.archives-ouvertes.fr/hal-01222016

M. Schreiber, S. S. Hodgman, P. Bordia, H. P. Lüschen, M. H. Fischer et al., Observation of many-body localization of interacting fermions in a quasirandom optical lattice, Science, vol.326, issue.4, p.842, 2015.
DOI : 10.1016/j.aop.2010.09.012

J. Choi, S. Hild, J. Zeiher, P. Schauß, A. Rubio-abadal et al., Exploring the many-body localization transition in two dimensions, Science, vol.24, issue.6053, p.1547, 2016.
DOI : 10.1364/JOSAB.24.001268

B. Shapiro, Cold atoms in the presence of disorder, Journal of Physics A: Mathematical and Theoretical, vol.45, issue.14, p.143001, 2012.
DOI : 10.1088/1751-8113/45/14/143001

E. Akkermans and G. Montambaux, Mesoscopic physics of electrons and photons, 2007.
DOI : 10.1017/CBO9780511618833

S. Roche and D. Mayou, Conductivity of Quasiperiodic Systems: A Numerical Study, Physical Review Letters, vol.7, issue.13, p.2518, 1997.
DOI : 10.1051/jp1:1995191

H. Fehske, J. Schleede, G. Schubert, G. Wellein, V. S. Filinov et al., Numerical approaches to time evolution of complex quantum systems, Physics Letters A, vol.373, issue.25, p.2182, 2009.
DOI : 10.1016/j.physleta.2009.04.022

G. A. Baker-jr, Essentials of Padé Approximants

E. To-obtain, one starts from ? k 0 (x) ? exp(?x 2 /2? 2 )cos(k0x), i.e. from a state having a momentum distribution symmetric with respect to k = 0

M. Mulansky, K. Ahnert, A. Pikovsky, and D. L. Shepelyansky, Dynamical thermalization of disordered nonlinear lattices, Physical Review E, vol.80, issue.5, p.56212, 2009.
DOI : 10.1103/PhysRevE.76.056607
URL : https://hal.archives-ouvertes.fr/hal-00368167

A. Iomin, Subdiffusion in the nonlinear Schr??dinger equation with disorder, Physical Review E, vol.81, issue.1, p.17601, 2010.
DOI : 10.1103/PhysRevB.36.7353

N. Cherroret, A self-consistent theory of localization in nonlinear random media, Journal of Physics: Condensed Matter, vol.29, issue.2, p.24002, 2017.
DOI : 10.1088/0953-8984/29/2/024002