W. Aschbacher, V. Jak?i´cjak?i´c, Y. Pautrat, and C. Pillet, Transport properties of quasi-free fermions, Journal of Mathematical Physics, vol.48, issue.3, p.32101, 2007.
DOI : 10.1063/1.2709849
URL : https://hal.archives-ouvertes.fr/hal-00109016

. Av and A. Avila, On the Kotani-Last and Schrödinger conjectures

B. Sâad, R. Pillet, and C. , A geometric approach to the Landauer-B??ttiker formula, Journal of Mathematical Physics, vol.55, issue.7, p.75202, 2014.
DOI : 10.1063/1.4879238

J. Breuer, Y. Last, and Y. Strauss, Eigenvalue spacings and dynamical upper bounds for discrete one-dimensional Schr??dinger operators, Duke Mathematical Journal, vol.157, issue.3, pp.425-460, 2011.
DOI : 10.1215/00127094-2011-006

L. Bruneau, V. Jak?i´cjak?i´c, and C. A. Pillet, Landauer-B??ttiker Formula and Schr??dinger Conjecture, Communications in Mathematical Physics, vol.124, issue.2, pp.501-513, 2013.
DOI : 10.1007/s00220-012-1628-3
URL : http://arxiv.org/abs/1201.3190

L. Bruneau, V. Jak?i´cjak?i´c, Y. Last, and C. A. Pillet, Landauer-Büttiker and Thouless conductance, Commun. Math. Phys., online first, 2015.

L. Bruneau, V. Jak?i´cjak?i´c, Y. Last, and C. A. Pillet, What is absolutely continuous spectrum? In preparation

M. Büttiker, Y. Imry, R. Landauer, and S. Pinhas, Generalized many-channel conductance formula with application to small rings, Physical Review B, vol.31, issue.10, p.6207, 1985.
DOI : 10.1103/PhysRevB.31.6207

. Ca and R. Carmona, One dimensional Schrödinger operators with random or deterministic potentials: New spectral types, J. Funct. Anal, vol.51, pp.229-258, 1983.

G. Cgm-]-casati, I. Guarneri, and G. Maspero, Landauer and Thouless Conductance: a Band Random Matrix Approach, Journal de Physique I, vol.7, issue.5, p.729, 1997.
DOI : 10.1051/jp1:1997187

H. D. Cjm-]-cornean, A. Jensen, and V. Moldoveanu, A rigorous proof of the Landauer???B??ttiker formula, Journal of Mathematical Physics, vol.46, issue.4, p.42106, 2005.
DOI : 10.1063/1.1862324

P. Ds-]-deift and B. Simon, Almost periodic Schr???dinger operators, Communications in Mathematical Physics, vol.5, issue.3, pp.389-411, 1983.
DOI : 10.1007/BF01206889

J. T. Edwards and D. J. Thouless, Numerical studies of localization in disordered systems, Journal of Physics C: Solid State Physics, vol.5, issue.8, pp.807-820, 1972.
DOI : 10.1088/0022-3719/5/8/007

F. Gs-]-gesztesy and B. Simon, The xi function, Acta Mathematica, vol.176, issue.1, pp.49-71, 1996.
DOI : 10.1007/BF02547335

D. J. Gilbert and D. Pearson, On subordinacy and analysis of the spectrum of one-dimensional Schr??dinger operators, Journal of Mathematical Analysis and Applications, vol.128, issue.1, p.30, 1987.
DOI : 10.1016/0022-247X(87)90212-5

. Jlpa, V. Jak?i´cjak?i´c, B. Landon, and A. Panati, A note on reflectionless Jacobi matrices, Commun. Math. Phys, vol.332, pp.827-838, 2014.

V. Jak?i´cjak?i´c, Y. Ogata, Y. Pautrat, and C. Pillet, Entropic fluctuations in quantum statistical mechanics?an introduction. In Quantum Theory from Small to Large Scales, 2012.

. Ko and S. Kotani, Lyapunov indices determine absolutely continuous spectra of stationary random one-dimensional Schrödinger operators, pp.225-247, 1984.

D. Kr-]-krutikov, R. , and C. , Schr??dinger Operators with Sparse Potentials: Asymptotics of the Fourier Transform??of the Spectral Measure, Communications in Mathematical Physics, vol.223, issue.3, pp.509-532, 2001.
DOI : 10.1007/s002200100552

R. Landauer, Electrical resistance of disordered one-dimensional lattices, Philosophical Magazine, vol.1, issue.172, p.863, 1970.
DOI : 10.1080/00018736100101271

Y. Last, Conductance and spectral properties, 1994.

. Las2 and Y. Last, On the measure of gaps and spectra for discrete 1D Schrödinger operators, Commun. Math. Phys, vol.149, pp.347-360, 1992.

. Las3 and Y. Last, A relation between a.c. spectrum of ergodic Jacobi matrices and the spectra of periodic approximants, Commun. Math. Phys, vol.151, pp.183-192, 1993.

. Las, Y. Last, and B. Simon, Eigenfunctions, transfer matrices, and absolutely continuous spectrum of one-dimensional Schrödinger operators, Invent. Math, vol.135, p.329, 1999.

V. P. Mmg-]-maslov, S. A. Molchanov, A. Gordon, and . Ya, Behavior of generalized eigenfunctions at infinity and the Schrödinger conjecture, Russian J. Math. Phys, vol.1, p.71, 1993.

[. Nenciu and G. , Independent electron model for open quantum systems: Landauer-B??ttiker formula and strict positivity of the entropy production, Journal of Mathematical Physics, vol.48, issue.3, p.33302, 2007.
DOI : 10.1063/1.2712418

. Re and C. Remling, The absolutely continuous spectrum of Jacobi matrices, Annals of Mathematics, vol.174, issue.1, pp.125-171, 2011.

. Shso, M. Shamis, and S. Sodin, On the measure of the absolutely continuous spectrum for Jacobi matrices, J. Spectr. Theory, vol.1, pp.349-362, 2011.

B. Si1-]-simon, Bounded eigenfunctions and absolutely continuous spectra for one dimensional Schrödinger operators, Proc. Amer, p.3361, 1996.

B. Simon, Schr??dinger semigroups, Bulletin of the American Mathematical Society, vol.7, issue.3, p.447, 1982.
DOI : 10.1090/S0273-0979-1982-15041-8

B. Si3-]-simon, Szegö's Theorem and Its Descendants. Spectral theory for L 2 Perturbations of Orthogonal Polynomials. M.B. Porter Lectures, 2011.

B. Si4-]-simon, Kotani theory for one dimensional stochastic Jacobi matrices, Communications in Mathematical Physics, vol.75, issue.2, pp.227-234, 1983.
DOI : 10.1007/BF01211829

B. Si5-]-simon, Orthogonal polynomials with exponentially decaying recursion coefficients. Probability and Mathematical Physics, CRM Proc. and Lecture Notes, pp.453-463, 2007.

[. Yafaev and D. R. , Mathematical scattering theory. General theory. Translated from the Russian by, J. R. Schulenberger. Translations of Mathematical Monographs, vol.105, 1992.
URL : https://hal.archives-ouvertes.fr/hal-00707502