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A random phase property establishing in the weak coupling limit a link between quasi-one-dimensional random Schrödinger operators and full random matrix theory is advocated. Briefly summarized it states that the random transfer matrices placed into a normal system of coordinates act on the isotropic frames and lead to a Markov process with a unique invariant measure which is of geometric nature. On the elliptic part of the transfer matrices, this measure is invariant under the unitaries in the hermitian symplectic group of the universality class under study. While the random phase property can up to now only be proved in special models or in a restricted sense, we provide strong numerical evidence that it holds in the Anderson model of localization. A main outcome of the random phase property is a perturbative calculation of the Lyapunov exponents which shows that the Lyapunov spectrum is equidistant and that the localization lengths for large systems in the unitary, orthogonal and symplectic ensemble differ by a factor 2 each. In an Anderson-Ando model on a tubular geometry with magnetic field and spin-orbit coupling, the normal system of coordinates is calculated and this is used to derive explicit energy dependent formulas for the Lyapunov spectrum. \ud
[EF] K. B. Efetov, A. I. Larkin, Kinetics of a quantum particle in long metallic wires, Sov. Phys. JETP 58, 444-451 (1983).
[FYMS] L. S. Froufe-P´erez, M. Y´epez, P. A. Mello, J. . S´aenz, Statistical scattering of waves in disordered waveguides: From microscopic potentials to limiting macroscopic statistics, Phys. Rev. E 75, 031113-031141 (2007).
[HP] F. Hiai, D. Petz, The Semicircle Law, Free Random Variables and Entropy, (AMS, Providence, 2000).
[HM] J. E. Howard, R. S. MacKay, Linear stability of symplectic maps, J. Math. Phys. 28, 1036-1051 (1987).
[MK] A. MacKinnon, B. Kramer, One-parameter scaling of localization length and conductance in disordered systems, Phys. Rev. Lett. 47, 1546-1549 (1981).
[MC] A. M. S. Macˆedo, J. T. Chalker, Effects of spin-orbit interactions in disordered conductors: A random-matrix approach, Phys. Rev. B 46, 14985-14994 (1992).
[Meh] M. L. Mehta, Random Matrices, Second Edition, (Academic Press, San Diego, 1991).
[MPK] P. A. Mello, P. Pereyra, N. Kumar, Macroscopic approach to multichannel disordered conductors, Ann. Phys. 181, 290-317 (1988).
[MS] P. A. Mello, B. Shapiro, Existence of a limiting distribution for disordered electronic conductors, Phys. Rev. B 37, 5860-5863 (1988).
[MSt] P. A. Mello, A. D. Stone, Maximum-entropy model for quantum-mechanical interference effects in metallic conductors, Phys. Rev. B 44, 3559-3576 (1991).
[MT] P. A. Mello, S. Tomsovic, Scattering approach to quantum electronic transport, Phys. Rev. B 46, 15963-15981 (1992).
[PF] L. Pastur, A. Figotin, Spectra of Random and Almost-Periodic Operators, (Springer, Berlin, 1992).
[PS] J.-L. Pichard, G. Sarma, Finite-size scaling approach to Anderson localisation I and II, J. Phys. C 14, L127-132 and L617-625 (1981).
[Tho] D. J. Thouless, Maximum metallic resistance in thin wires, Phys. Rev. Lett. 39, 1167- 1170 (1977).
[ATAF] P. W. Anderson, D. J. Thouless, E. Abrahams, D. S. Fisher, New method for a scaling theory of localization, Phys. Rev. B 22, 3519-3526 (1980).
[CB] J. T. Chalker, M. Bernhardt, Scattering theory, transfer matrices, and Anderson localization, Phys. Rev. Lett. 70, 982-985 (1993)
[Do1] O. N. Dorokhov, Electron localization in a multichannel conductor, Sov. Phys. JETP 58, 606-615 (1983).
[Do2] O. N. Dorokhov, On the coexistence of localized and extended electronic states in the metalic phase, Solid State Commun. 51, 381-384 (1984).
[Do3] O. N. Dorokhov, Solvable model of multichannel localization, Phys. Rev. B 37, 10526- 10541 (1988).
[Dys] F. Dyson, The dynamics of a disordered linear chain, Phys. Rev. 92, 1331-1338 (1953).
[EF] K. B. Efetov, A. I. Larkin, Kinetics of a quantum particle in long metallic wires, Sov. Phys. JETP 58, 444-451 (1983).
[FYMS] L. S. Froufe-P´erez, M. Y´epez, P. A. Mello, J. . S´aenz, Statistical scattering of waves in disordered waveguides: From microscopic potentials to limiting macroscopic statistics, Phys. Rev. E 75, 031113-031141 (2007).
[PS] J.-L. Pichard, G. Sarma, Finite-size scaling approach to Anderson localisation I and II, J. Phys. C 14, L127-132 and L617-625 (1981).