Abstract
The weak disorder expansion for a random Schrödinger equation with off-diagonal disorder in one dimension is studied. The invariant measure, the density of states, and the Lyapunov exponent are computed. The most interesting feature in this model appears at the band center, where the differentiated density of states diverges, while the Lyapunov exponent vanishes. The invariant measure approaches an atomic measure concentrated on zero and infinity. The results extend previous work of Markos to all orders of perturbation theory.
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References
P. Bougerol and J. Lacroix,Products of Random Matrices with Applications to Schrödinger Operators (Birkhäuser, Boston, 1985).
A. Bovier and A. Klein,J. Stat. Phys. 51:501 (1988).
M. Campanino and J. F. Perez,Commun. Math. Phys. (1989), to appear.
B. Derrida and E. Gardner,J. Phys. (Paris)45:1283 (1984).
F. Dyson,Phys. Rev. 92:1331 (1953).
H. Fürstenberg,Trans. Am. Math. Soc. 108:377 (1963).
M. Kappus and F. Wegner,Z. Phys. B 45:15 (1981).
P. Markos,J. Phys. C 21:2147 (1988).
P. Markos,Z. Phys. B 73:17 (1988).
D. Ruelle,IHES Publ. 50:275 (1979).
E. Roman and C. Wiecko,Z. Phys. B 62:163 (1986);69:81 (1987).
B. Simon and M. Taylor,Commun. Math. Phys. 101:1 (1985).
G. Theodorou and M. H. Cohen,Phys. Rev. B 13:4597 (1976).
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Bovier, A. Perturbation expansion for a one-dimensional Anderson model with off-diagonal disorder. J Stat Phys 56, 645–668 (1989). https://doi.org/10.1007/BF01016772
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DOI: https://doi.org/10.1007/BF01016772