Schulz-Baldes H (2006)
Publication Type: Book chapter / Article in edited volumes
Publication year: 2006
Publisher: Springer Verlag
Edited Volumes: Mathematical Physics of Quantum Mechanics
Series: Lecture Notes in Physics
City/Town: Erlangen
Book Volume: 690
Pages Range: 343-350
ISBN: 3540310266
URI: http://de.arxiv.org/abs/math-ph/0607027
DOI: 10.1007/b11573432
A perturbative formula for the Lyapunov exponent of a one-dimensional random medium for weakly coupled disorder was first given by Thouless [12] and then proven rigorously by Pastur and Figotin [9]. Anomalies in the perturbation theory at the band center were discovered by Kappus and Wegner [7] and further discussed by various other authors [2,3,11]. The Lyapunov exponent is then identified with the inverse localization length of the system. This short note concerns the behavior of the Lyapunov exponent for a low density of impurities, each of which may, however, be large. The presented method is as [6,10,11] a further application of diagonalizing the transfer matrices without perturbation (here the low density of impurities) and then rigorously controlling the error terms by means of oscillatory sums of rotating modified Prüer phases. Some of the oscillatory sums remain large if the rotation phases (here the quasi-momenta) are rational. This leads to supplementary contributions of the Kappus-Wegner type. © Springer 2006.
APA:
Schulz-Baldes, H. (2006). Low density expansion for Lyapunov exponents. In J. Asch, J. Joye (Eds.), Mathematical Physics of Quantum Mechanics. (pp. 343-350). Erlangen: Springer Verlag.
MLA:
Schulz-Baldes, Hermann. "Low density expansion for Lyapunov exponents." Mathematical Physics of Quantum Mechanics. Ed. J. Asch, J. Joye, Erlangen: Springer Verlag, 2006. 343-350.
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