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DY: Dynamik und Statistische Physik

DY 40: Lyapunov Instability of Many-Body Systems

DY 40.7: Talk

Thursday, March 11, 2004, 11:15–11:30, H2

Anomalous behavior of the localization length in one-dimensional Anderson localization. — •Rüdiger Zillmer — Institut für Physik, Universität Potsdam

A common example of exponential localization of the wavefunction in disordered systems is given by the Anderson model. The localization length can be assigned to the Lyapunov exponent of the corresponding product of random transfer matrices. We consider the largest Lyapunov exponent and the second generalized one, which are associated to different average procedures. In case that single parameter scaling holds, these two exponents coincide. We show analytically and numerically that at the band center the largest exponent is not differentiable with respect to the energy whereas the generalized exponent behaves regularly. This difference corresponds to a different behavior of the typical and the average conductivity, respectively.