Statistical properties and scaling of the Lyapunov exponents in stochastic systems [Elektronische Ressource] / von Rüdiger Zillmer

Aus dem Institut f r Physik der Universit t PotsdamStatistical Properties and Scalingof the Lyapunov Exponentsin Stochastic SystemsDissertationzur Erlangung des akademischen GradesDoktor der Naturwissenschaften (Dr. rer. nat.)in der Wissenschaftsdisziplin Theoretische Physikeingereicht an derMathematisch-Naturwissenschaftlichen Fakult tder Universit t PotsdamvonR? DIGER ZILLMERgeboren am 21. M rz 1969 in SchwedtPotsdam, im Oktober 2003AbstractThis work incorporates three treatises which are commonly concerned with a stochastic theory ofthe Lyapunov exponents. With the help of this theory universal scaling laws are investigated whichappear in coupled chaotic and disordered systems.First, two continuous-time stochastic models for weakly coupled chaotic systems are introducedto study the scaling of the Lyapunov exponents with the coupling strength (coupling sensitivityof chaos). By means of the the Fokker-Planck formalism scaling relations are derived, which arecon rmed by results of numerical simulations.Next, coupling sensitivity is shown to exist for coupled disordered chains, where it appears as asingular increase of the localization length. Numerical ndings for coupled Anderson models arecon rmed by analytic results for coupled continuous-space Schr dinger equations. The resultingscaling relation of the localization length resembles the scaling of the Lyapunov exponent of coupledchaotic systems.