Scaling diagram for the localization length at a band edge
Christian Sadel, Hermann Schulz-Baldes
TL;DR
This paper develops a scaling diagram for the localization length at a band edge in random Jacobi matrices, using a Fokker-Planck approach to analyze Lyapunov exponents and density of states.
Contribution
It introduces a weak-coupling scaling diagram for localization properties near band edges, utilizing a Fokker-Planck operator for Pr"ufer phase analysis.
Findings
Derived a scaling diagram for the Lyapunov exponent
Connected the density of states with localization length
Applied Fokker-Planck operator to Pr"ufer phases
Abstract
A weak-coupling scaling diagram for the Lyapunov exponent and the integrated density of states near a band edge of a random Jacobi matrix is obtained. The analysis is based on the use of a Fokker-Planck operator describing the drift-diffusion of the Pr\"ufer phases.
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