Fluctuations of the Lyapunov exponent in 2D disordered systems

Abstract

We report a numerical investigation of the fluctuations of the Lyapunov exponent of a two dimensional non-interacting disordered system. While the ratio of the mean to the variance of the Lyapunov exponent is not constant, as it is in one dimension, its variation is consistent with the single parameter scaling hypothesis.

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• Phase diagrams of Weyl semimetals with competing intraorbital and interorbital disorders
• Topological inverse Anderson insulator
• Delocalization and scaling properties of low-dimensional quasiperiodic systems
• Breaking the chains: extreme value statistics and localization in random spin chains
• Identities and exponential bounds for transfer matrices
• Crossover from diffusive to strongly localized regime in two-dimensional systems
• Scaling properties of one-dimensional off-diagonal disorder
• Quantum transport phenomena in disordered electron systems with spin-orbit coupling in two dimensions and below
• Boundary hopping and the mobility edge in the Anderson model in three dimensions
• Quantum transport in the black-hole configuration of an atom condensate outcoupled through an optical lattice
• A stochastic method to compute the $L^2$ localisation landscape
• Universal scheme to generate metal-insulator transition in disordered systems
• Counting the exponents of single transfer matrices