The Lyapunov exponent of products of random \(2\times 2\) matrices close to the identity

DOI10.1007/s10955-012-0674-8zbMath1259.82049arXiv1208.6430OpenAlexW3103402445MaRDI QIDQ1942210

Christophe Texier, Jean-Marc Luck, Alain Comtet, Yves Tourigny

Publication date: 18 March 2013

Published in: Journal of Statistical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1208.6430

zbMATH Keywords

random matricesquantum mechanicsLyapunov exponentAnderson localizationIwasawa decompositiondisordered one-dimensional systems

Mathematics Subject Classification ID

Disordered systems (random Ising models, random Schrödinger operators, etc.) in equilibrium statistical mechanics (82B44) Random matrices (algebraic aspects) (15B52) Bessel and Airy functions, cylinder functions, ({}_0F_1) (33C10) Classical hypergeometric functions, ({}_2F_1) (33C05)

Related Items (14)

An investigation of PT -symmetry breaking in tight-binding chains ⋮ Scaling laws for weakly disordered 1D flat bands ⋮ Lyapunov exponents for products of complex Gaussian random matrices ⋮ Fluctuations of the product of random matrices and generalized Lyapunov exponent ⋮ Lyapunov exponent, universality and phase transition for products of random matrices ⋮ Continuum limit of random matrix products in statistical mechanics of disordered systems ⋮ On the coexistence of competing languages ⋮ Fluctuations of random matrix products and 1D Dirac equation with random mass ⋮ The open quantum Brownian motions ⋮ Dyson’s disordered linear chain from a random matrix theory viewpoint ⋮ One-dimensional disordered quantum mechanics and Sinai diffusion with random absorbers ⋮ Lyapunov exponent for products of random Ising transfer matrices: the balanced disorder case ⋮ Exponential number of equilibria and depinning threshold for a directed polymer in a random potential ⋮ Large deviations of the Lyapunov exponent in 2D matrix Langevin dynamics with applications to one-dimensional Anderson localization models

Uses Software

• DLMF

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