Some Results on Lyapunov Exponents for Products of Random Matrices

Abstract

Many problems in physics can be reduced to product of random matrices [1,2]. Let us briefly discuss some cases. In the one dimensional disordered systems, i.e., with Hamiltonian containing random couplings and random fields (for example a disordered Ising chain) the free energy is related to the maximum Lyapunov exponent λ1 of the product of suitable random transfer matrices. Another example is given by the discretized Schrödinger equation on a one dimensional lattice with a random potential [2]. Indeed, one can write the equation in terms of product of random matrices and in this case λ1 is the inverse of the characteristic length of the localized wave functions.KeywordsLyapunov ExponentRandom MatriceAsymptotic DistributionRandom MatrixRandom PotentialThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.