Products of random matrices and generalised quantum point scatterers
arXiv:1004.2415 · doi:10.1007/s10955-010-0005-x
Abstract
To every product of $2\times2$ matrices, there corresponds a one-dimensional Schrödinger equation whose potential consists of generalised point scatterers. Products of {\em random} matrices are obtained by making these interactions and their positions random. We exhibit a simple one-dimensional quantum model corresponding to the most general product of matrices in $\text{SL}(2, {\mathbb R})$. We use this correspondence to find new examples of products of random matrices for which the invariant measure can be expressed in simple analytical terms.
38 pages, 13 pdf figures. V2 : conclusion added ; Definition of function $Ω$ changed