Products of random matrices and generalised quantum point scatterers

Alain Comtet; Christophe Texier; Yves Tourigny

hal-00504069, version 1

Products of random matrices and generalised quantum point scatterers

Alain Comtet ^1, 2, Christophe Texier ^2, 3, Yves Tourigny ⁴

Journal of Statistical Physics 140 (2010) 427-466

Résumé : To every product of $2\times2$ matrices, there corresponds a one-dimensional Schr\"{o}dinger 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.

1 : Unite mixte de service de l'institut Henri Poincaré (UMSIHP)
CNRS : UMS839 – Université Pierre et Marie Curie [UPMC] - Paris VI
2 : Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS)
CNRS : UMR8626 – Université Paris XI - Paris Sud
3 : Laboratoire de Physique des Solides (LPS)
CNRS : UMR8502 – Université Paris XI - Paris Sud
4 : School of Mathematics
University of Bristol

hal-00504069, version 1
http://hal.archives-ouvertes.fr/hal-00504069
oai:hal.archives-ouvertes.fr:hal-00504069
Contributeur : Claudine Le Vaou <>
Soumis le : Lundi 19 Juillet 2010, 17:05:11
Dernière modification le : Lundi 19 Juillet 2010, 17:05:11

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arXiv : 1004.2415

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