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Products of Random Matrices and Generalised Quantum Point Scatterers

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Abstract

To every product of 2×2 matrices, there corresponds a one-dimensional Schrödinger equation whose potential consists of generalised point scatterers. Products of 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 SL(2,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.

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Authors and Affiliations

  1. UPMC Univ. Paris 6, 75005, Paris, France

    Alain Comtet

  2. Univ. Paris Sud, CNRS, LPTMS, UMR8626, Bât. 100, 91405, Orsay, France

    Alain Comtet & Christophe Texier

  3. Univ. Paris Sud, CNRS, LPS, UMR8502, Bât. 510, 91405, Orsay, France

    Christophe Texier

  4. School of Mathematics, University of Bristol, Bristol, BS8 1TW, UK

    Yves Tourigny

Authors
  1. Alain Comtet
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  2. Christophe Texier
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  3. Yves Tourigny
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Corresponding author

Correspondence to Christophe Texier.

Additional information

We thank Jean-Marc Luck for drawing to our attention the work of T.M. Nieuwenhuizen, and Tom Bienaimé for participating in the study of the supersymmetric model.

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Comtet, A., Texier, C. & Tourigny, Y. Products of Random Matrices and Generalised Quantum Point Scatterers. J Stat Phys 140, 427–466 (2010). https://doi.org/10.1007/s10955-010-0005-x

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