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Products of Random Matrices and Generalised Quantum Point Scatterers


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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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).

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  • Random matrices
  • Disordered one-dimensional quantum mechanics
  • Anderson localisation
  • Lyapunov exponent
  • Generalised point scatterers
  • Supersymmetric quantum mechanics