Generalized Lyapunov exponent for the one-dimensional Schrödinger equation with Cauchy disorder: Some exact results

  title={Generalized Lyapunov exponent for the one-dimensional Schr{\"o}dinger equation with Cauchy disorder: Some exact results},
  author={Alain Comtet and Christophe Texier and Yves Tourigny},
  journal={Physical Review E},
We consider the one-dimensional Schrödinger equation with a random potential and study the cumulant generating function of the logarithm of the wave function ψ(x), known in the literature as the generalized Lyapunov exponent; this is tantamount to studying the statistics of the so-called “finite size Lyapunov exponent”. The problem reduces to that of finding the leading eigenvalue of a certain non-random non-self-adjoint linear operator defined on a somewhat unusual space of functions. We focus… 

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