Abstract
We give an upper bound for the high-energy behavior of the Lyapunov exponent of the one-dimensional Schrödinger equation. We relate this behavior to the diffrentiability properties of the potential. As an application, this result provides an upper bound for the asymptotic length of the gaps of the Schrödinger equation.
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Delyon, F., Foulon, P. Adiabatic invariants and asymptotic behavior of Lyapunov exponents of the Schrödinger equation. J Stat Phys 45, 41–47 (1986). https://doi.org/10.1007/BF01033075
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DOI: https://doi.org/10.1007/BF01033075