Abstract
Let λ(σ) be the Lyapunov exponent associated to Hy = Ey, H = −d2/dx2 + ση the one-dimensional Schrödinger operator with random potential ση. For positive eigenvalues E (or non-overdamped oscillator \(\ddot z\)+2βż+(c-ση)z=0, z=y exp(βt), E = c-β2>0) we expand λ(σ) analytically in terms of σ and compute the coefficients using regular perturbation theory.
Keywords
- Weak Solution
- Lyapunov Exponent
- Regular Semigroup
- Continuous Semigroup
- Analytic Semigroup
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References
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© 1985 Springer-Verlag
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Wihstutz, V. (1985). Analytic expansion of Lyapunov exponents associated to the Schrödinger operator. In: Albeverio, S., Combe, P., Sirugue-Collin, M. (eds) Stochastic Aspects of Classical and Quantum Systems. Lecture Notes in Mathematics, vol 1109. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0101544
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DOI: https://doi.org/10.1007/BFb0101544
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