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In [10] Jitomirskaya, Kr\"uger and Liu analysed the dynamical decay inexpectation for the super-critical almost-Mathieu operator in function of thecoupling parameter , showing that it is equal to the Lyapunov exponent of itstransfer matrix cocycle, and asked whether the same is true for the 1d Andersonmodel. We show that this is essentially never true when the disorder parameteris sufficiently large.

Non-Lyapunov annealed decay for 1d Anderson eigenfunctions