more likely that the fitting procedures overestimate the infinite-time value $\langle Y_2\rangle^{(dyn)}_{p_0, \tau}$. Nevertheless, Eq. (\[equ:BBconjecture\]) gives a simple and elegant approximation.

Participation ratio and other localization measures {#sec:dynloc}
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What does dynamical localization (not) mean? {#subsec:locmeasures}
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The localization of states was extensively studied for vibrational excitations and in quantum models, where different localization criteria were applied mostly to the eigenstates of the corresponding Hamiltonians; in a typical case all of them lead to the same kind of conclusions on whether the corresponding state is localized or not. Thus, the participation ratio quantifies to what extent the localized state is *concentrated* on a small subset of all sites. The standard criterion for localization which is both theoretically transparent and easy for numerical implementation, especially in one dimension, is based on the evaluation of the Lyapunov exponent $\gamma$ which corresponds to the rate of exponential growth of the amplitude with the coordinate [@Ishii1973; @Comtet2013; @Thouless1972], and determines the behavior of the state outside of its localization region. We will consider the behavior of the Lyapunov exponent later on in this paper.

One can also quantify the localization by the radius of gyration $R_G$ of the corresponding state, which indicates the 