,

The classical figure 1.4 shows that, at least for

, there are invariant lines in the phase portrait encircling the origin. In order to exclude the possibility that these classical invariant lines account for the observed localized quantum dynamics, in the present section initial states are used that are shifted to

, well beyond the outermost surviving invariant line. Essentially, the same localized rotation dynamics as in the previous subsection is obtained.

$\begin{figure} % latex2html id marker 42139 \par \vspace*{-0.0cm} \par \hspace*{... ...Initial state: $\left\vert \psi_0 \right>=\left\vert 0 \right>$. } \end{figure}$

$\begin{figure} % latex2html id marker 42425 \par \vspace*{-0.0cm} \par \hspace*{... ...Initial state: $\left\vert \psi_0 \right>=\left\vert 5 \right>$. } \end{figure}$

$\begin{figure} % latex2html id marker 42696 \par \vspace*{-0.0cm} \par \hspace*{... ...Initial state: $\left\vert \psi_0 \right>=\left\vert 5 \right>$. } \end{figure}$

$\begin{figure} % latex2html id marker 42967 \par \vspace*{-0.0cm} \par \hspace*{... ...Initial state: $\left\vert \psi_0 \right>=\left\vert 5 \right>$. } \end{figure}$

$\begin{figure} % latex2html id marker 43238 \par \vspace*{-0.0cm} \par \hspace*{... ...nitial state: $\left\vert \psi_0 \right>=\left\vert 50 \right>$. } \end{figure}$

$\begin{figure} % latex2html id marker 43499 \par \vspace*{-0.0cm} \par \hspace*{... ...nitial state: $\left\vert \psi_0 \right>=\left\vert 50 \right>$. } \end{figure}$

$\begin{figure} % latex2html id marker 43710 \par \vspace*{-0.0cm} \par \hspace*{... ...ert \psi_0 \right>=\hat{D}\big(0,12.5\big)\left\vert 0 \right>$. } \end{figure}$

$\begin{figure} % latex2html id marker 43934 \par \vspace*{-0.0cm} \par \hspace*{... ...ert \psi_0 \right>=\hat{D}\big(0,12.5\big)\left\vert 0 \right>$. } \end{figure}$

$\begin{figure} % latex2html id marker 44206 \par \vspace*{-0.0cm} \par \hspace*{... ...ert \psi_0 \right>=\hat{D}\big(0,12.5\big)\left\vert 0 \right>$. } \end{figure}$

$\begin{figure} % latex2html id marker 44478 \par \vspace*{-0.0cm} \par \hspace*{... ...ert \psi_0 \right>=\hat{D}\big(0,12.5\big)\left\vert 5 \right>$. } \end{figure}$

$\begin{figure} % latex2html id marker 44740 \par \vspace*{-0.0cm} \par \hspace*{... ...ert \psi_0 \right>=\hat{D}\big(0,12.5\big)\left\vert 5 \right>$. } \end{figure}$

$\begin{figure} % latex2html id marker 44952 \par \vspace*{-0.0cm} \par \hspace*{... ...ert \psi_0 \right>=\hat{D}\big(0,12.5\big)\left\vert 5 \right>$. } \end{figure}$