Statistics of quantum recurrences in the Hilbert space
A. Iomin$^{a}$ and G.M. Zaslavsky$^{b,c}$
This paper has been withdrawn by the authors due to a crucial error.
nlin0506031.tex
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\begin{document}

\title{Statistics of quantum recurrences in the Hilbert space}
\author{A. Iomin$^{a}$ and G.M. Zaslavsky$^{b,c}$ }
\affiliation{$^a$ Department of Physics, Technion, Haifa, 32000, Israel
\\
$^b$ Courant Institute of Mathematical Sciences,  
New York University, 251 Mercer Str., New York, NY 10012  \\
$^c$  Department of Physics, New York University, 
2-4 Washington Place, New York, NY 10003 }

\date{\today}
\begin{abstract}
This paper has been withdrawn by the authors due to a crucial error. 
\end{abstract}
\pacs{05.45.Mt}

\maketitle


%%\section*{Acknowledgments}  
A.I. was supported  by the Israel Science Foundation and  the  Minerva 
Center for Nonlinear Physics of Complex Systems. G.M.Z. was supported by 
the Office of Naval Research Grants no. N00014-02-1-0056, N00014-97-1-0426.

\begin{thebibliography}{99}

\bibitem{phyrep} G.M. Zaslavsky, Phys. Rep. {\bf 371}, 461 (2002).

\bibitem{margulis} G.A. Margulis, Functs. Ann. i Prilozh. {\bf 3}, 80 
(1969); {\bf 4}, 62 (1970).

\bibitem{kac} M.Kac, {\em Probability and Related Topics in Physical 
Sciences}. (Interscience, New York, 1958).

\bibitem{meiss97} J.D. Meiss, Chaos {\bf 7}, 39 (1997).

\bibitem{tippet} G.M. Zaslavsky and M.K. Tippett, Phys. Rev. Lett.
{\bf 67}, 325 (1991).

\bibitem{afraimovich} V. Afraimovich and G.M. Zaslavsky, Chaos
{\bf 13}, 519 (2003).

\bibitem{revival} J.H. Eberly N.B. Narozhny, and J.J. 
S\'anches-Mondrag\'on, Phys. Rev. Lett. {\bf 44}, 1323 (1980);
J. Parker and C.R. Stroud Jr., Phys. Rev. Lett. {\bf 56}, 716 (1986);
B. Yurke and D. Stoler, Phys. Rev. Lett. {\bf 57}, 13 (1986);
G. Alber, H. Ritsch, and P. Zoller, Phys. Rev. A {\bf 34}, 1058 (1986).

\bibitem{kar} C.F.F. Karney, Physica D {\bf8}, 360 (1983).

\bibitem{meln} V.K. Melnikov, in {\em Transport, Chaos and Plasma Physics,
II, Proceedings, Marseille}, edited by F. Doveil, S. Benkadda, and
Y. Elskens (World Scientific, Singapore, 1996), p. 142.

\bibitem{vered} V. Rom-Kedar and G.M. Zaslavsky, Chaos, {\bf 9},
697 (1999).

\bibitem{zen} G.M. Zaslavsky, M. Edelman, and B.A. Niyazov,
Chaos, {\bf 7}, 159 (1997).

\bibitem{hoa} J.D. Hanson, E. Ott, and T.M. Antonsen,
Phys. Rev. A {\bf 29}, 819 (1984).

\bibitem{dana} I. Dana, Phys. Rev. E {\bf 69}, 016212 (2004);
O. Barash and I. Dana, Phys. Rev. E {\bf 71}, 036222 (2005). 

\bibitem{ze} A. Iomim and G.M. Zaslavsky, Phys. Rev. E {\bf 60}, 7580 
(1999); G. M. Zaslavsky and M. Edelman, Chaos {\bf 10}, 135 (2000).

\bibitem{12zz} S. Benkadda, S. Kassibrakis, R. White, and G. Zaslavsky,
Phys. Rev. E {\bf 55}, 4909 (1997);
S. Benkadda, S. Kassibrakis, R. White, and G. Zaslavsky, Phys. Rev. E
{\bf 59}, 3761 (1999).

\bibitem{sz} B. Sundaram and G.M. Zaslavsky, Phys. Rev. E {\bf 59}, 7231
(1999).

\bibitem{ifz} A. Iomin and G.M. Zaslavsky, Phys. Rev. E {\bf63}, 047203
(2001); A. Iomin, S. Fishman, and G.M. Zaslavsky, Phys. Rev. E
{\bf 65}, 036215 (2002).

\bibitem{chang} S-J Chang and K-J Shi, Phys. Rev. A {\bf 34}, 7 (1986).

\bibitem{izshep} F.M. Izrailev and D.L. Shepelyansky, Sov. Phys. 
Dokl. {\bf 24}, 996 (1979).

\bibitem{yel} E. Janke, F. Emde, F. L\"osh, {\em Tables of Higher 
Functions}, (McGraw--Hill, NY, 1960).

\bibitem{rol} R. Ketzmerick, K. Kruse, and T. Geisel, Physica D
{\em 131}, 247 (1999).

\bibitem{izrailev} F.M. Izrailev, Phys. Rep. {\bf 196}, 299 (1990).

\bibitem{zyfn} G.M. Zaslavsky, Phys. Rep. {\bf 80}, 157 (1981);
Sov. Phys. Uspekhi {\bf 16}, 761 (1974).

\bibitem{procaccia} P. Grassberger and I. Procaccia, Physica D {\bf 9},
189 (1983).

\bibitem{sauer} T. Sauer, Phys. Rev. Lett. {\bf 72} 3811 (1994); R. 
Castro, T. Sauer, Phys. Rev. E {\bf 55} 287 (1997).

\end{thebibliography}
\end{document}


nlin0506031.extracted_bib
\begin{thebibliography}{99}

\bibitem{phyrep} G.M. Zaslavsky, Phys. Rep. {\bf 371}, 461 (2002).

\bibitem{margulis} G.A. Margulis, Functs. Ann. i Prilozh. {\bf 3}, 80 
(1969); {\bf 4}, 62 (1970).

\bibitem{kac} M.Kac, {\em Probability and Related Topics in Physical 
Sciences}. (Interscience, New York, 1958).

\bibitem{meiss97} J.D. Meiss, Chaos {\bf 7}, 39 (1997).

\bibitem{tippet} G.M. Zaslavsky and M.K. Tippett, Phys. Rev. Lett.
{\bf 67}, 325 (1991).

\bibitem{afraimovich} V. Afraimovich and G.M. Zaslavsky, Chaos
{\bf 13}, 519 (2003).

\bibitem{revival} J.H. Eberly N.B. Narozhny, and J.J. 
S\'anches-Mondrag\'on, Phys. Rev. Lett. {\bf 44}, 1323 (1980);
J. Parker and C.R. Stroud Jr., Phys. Rev. Lett. {\bf 56}, 716 (1986);
B. Yurke and D. Stoler, Phys. Rev. Lett. {\bf 57}, 13 (1986);
G. Alber, H. Ritsch, and P. Zoller, Phys. Rev. A {\bf 34}, 1058 (1986).

\bibitem{kar} C.F.F. Karney, Physica D {\bf8}, 360 (1983).

\bibitem{meln} V.K. Melnikov, in {\em Transport, Chaos and Plasma Physics,
II, Proceedings, Marseille}, edited by F. Doveil, S. Benkadda, and
Y. Elskens (World Scientific, Singapore, 1996), p. 142.

\bibitem{vered} V. Rom-Kedar and G.M. Zaslavsky, Chaos, {\bf 9},
697 (1999).

\bibitem{zen} G.M. Zaslavsky, M. Edelman, and B.A. Niyazov,
Chaos, {\bf 7}, 159 (1997).

\bibitem{hoa} J.D. Hanson, E. Ott, and T.M. Antonsen,
Phys. Rev. A {\bf 29}, 819 (1984).

\bibitem{dana} I. Dana, Phys. Rev. E {\bf 69}, 016212 (2004);
O. Barash and I. Dana, Phys. Rev. E {\bf 71}, 036222 (2005). 

\bibitem{ze} A. Iomim and G.M. Zaslavsky, Phys. Rev. E {\bf 60}, 7580 
(1999); G. M. Zaslavsky and M. Edelman, Chaos {\bf 10}, 135 (2000).

\bibitem{12zz} S. Benkadda, S. Kassibrakis, R. White, and G. Zaslavsky,
Phys. Rev. E {\bf 55}, 4909 (1997);
S. Benkadda, S. Kassibrakis, R. White, and G. Zaslavsky, Phys. Rev. E
{\bf 59}, 3761 (1999).

\bibitem{sz} B. Sundaram and G.M. Zaslavsky, Phys. Rev. E {\bf 59}, 7231
(1999).

\bibitem{ifz} A. Iomin and G.M. Zaslavsky, Phys. Rev. E {\bf63}, 047203
(2001); A. Iomin, S. Fishman, and G.M. Zaslavsky, Phys. Rev. E
{\bf 65}, 036215 (2002).

\bibitem{chang} S-J Chang and K-J Shi, Phys. Rev. A {\bf 34}, 7 (1986).

\bibitem{izshep} F.M. Izrailev and D.L. Shepelyansky, Sov. Phys. 
Dokl. {\bf 24}, 996 (1979).

\bibitem{yel} E. Janke, F. Emde, F. L\"osh, {\em Tables of Higher 
Functions}, (McGraw--Hill, NY, 1960).

\bibitem{rol} R. Ketzmerick, K. Kruse, and T. Geisel, Physica D
{\em 131}, 247 (1999).

\bibitem{izrailev} F.M. Izrailev, Phys. Rep. {\bf 196}, 299 (1990).

\bibitem{zyfn} G.M. Zaslavsky, Phys. Rep. {\bf 80}, 157 (1981);
Sov. Phys. Uspekhi {\bf 16}, 761 (1974).

\bibitem{procaccia} P. Grassberger and I. Procaccia, Physica D {\bf 9},
189 (1983).

\bibitem{sauer} T. Sauer, Phys. Rev. Lett. {\bf 72} 3811 (1994); R. 
Castro, T. Sauer, Phys. Rev. E {\bf 55} 287 (1997).

\end{thebibliography}