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@ARTICLE{Manos:840317,
      author       = {Manos, Thanos and Robnik, Marko},
      title        = {{S}tatistical properties of the localization measure in a
                      finite-dimensional model of the quantum kicked rotator},
      journal      = {Physical review / E},
      volume       = {91},
      number       = {4},
      issn         = {1539-3755},
      address      = {Woodbury, NY},
      publisher    = {Inst.},
      reportid     = {FZJ-2017-07859},
      pages        = {042904},
      year         = {2015},
      abstract     = {We study the quantum kicked rotator in the classically
                      fully chaotic regime K=10 and for various values of the
                      quantum parameter k using Izrailev's N-dimensional model for
                      various N≤3000, which in the limit N→∞ tends to the
                      exact quantized kicked rotator. By numerically calculating
                      the eigenfunctions in the basis of the angular momentum we
                      find that the localization length L for fixed parameter
                      values has a certain distribution; in fact, its inverse is
                      Gaussian distributed, in analogy and in connection with the
                      distribution of finite time Lyapunov exponents of Hamilton
                      systems. However, unlike the case of the finite time
                      Lyapunov exponents, this distribution is found to be
                      independent of N and thus survives the limit N=∞. This is
                      different from the tight-binding model of Anderson
                      localization. The reason is that the finite bandwidth
                      approximation of the underlying Hamilton dynamical system in
                      the Shepelyansky picture [Phys. Rev. Lett. 56, 677 (1986)]
                      does not apply rigorously. This observation explains the
                      strong fluctuations in the scaling laws of the kicked
                      rotator, such as the entropy localization measure as a
                      function of the scaling parameter Λ=L/N, where L is the
                      theoretical value of the localization length in the
                      semiclassical approximation. These results call for a more
                      refined theory of the localization length in the quantum
                      kicked rotator and in similar Floquet systems, where we must
                      predict not only the mean value of the inverse of the
                      localization length L but also its (Gaussian) distribution,
                      in particular the variance. In order to complete our studies
                      we numerically analyze the related behavior of finite time
                      Lyapunov exponents in the standard map and of the 2×2
                      transfer matrix formalism. This paper extends our recent
                      work},
      cin          = {INM-7},
      ddc          = {530},
      cid          = {I:(DE-Juel1)INM-7-20090406},
      pnm          = {333 - Anti-infectives (POF3-333)},
      pid          = {G:(DE-HGF)POF3-333},
      typ          = {PUB:(DE-HGF)16},
      pubmed       = {pmid:25974559},
      UT           = {WOS:000352471700005},
      doi          = {10.1103/PhysRevE.91.042904},
      url          = {https://juser.fz-juelich.de/record/840317},
}