Localization and delocalization in a dissipative quantum map

  • Th. Dittrich
  • R. Graham
Invited Lectures Part I: Chaos in Quantum Systems
Part of the Lecture Notes in Physics book series (LNP, volume 282)


The time evolution of the density matrix generated by a quantum version of the ‘standard map’ (kicked rotator) with dissipation is studied. The quantum ensemble corresponding to the classical invariant measure on the strange attractor is obtained and discussed. The influence of weak dissipation on localization phenomena in the quantized standard map is assessed qualitatively and studied quantitatively in numerical experiments. Complete delocalization is found for sufficiently strong dissipation. For extremely weak dissipation a remnant of quantum localization is found to survive even in the steady state.


Angular Momentum Wigner Function Strange Attractor Rydberg Atom Semiclassical Approximation 
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Copyright information

© Springer-Verlag 1987

Authors and Affiliations

  • Th. Dittrich
    • 1
  • R. Graham
    • 1
  1. 1.Fachbereich PhysikUniversität Essen GHSEssenGermany

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