Dissipative Systems

  • Fritz Haake
Part of the Springer Series in Synergetics book series (SSSYN, volume 54)

Abstract

Regular classical trajectories of dissipative systems eventually end up on limit cycles or settle on fixed points. Chaotic trajectories, on the other hand, approach so-called strange attractors whose geometry is determined by Cantor sets and their fractal dimension. In analogy with the Hamiltonian case, the two classical possibilities of simple and strange attractors are washed out by quantum fluctuations. Nevertheless, genuinely quantum mechanical distinctions between regular and irregular motion can be identified. The main goal of this chapter is the development of one such distinction, based on the generalization of energy levels to complex quantities whose imaginary parts are related to damping. An important time scale separation arising for dissipative quantum systems will also be expounded: Coherences between macroscopically distinct states tend to decay much more rapidly than quantities with well-defined classical limits. An example relevant in the present context is the dissipative destruction of quantum localization for the kicked rotator.

Keywords

Migration Microwave Manifold Attenuation Covariance 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Fritz Haake
    • 1
  1. 1.Institut für Theoretische Physik, Fachbereich 7, PhysikUniversity of EssenEssenGermany

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