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Eigenstates ignoring regular and chaotic phase-space structures.

Lars Hufnagel1, Roland Ketzmerick, Marc-Felix Otto

  • 1Max-Planck-Institut für Strömungsforschung und Institut für Nichtlineare Dynamik der Universität Göttingen, Bunsenstrasse 10, Germany.

Physical Review Letters
|October 9, 2002
PubMed
Summary
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The semiclassical eigenfunction hypothesis fails when regular and chaotic dynamics coexist. Eigenstates disregard classical structures, extending into both regular and chaotic regions in quantum transport systems.

Area of Science:

  • Quantum mechanics
  • Classical dynamics
  • Statistical physics

Background:

  • The semiclassical eigenfunction hypothesis posits that quantum eigenstates in classically chaotic systems localize to regions of phase space.
  • Understanding quantum-classical correspondence is crucial for describing complex dynamical systems.

Purpose of the Study:

  • To investigate the validity of the semiclassical eigenfunction hypothesis in systems exhibiting coexisting regular and chaotic dynamics.
  • To determine how quantum eigenstates behave when regular classical transport structures are present alongside chaotic seas.

Main Methods:

  • Analysis of quantum transport in systems with mixed phase-space structures.
  • Examination of eigenstates in the semiclassical limit.
  • Consideration of systems like the standard map with accelerator modes.

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Main Results:

  • The semiclassical eigenfunction hypothesis fails when regular classical transport coexists with chaotic dynamics.
  • Quantum eigenstates are not restricted to either regular islands or the chaotic sea.
  • Eigenstates extend across these classical phase-space structures, irrespective of their nature.

Conclusions:

  • The coexistence of regular and chaotic dynamics fundamentally challenges the semiclassical eigenfunction hypothesis.
  • Quantum behavior in such systems does not follow classical phase-space localization predictions.
  • This finding has implications for understanding quantum dynamics in extended systems with mixed regular-chaotic features.