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Border between regular and chaotic quantum dynamics.

Yaakov S Weinstein1, Seth Lloyd, Constantino Tsallis

  • 1Department of Nuclear Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA.

Physical Review Letters
|November 22, 2002
PubMed
Summary
This summary is machine-generated.

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Researchers found a distinct boundary between regular and chaotic quantum dynamics. This edge of chaos is marked by a specific power-law decay in state overlap, revealing key insights into quantum chaos.

Area of Science:

  • Quantum dynamics
  • Chaos theory
  • Statistical mechanics

Background:

  • Distinguishing between regular and chaotic behavior in quantum systems is crucial for understanding their long-term evolution.
  • The transition to chaos in quantum systems often differs from classical systems due to quantum effects like interference.

Purpose of the Study:

  • To identify and characterize the boundary between regular and chaotic quantum dynamics.
  • To establish a quantitative measure for the 'edge of chaos' in quantum systems.

Main Methods:

  • Analyzing the overlap between quantum states evolved under slightly different dynamics.
  • Fitting the observed overlap decay to a power-law function, specifically [1+(q-1)(t/tau)2](1/(1-q)).
  • Comparing quantum dynamics with the corresponding classical map's behavior.

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Main Results:

  • A clear border between regular and chaotic quantum dynamics was identified.
  • The overlap decay follows a power-law, characterized by the nonextensive entropic index q and timescale tau.
  • The observed region precedes the onset of quantum interference effects.

Conclusions:

  • The identified border represents the quantum 'edge of chaos'.
  • The power-law decay serves as a robust indicator of this transition.
  • This finding bridges the understanding of classical and quantum chaos.