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Chaos and quantum mechanics.

Salman Habib1, Tanmoy Bhattacharya, Benjamin Greenbaum

  • 1MS B285, Theoretical Division, The University of California, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA. habib@lanl.gov

Annals of the New York Academy of Sciences
|June 28, 2005
PubMed
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Quantum mechanics and chaos dynamics can be reconciled through measurement. Observed quantum systems exhibit nonlinear dynamics, leading to chaotic behavior and effective classicality, verifiable in future experiments.

Area of Science:

  • Quantum mechanics
  • Chaos theory
  • Nonlinear dynamics

Background:

  • The relationship between quantum mechanics and chaos theory is often perceived as problematic.
  • Previous comparisons have been hindered by formal analytical approaches rather than experimental relevance.

Purpose of the Study:

  • To provide a unified dynamical description of quantum systems incorporating measurement.
  • To elucidate the emergence of chaos and classical behavior in quantum mechanics.

Main Methods:

  • Analyzing the evolution of measured quantum systems, considering measurement outcomes.
  • Examining the nonlinear dynamics of quantum state distribution functions.

Main Results:

  • Measurement-conditioned dynamics introduce intrinsic nonlinearity, enabling chaotic regimes absent in unobserved systems.

Related Experiment Videos

  • Effective classical behavior arises from observed quantum systems at both trajectory and distribution function levels.
  • Time-series from measured quantum systems can exhibit chaos distinct from classical predictions, with unique Lyapunov exponents.

    • Conclusions:

    • A complete dynamical description of quantum systems necessitates accounting for measurement.
    • This framework resolves the apparent conflict between quantum mechanics and chaos.
    • Predictions offer testable avenues for next-generation quantum experiments.