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Salt particles that have dissolved in water never spontaneously come back together in solution to reform solid particles. Moreover, a gas that has expanded in a vacuum remains dispersed and never spontaneously reassembles. The unidirectional nature of these phenomena is the result of a thermodynamic state function called entropy (S). Entropy is the measure of the extent to which the energy is dispersed throughout a system, or in other words, it is proportional to the degree of disorder of a...
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A Fluorescence-based Assay of Phospholipid Scramblase Activity
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Does Scrambling Equal Chaos?

Tianrui Xu1,2, Thomas Scaffidi3, Xiangyu Cao1

  • 1Department of Physics, University of California, Berkeley, California 94720, USA.

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|April 28, 2020
PubMed
Summary
This summary is machine-generated.

Scrambling, or the exponential growth of out-of-time order correlators (OTOCs), does not require chaos. Unstable fixed points in phase space can drive scrambling even in classically integrable systems, suggesting a distinction from chaos.

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Area of Science:

  • Quantum mechanics
  • Statistical mechanics
  • Dynamical systems theory

Background:

  • Out-of-time order correlators (OTOCs) are a key diagnostic for quantum chaos.
  • Exponential growth of OTOCs, termed scrambling, is often associated with chaotic dynamics.
  • Distinguishing scrambling from chaos is crucial for understanding complex quantum systems.

Purpose of the Study:

  • To investigate whether quantum chaos is a necessary condition for scrambling.
  • To explore alternative mechanisms driving the exponential growth of OTOCs.
  • To establish a new framework for understanding scrambling in semiclassical systems.

Main Methods:

  • Analysis of semiclassical systems.
  • Derivation of a lower bound for the OTOC Lyapunov exponent.
  • Investigation of dynamics around unstable fixed points in phase space.
  • Examination of classically integrable models exhibiting scrambling.

Main Results:

  • Demonstrated that scrambling (long exponential growth of OTOCs) can occur without chaos.
  • Showed that unstable fixed points in phase space are sufficient to induce scrambling.
  • Derived a tight lower bound on the OTOC Lyapunov exponent dependent on local fixed-point properties.
  • Identified specific models where scrambling is dominated by local dynamics near fixed points.

Conclusions:

  • Scrambling is not synonymous with chaos; it can arise from local dynamics around unstable fixed points.
  • The derived lower bound provides a new tool for quantifying scrambling.
  • Proposes a clear distinction between the concepts of scrambling and chaos in physical systems.