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Novel Techniques for Observing Structural Dynamics of Photoresponsive Liquid Crystals
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Regularizations of time-crystal dynamics.

Alfred D Shapere1, Frank Wilczek2,3,4,5,6

  • 1Department of Physics and Astronomy, University of Kentucky, Lexington, KY 40506.

Proceedings of the National Academy of Sciences of the United States of America
|August 16, 2019
PubMed
Summary
This summary is machine-generated.

Nonconvex Lagrangians, relevant to time crystals, can emerge in real physical systems, resolving singularities. This leads to "Sisyphus dynamics," characterized by fixed velocities and rapid resets, which can be regularized in quantum mechanics.

Keywords:
Lagrangianmicrostructuretime crystal

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Area of Science:

  • Theoretical Physics
  • Condensed Matter Physics

Background:

  • Nonconvex Lagrangians are theoretical constructs.
  • Time crystals are a novel phase of matter.
  • Dynamical singularities pose challenges in physical system descriptions.

Purpose of the Study:

  • To demonstrate the emergence of nonconvex Lagrangians in conventional systems.
  • To show how these Lagrangians resolve dynamical singularities.
  • To investigate the resulting physical microstructure and its quantum mechanical behavior.

Main Methods:

  • Effective description of physically realizable systems.
  • Analysis of reduced descriptions to identify singularities.
  • Characterization of emergent microstructure, termed "Sisyphus dynamics".

Main Results:

  • Nonconvex Lagrangians can arise from conventional, realizable systems.
  • The emergence of these Lagrangians resolves dynamical singularities.
  • A generic microstructure of "Sisyphus dynamics" (fixed velocity intervals with resets) is observed.
  • Quantum mechanics can regularize this microstructure.

Conclusions:

  • Nonconvex Lagrangians are not purely theoretical but can be physically realized.
  • The study provides a mechanism for resolving singularities in effective descriptions.
  • The findings offer insights into the behavior of physical systems with complex dynamics.