Regularizations of time-crystal dynamics

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.