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When an object is in equilibrium, it is either at rest or moving with a constant velocity. There are two types of equilibrium: static and dynamic. Static equilibrium occurs when an object is at rest, while dynamic equilibrium occurs when an object is moving with a constant velocity. In both cases, there must be a balance of forces acting on the object.
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A rigid body is said to be in dynamic equilibrium when both its linear and angular acceleration are zero, relative to an inertial frame of reference. This means that a body in equilibrium can be moving, but only when its linear and angular velocities are constant. A rigid body is said to be in static equilibrium when it is at rest in the selected frame of reference. The distinction between static equilibrium (e.g., a state of rest) and dynamic equilibrium (e.g, a state of uniform motion) is...
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Understanding the stability of equilibrium configurations is a fundamental part of mechanical engineering. In any system, there are three distinct types of equilibrium: stable, neutral, and unstable.
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Intermittent many-body dynamics at equilibrium.

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Summary
This summary is machine-generated.

Researchers studied many-body systems using trajectory piercings to measure relaxation times and equilibrium dynamics. This revealed power-law distributions and sticky dynamics, predicting transitions to nonergodic behavior in complex systems.

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Area of Science:

  • Statistical Mechanics
  • Nonlinear Dynamics
  • Condensed Matter Physics

Background:

  • Ergodic and equipartitioned many-body systems exhibit complex dynamics.
  • The equilibrium manifold in phase space is frequently intersected by system trajectories.

Purpose of the Study:

  • To measure the relaxation time of the Fermi-Pasta-Ulam chain's lowest frequency eigenmode.
  • To characterize equilibrium dynamics and fluctuations using trajectory piercings.
  • To generalize the method for analyzing sticky dynamics in different lattice systems.

Main Methods:

  • Analyzing trajectory piercings of the equilibrium manifold in phase space.
  • Measuring relaxation times and fluctuation dynamics.
  • Characterizing excursion time distributions and identifying localized dynamics (q-breathers, discrete breathers).

Main Results:

  • A power-law distribution of excursion times with diverging variance was observed in equilibrium dynamics.
  • Sticky dynamics near q-breathers in normal mode space cause long excursions.
  • The method was generalized to Klein-Gordon lattices, identifying discrete breathers in real space.

Conclusions:

  • Trajectory piercings provide a method to measure relaxation times and characterize equilibrium dynamics.
  • Sticky dynamics and localized modes (breathers) are crucial for understanding deviations from ergodicity.
  • The findings offer insights into transitions to nonergodic dynamics in many-body systems.