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Related Experiment Videos

Broken ergodicity in a stochastic model with condensation.

Frank Zielen1, Andreas Schadschneider

  • 1Institute for Theoretical Physics, University of Cologne, Zülpicher Strasse 77, D-50937 Köln, Germany.

Physical Review Letters
|August 23, 2002
PubMed
Summary

This study reveals a phase transition in a continuous asymmetric random average process with restricted mass transport. A finite system exhibits alternating states with diverging lifetimes, breaking ergodicity in the thermodynamic limit.

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Area of Science:

  • Statistical Physics
  • Stochastic Processes

Background:

  • Asymmetric random average processes model particle systems.
  • Continuous state variables and restricted mass transport introduce novel dynamics.

Purpose of the Study:

  • To investigate a variant of the asymmetric random average process with a cutoff on maximal mass transport.
  • To analyze the phase transitions and ergodicity breaking in this system.

Main Methods:

  • Analysis of a continuous asymmetric random average process.
  • Investigation under periodic boundary conditions.
  • Examination of system behavior in the thermodynamic limit.

Main Results:

  • Demonstrated a phase transition between a pure high flow phase and a mixed phase.

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  • The mixed phase comprises a homogeneous high flow and a condensed low flow substate.
  • Identified broken ergodicity in the infinite system due to diverging lifetimes of finite system substates.

    • Conclusions:

    • The system exhibits distinct scaling behaviors for substate lifetimes based on flipping mechanisms.
    • Ergodicity is broken in the thermodynamic limit due to the long-lived, alternating substates.