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Interaction-free ergodicity-breaking driven by temporally hyperuniform noise.

Harukuni Ikeda1

  • 1Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto 606-8502, Japan.

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|December 23, 2025
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Summary

Spin models driven by temporally hyperuniform noise show a sharp transition to a nonergodic phase without interactions. Dynamics freeze based on initial conditions, revealing a new mechanism for ergodicity breaking.

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Area of Science:

  • Statistical Mechanics
  • Condensed Matter Physics
  • Complex Systems

Background:

  • Ergodicity breaking is a fundamental concept in statistical mechanics, typically associated with interacting systems.
  • Hyperuniformity describes disordered systems with suppressed large-scale density fluctuations.

Purpose of the Study:

  • To investigate ergodicity breaking in norm-conserving spin models driven by temporally hyperuniform noise.
  • To explore the role of interactions and noise properties in phase transitions.

Main Methods:

  • Analysis of norm-conserving spin models.
  • Driving the system with temporally hyperuniform noise.
  • Investigating the absence of inter-particle interactions.

Main Results:

  • A sharp ergodicity-breaking transition was observed in the absence of interactions.
  • In the nonergodic phase, system dynamics become frozen, dependent on the initial state.
  • Interaction-free ergodicity breaking occurs with global constraints and class-I hyperuniform noise.

Conclusions:

  • Temporally hyperuniform noise can induce ergodicity breaking even without interactions.
  • The transition is analogous to Bose-Einstein condensation, involving fluctuation condensation into the zero-frequency mode.