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Dynamical Glass and Ergodization Times in Classical Josephson Junction Chains.

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Classical Josephson junction chains exhibit a dynamical glass near integrable limits. Ergodization time (T_{E}) grows anomalously fast, revealing a robust phenomenon in superconducting networks.

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Area of Science:

  • Condensed Matter Physics
  • Quantum Computing
  • Nonlinear Dynamics

Background:

  • Classical Josephson junction chains can become integrable under specific conditions (high energy density or low Josephson energy).
  • Near these limits, Josephson coupling introduces nonintegrability, creating complex network dynamics.

Purpose of the Study:

  • To investigate the ergodization time (T_{E}) in Josephson junction networks.
  • To understand the relationship between ergodization time and fluctuation dynamics.
  • To explore the microscopic origins of the observed dynamical glass behavior.

Main Methods:

  • Computation of finite-time averages of grain charges.
  • Analysis of charge fluctuation time statistics, identifying fat-tailed distributions.
  • Comparison of ergodization time (T_{E}) with Lyapunov time (T_{Λ}).

Main Results:

  • Ergodization time (T_{E}) was extracted, quantifying convergence to ergodic distributions.
  • A strong correlation between T_{E} and charge fluctuation times was established.
  • Anomalously fast growth of T_{E} was observed approaching the integrable limit, with T_{E}/T_{Λ} ratios reaching 10^8.
  • The dynamical glass is attributed to a subset of grains evolving regularly due to infrequent resonant interactions.

Conclusions:

  • The study reveals a dynamical glass in Josephson junction networks near integrable regimes.
  • The findings suggest this dynamical glass is a generic property, independent of network dimensionality.
  • The research provides insights into the complex dynamics and ergodization processes in superconducting systems.