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Thermalization slowing down in multidimensional Josephson junction networks.

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We found two universal ways Josephson junction networks slow down thermalization. These regimes depend on the ratio of Josephson coupling to energy density, impacting chaos and conserved quantities.

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Area of Science:

  • Condensed Matter Physics
  • Quantum Chaos
  • Statistical Mechanics

Background:

  • Understanding thermalization is crucial for quantum systems.
  • Josephson junction networks are key models for studying complex quantum dynamics.
  • Previous studies lacked a comprehensive analysis of thermalization in multi-dimensional networks.

Purpose of the Study:

  • To characterize the slowing down of thermalization in Josephson junction networks.
  • To identify universality classes governing this phenomenon across different dimensions.
  • To analyze the role of coupling strength and energy density in thermalization dynamics.

Main Methods:

  • Computation of entire Lyapunov spectra for large networks (hundreds of sites).
  • Analysis of the largest Lyapunov exponent and fitting of the rescaled spectrum.
  • Extraction of characteristic scales: Lyapunov time and spectral decay exponent.

Main Results:

  • Two distinct universality classes of thermalization slowing down were identified, dependent on the ratio E_J/h.
  • These classes are characterized by different divergences of Lyapunov time and spectral decay.
  • The weak-coupling regime exhibits universal critical exponents and coexistence of chaos with near-conserved quantities.

Conclusions:

  • The identified universality classes are independent of network dimensionality.
  • Findings suggest a general feature applicable to diverse Hamiltonian systems.
  • Perturbation theory explains the observed thermalization dynamics.