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We uncovered a universal hydrodynamic description for thermalizing many-body systems. This explains the late-time behavior of correlation functions, a key missing piece of the eigenstate thermalization hypothesis (ETH).

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Area of Science:

  • Statistical mechanics
  • Condensed matter physics
  • Quantum chaos

Background:

  • The eigenstate thermalization hypothesis (ETH) describes thermalization in many-body systems.
  • ETH postulates smooth functions for observables in the energy eigenbasis, but their form is undetermined.
  • This lack of determination is a key gap in the ETH framework.

Purpose of the Study:

  • Investigate the structure of smooth functions within the ETH framework.
  • Determine the universal scaling of late-time behavior of time-ordered free cumulants.
  • Provide a hydrodynamic description for correlation functions in thermalizing systems.

Main Methods:

  • Focusing on the Fourier transform of smooth functions, identified as free cumulants.
  • Utilizing nonlinear hydrodynamics to predict universal scaling.
  • Performing large-scale numerical simulations of nonintegrable one-dimensional spin models.

Main Results:

  • Predicted the universal scaling of late-time behavior of time-ordered free cumulants.
  • Numerical simulations corroborated the hydrodynamic predictions.
  • Observed good agreement across infinite and finite-temperature regimes for local observables.

Conclusions:

  • Smooth multipoint correlation functions within ETH admit a universal hydrodynamic description at low frequencies.
  • This work fills a critical gap in the ETH framework by determining the form of these functions.
  • The findings offer new insights into thermalization dynamics in quantum systems.