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Macroscopic thermalization and transport constrain matrix elements in the eigenstate thermalization hypothesis (ETH). Random matrix theory (RMT) emergence occurs at a smaller energy scale than previously thought, coinciding with transport breakdown.

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Area of Science:

  • Quantum statistical mechanics
  • Condensed matter physics

Background:

  • The Eigenstate Thermalization Hypothesis (ETH) describes thermalization in isolated quantum systems.
  • Random Matrix Theory (RMT) is often applied to describe ETH at energy scales below the Thouless energy.
  • The self-consistency of this conventional picture has not been rigorously established.

Purpose of the Study:

  • To investigate the relationship between macroscopic thermalization, transport, and the matrix elements within the ETH.
  • To determine the correct energy scale for the emergence of RMT behavior in quantum systems.
  • To reconcile the onset of RMT with the breakdown of hydrodynamic transport descriptions.

Main Methods:

  • Analysis of constraints imposed by macroscopic thermalization and transport on ETH matrix elements.
  • Theoretical derivation of the energy scale for RMT emergence.
  • Comparison of the RMT emergence timescale with thermalization and transport timescales.

Main Results:

  • Macroscopic thermalization and transport necessitate correlations among matrix elements in the ETH ansatz.
  • The conventional assumption of ETH reducing to RMT below the Thouless energy is shown to be inconsistent.
  • The energy scale for RMT emergence is proven to be parametrically smaller than the inverse timescale of the slowest thermalization mode.

Conclusions:

  • The emergence of RMT behavior is linked to a specific energy scale that is smaller than anticipated.
  • The timescale for RMT onset is identical to the timescale at which hydrodynamic transport description fails.
  • These findings necessitate a revision of the conventional understanding of thermalization and RMT in quantum systems.