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Quantum integrable systems exhibit accurate hydrodynamic predictions from local equilibria, validated by the Bethe-Boltzmann equation and experimental ultracold Bose gases.

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Area of Science:

  • Quantum physics
  • Statistical mechanics
  • Condensed matter theory

Background:

  • Hydrodynamics describes chaotic many-particle systems' evolution to equilibrium.
  • Quantum integrable systems reach local equilibrium via generalized Gibbs ensembles or pseudomomentum distributions.

Purpose of the Study:

  • Investigate time evolution from local equilibria in quantum integrable systems.
  • Solve the Bethe-Boltzmann kinetic equation for local pseudomomentum density.
  • Compare theoretical predictions with numerical simulations and experimental data.

Main Methods:

  • Solving the Bethe-Boltzmann kinetic equation.
  • Utilizing density matrix renormalization group (DMRG) for time evolution.
  • Analyzing ultracold one-dimensional Bose gas experiments (Lieb-Liniger model).

Main Results:

  • Hydrodynamic predictions show remarkable accuracy for smooth initial conditions, even in small systems.
  • Solutions obtained for free expansion and particle collisions in the Lieb-Liniger model.
  • The Bethe-Boltzmann equation accurately models pseudomomentum density evolution.

Conclusions:

  • The Bethe-Boltzmann equation provides a valid framework for describing quantum integrable systems' hydrodynamics.
  • Theoretical models align well with experimental observations in ultracold atomic gases.
  • This work bridges theoretical hydrodynamics and quantum many-body physics.