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Infinite Order Hydrodynamics: An Analytical Example.

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  • 1Department of Mathematics, <a href="https://ror.org/02vm5rt34">Vanderbilt University</a>, Nashville, Tennessee 37240, USA.

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Researchers developed a kinetic model for matter-radiation interactions, allowing analytical computation of hydrodynamic gradient expansions. They identified the cause of gradient series divergence and proposed a universal framework to predict its breakdown.

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Area of Science:

  • Theoretical Physics
  • Kinetic Theory
  • Quantum Field Theory

Background:

  • Hydrodynamic gradient expansions are crucial for describing complex systems.
  • Understanding the limitations and divergence of these expansions is essential for accurate modeling.
  • Previous studies indicated gradient series divergence in certain regimes.

Purpose of the Study:

  • To construct a kinetic model for matter-radiation interactions.
  • To analytically compute the hydrodynamic gradient expansion in the nonlinear regime.
  • To identify the mechanism of gradient series divergence and propose a regularization scheme.

Main Methods:

  • Developed a kinetic model for matter-radiation interactions.
  • Modeled frequency-dependent opacity to mimic a self-interacting scalar field's relaxation time.
  • Computed the hydrodynamic gradient expansion analytically to infinite order.
  • Identified the divergence mechanism and developed a regularization scheme.

Main Results:

  • The hydrodynamic gradient expansion was computed analytically for arbitrary flows in the nonlinear regime.
  • The gradient series was found to diverge for most flows, consistent with prior research.
  • A mechanism for divergence was identified, and a successful regularization scheme was provided.
  • A universal framework for predicting gradient expansion breakdown was proposed and validated.

Conclusions:

  • The study provides a novel kinetic model and analytical framework for hydrodynamic gradient expansions.
  • A universal mechanism for gradient expansion divergence was identified, applicable to various microscopic systems.
  • The proposed framework correctly predicts known divergence instances and offers new predictions, such as divergence when the mean free path is unbounded.