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Hydrodynamic gradient expansion diverges beyond Bjorken flow

Michal Heller (UGent) , Alexandre Serantes, Michał Spaliński, Viktor Svensson and Benjamin Withers
(2022) PHYSICAL REVIEW LETTERS. 128(12).
Author
Organization
Abstract
The gradient expansion is the fundamental organizing principle underlying relativistic hydrodynamics, yet understanding its convergence properties for general nonlinear flows has posed a major challenge. We introduce a simple method to address this question in a class of fluids modeled by Israel-Stewart-type relaxation equations. We apply it to (1 thorn 1)-dimensional flows and provide numerical evidence for factorially divergent gradient expansions. This generalizes results previously only obtained for (0 thorn 1)dimensional comoving flows, notably Bjorken flow. We also demonstrate that the only known nontrivial case of a convergent hydrodynamic gradient expansion at the nonlinear level relies on Bjorken flow symmetries and becomes factorially divergent as soon as these are relaxed. Finally, we show that factorial divergence can be removed using a momentum space cutoff, which generalizes a result obtained earlier in the context of linear response.
Keywords
General Physics and Astronomy, THERMODYNAMICS, COLLISIONS

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MLA
Heller, Michal, et al. “Hydrodynamic Gradient Expansion Diverges beyond Bjorken Flow.” PHYSICAL REVIEW LETTERS, vol. 128, no. 12, 2022, doi:10.1103/physrevlett.128.122302.
APA
Heller, M., Serantes, A., Spaliński, M., Svensson, V., & Withers, B. (2022). Hydrodynamic gradient expansion diverges beyond Bjorken flow. PHYSICAL REVIEW LETTERS, 128(12). https://doi.org/10.1103/physrevlett.128.122302
Chicago author-date
Heller, Michal, Alexandre Serantes, Michał Spaliński, Viktor Svensson, and Benjamin Withers. 2022. “Hydrodynamic Gradient Expansion Diverges beyond Bjorken Flow.” PHYSICAL REVIEW LETTERS 128 (12). https://doi.org/10.1103/physrevlett.128.122302.
Chicago author-date (all authors)
Heller, Michal, Alexandre Serantes, Michał Spaliński, Viktor Svensson, and Benjamin Withers. 2022. “Hydrodynamic Gradient Expansion Diverges beyond Bjorken Flow.” PHYSICAL REVIEW LETTERS 128 (12). doi:10.1103/physrevlett.128.122302.
Vancouver
1.
Heller M, Serantes A, Spaliński M, Svensson V, Withers B. Hydrodynamic gradient expansion diverges beyond Bjorken flow. PHYSICAL REVIEW LETTERS. 2022;128(12).
IEEE
[1]
M. Heller, A. Serantes, M. Spaliński, V. Svensson, and B. Withers, “Hydrodynamic gradient expansion diverges beyond Bjorken flow,” PHYSICAL REVIEW LETTERS, vol. 128, no. 12, 2022.
@article{01H46NE8TW7CKE3GVEKFYBMPCX,
  abstract     = {{The gradient expansion is the fundamental organizing principle underlying relativistic hydrodynamics, yet understanding its convergence properties for general nonlinear flows has posed a major challenge. We introduce a simple method to address this question in a class of fluids modeled by Israel-Stewart-type relaxation equations. We apply it to (1 thorn 1)-dimensional flows and provide numerical evidence for factorially divergent gradient expansions. This generalizes results previously only obtained for (0 thorn 1)dimensional comoving flows, notably Bjorken flow. We also demonstrate that the only known nontrivial case of a convergent hydrodynamic gradient expansion at the nonlinear level relies on Bjorken flow symmetries and becomes factorially divergent as soon as these are relaxed. Finally, we show that factorial divergence can be removed using a momentum space cutoff, which generalizes a result obtained earlier in the context of linear response.}},
  articleno    = {{122302}},
  author       = {{Heller, Michal and Serantes, Alexandre and Spaliński, Michał and Svensson, Viktor and Withers, Benjamin}},
  issn         = {{0031-9007}},
  journal      = {{PHYSICAL REVIEW LETTERS}},
  keywords     = {{General Physics and Astronomy,THERMODYNAMICS,COLLISIONS}},
  language     = {{eng}},
  number       = {{12}},
  pages        = {{6}},
  title        = {{Hydrodynamic gradient expansion diverges beyond Bjorken flow}},
  url          = {{http://doi.org/10.1103/physrevlett.128.122302}},
  volume       = {{128}},
  year         = {{2022}},
}
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