Abstract
There is growing evidence that the hydrodynamic gradient expansion is factorially divergent. We advocate for using Dingle's singulants as a way to gain analytic control over its large-order behavior for nonlinear flows. Within our approach, singulants can be viewed as new emergent degrees of freedom which reorganize the large-order gradient expansion. We work out the physics of singulants for longitudinal flows, where they obey simple evolution equations which we compute in Müller-Israel-Stewart-like models, holography, and kinetic theory. These equations determine the dynamics of the large-order behavior of the hydrodynamic expansion, which we confirm with explicit numerical calculations. One of our key findings is a duality between singulant dynamics and a certain linear response theory problem. Finally, we discuss the role of singulants in optimal truncation of the hydrodynamic gradient expansion. A by-product of our analysis is a new Müller-Israel-Stewart-like model, where the qualitative behavior of singulants shares more similarities with holography than models considered hitherto.
| Original language | English |
|---|---|
| Article number | 041010 |
| Journal | Physical Review X |
| Volume | 12 |
| Issue number | 4 |
| DOIs | |
| Publication status | Published - 2022 Oct |
Bibliographical note
Funding Information:It is a pleasure to thank Inês Aniceto for comments on the manuscript. We would also like to thank our anonymous referees for their insightful comments and questions. The Gravity, Quantum Fields and Information group at A.E.I. was supported by the Alexander von Humboldt Foundation and the Federal Ministry for Education and Research through the Sofja Kovalevskaja Award. A. S. acknowledges financial support from Grant No. CEX2019-000918-M funded by Ministerio de Ciencia e Innovación (MCIN)/Agencia Estatal de Investigación (AEI)/10.13039/501100011033 and from the Polish National Science Centre Grant No. 2018/29/B/ST2/02457. M. S. is supported by the National Science Centre, Poland, under Grants No. 2018/29/B/ST2/02457 and No. 2021/41/B/ST2/02909. B. W. is supported by a Royal Society University Research Fellowship. Finally, we would like to thank the organizers and participants of the Applicable resurgent asymptotics: towards a universal theory program at the Isaac Newton Institute for Mathematical Sciences for stimulating atmosphere and for an opportunity to present for the first time some of the early results behind this work.
Publisher Copyright:
© 2022 authors. Published by the American Physical Society.
Subject classification (UKÄ)
- Atom and Molecular Physics and Optics