Relativistic Hydrodynamics: A Singulant Perspective

TL;DR

This paper introduces singulants as a novel tool to analyze and control the divergent behavior of hydrodynamic gradient expansions, providing new insights into nonlinear flow dynamics and model development.

Contribution

It proposes using Dingle's singulants to reorganize the large-order gradient expansion in hydrodynamics, establishing their dynamics and duality with linear response theory.

Findings

Singulants obey simple evolution equations in longitudinal flows.

Numerical confirmation of the large-order behavior dynamics.

Development of a new M"uller-Israel-Stewart-like model with holographic similarities.

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 behaviour for nonlinear flows. Within our approach, singulants can be viewed as new emergent degrees of freedom which reorganise 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 M\"uller-Israel-Stewart-like models, holography and kinetic theory. These equations determine the dynamics of the large-order behaviour 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 M\"uller-Israel-Stewart-like model, where the qualitative behaviour of singulants shares more similarities with holography than models considered hitherto.