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arXiv · 2012.15393

Convergence of hydrodynamic modes: insights from kinetic theory and holography

Michal P. Heller·Alexandre Serantes·Michał Spaliński·Viktor Svensson·Benjamin Withers
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Abstract

We study the mechanisms setting the radius of convergence of hydrodynamic dispersion relations in kinetic theory in the relaxation time approximation. This introduces a qualitatively new feature with respect to holography: a nonhydrodynamic sector represented by a branch cut in the retarded Green's function. In contrast with existing holographic examples, we find that the radius of convergence in the shear channel is set by a collision of the hydrodynamic pole with a branch point. In the sound channel it is set by a pole-pole collision on a non-principal sheet of the Green's function. More generally, we examine the consequences of the Implicit Function Theorem in hydrodynamics and give a prescription to determine a set of points that necessarily includes all complex singularities of the dispersion relation. This may be used as a practical tool to assist in determining the radius of convergence of hydrodynamic dispersion relations.

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Michal P. Heller, Alexandre Serantes, Michał Spaliński, Viktor Svensson, Benjamin Withers. 2021-06-06. Convergence of hydrodynamic modes: insights from kinetic theory and holography. https://doi.org/10.21468/scipostphys.10.6.123

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