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The hydrodynamic gradient expansion in linear response theory

MPS-Authors
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Heller,  Michal P.
Gravity, Quantum Fields and Information, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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Svensson,  Viktor
Gravity, Quantum Fields and Information, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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Fulltext (public)

2007.05524.pdf
(Preprint), 456KB

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Citation

Heller, M. P., Serantes, A., Spaliński, M., Svensson, V., & Withers, B. (in preparation). The hydrodynamic gradient expansion in linear response theory.


Cite as: http://hdl.handle.net/21.11116/0000-0006-CDF1-3
Abstract
One of the foundational questions in relativistic fluid mechanics concerns the properties of the hydrodynamic gradient expansion at large orders. Studies of expanding systems arising in heavy-ion collisions and cosmology show that the expansion in real space gradients is divergent. On the other hand, expansions of dispersion relations of hydrodynamic modes in powers of momenta have a non-vanishing radius of convergence. We resolve this apparent tension finding a beautifully simple and universal result: the real space hydrodynamic gradient expansion diverges if initial data have support in momentum space exceeding a critical value, and converges otherwise. This critical value is an intrinsic property of the microscopic theory, and corresponds to a branch point of the spectrum where hydrodynamic and nonhydrodynamic modes first collide.