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Free keywords:
High Energy Physics - Theory, hep-th,High Energy Physics - Phenomenology, hep-ph,Nuclear Theory, nucl-th, Physics, Fluid Dynamics, physics.flu-dyn
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.
