946 research outputs found
On the convergence of the gradient expansion in hydrodynamics
Hydrodynamic excitations corresponding to sound and shear modes in fluids are
characterised by gapless dispersion relations. In the hydrodynamic gradient
expansion, their frequencies are represented by power series in spatial
momenta. We investigate the analytic structure and convergence properties of
the hydrodynamic series by studying the associated spectral curve in the space
of complexified frequency and complexified spatial momentum. For the strongly
coupled supersymmetric Yang-Mills plasma, we use the holographic
duality methods to demonstrate that the derivative expansions have finite
non-zero radii of convergence. Obstruction to the convergence of hydrodynamic
series arises from level-crossings in the quasinormal spectrum at complex
momenta.Comment: V3: 5 pages, 2 figures. Final version. Published in Physical Review
Letters with the title "Convergence of the Gradient Expansion in
Hydrodynamics
The complex life of hydrodynamic modes
We study analytic properties of the dispersion relations in classical
hydrodynamics by treating them as Puiseux series in complex momentum. The radii
of convergence of the series are determined by the critical points of the
associated complex spectral curves. For theories that admit a dual
gravitational description through holography, the critical points correspond to
level-crossings in the quasinormal spectrum of the dual black hole. We
illustrate these methods in supersymmetric Yang-Mills theory in
3+1 dimensions, in a holographic model with broken translation symmetry in 2+1
dimensions, and in conformal field theory in 1+1 dimensions. We comment on the
pole-skipping phenomenon in thermal correlation functions, and show that it is
not specific to energy density correlations.Comment: V3: 54 pages, 18 figures. Appendix added. Version to appear in JHE
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