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Convergence of the Gradient Expansion in Hydrodynamics
Sašo Grozdanov1, Pavel K Kovtun2, Andrei O Starinets3
1Center for Theoretical Physics, MIT, Cambridge, Massachusetts 02139, USA.
Physical Review Letters
|July 27, 2019
Summary
This study reveals that hydrodynamic series in strongly coupled N=4 supersymmetric Yang-Mills plasma have finite convergence radii. Obstructions arise from quasinormal spectrum level crossings at complex momenta.
Area of Science:
- Theoretical physics
- Quantum field theory
- Plasma physics
Background:
- Hydrodynamic excitations like sound and shear modes exhibit gapless dispersion relations.
- Frequencies in hydrodynamic gradient expansions are power series in spatial momenta.
Purpose of the Study:
- Investigate the analytic structure and convergence properties of hydrodynamic series.
- Determine the convergence of derivative expansions in strongly coupled N=4 supersymmetric Yang-Mills plasma.
Main Methods:
- Studied the spectral curve in complexified frequency and momentum space.
- Applied holographic duality methods to analyze the plasma.
- Examined quasinormal spectrum level crossings at complex momenta.
Main Results:
- Demonstrated finite, nonzero radii of convergence for derivative expansions.
- Identified level crossings in the quasinormal spectrum as obstructions to convergence.
- Characterized the analytic structure of hydrodynamic series.
Conclusions:
- Hydrodynamic series in this plasma model exhibit limited convergence.
- Quasinormal mode analysis provides insights into the convergence of hydrodynamic expansions.
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