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Hydrodynamic gradient expansion in gauge theory plasmas.

Michal P Heller¹, Romuald A Janik, Przemysław Witaszczyk

¹Instituut voor Theoretische Fysica, Universiteit van Amsterdam, Science Park 904, 1090 GL Amsterdam, The Netherlands. m.p.heller@uva.nl

Physical Review Letters

|June 11, 2013

Summary

We explored the large order behavior of plasma dynamics using fluid-gravity duality. Our findings reveal a factorial growth in gradient contributions, indicating a breakdown of the hydrodynamic series convergence.

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Area of Science:

High-energy physics
Condensed matter theory
Quantum field theory

Background:

The fluid-gravity duality provides a powerful framework for studying strongly coupled systems.
Hydrodynamic expansions are crucial for describing the long-wavelength, low-frequency behavior of fluids.

Purpose of the Study:

To investigate the large order behavior of hydrodynamic gradient expansion in gauge theory plasma.
To explore the implications of high-order dissipative terms and transport coefficients.

Main Methods:

Utilizing the fluid-gravity duality.
Numerical calculation of the stress tensor for boost-invariant flow.
Analysis of hydrodynamic expansion up to 240 derivatives.

Main Results:

Observed factorial growth of gradient contributions at large orders.
Demonstrated a zero radius of convergence for the hydrodynamic series.
Identified the leading singularity in the Borel transform of hydrodynamic energy density.

Conclusions:

The hydrodynamic series for gauge theory plasma does not converge at large orders.
A 'nonhydrodynamic' quasinormal mode on the gravity side corresponds to the leading singularity.