# Hydrodynamic gradient expansion in gauge theory plasmas.

@article{Heller2013HydrodynamicGE, title={Hydrodynamic gradient expansion in gauge theory plasmas.}, author={Michal P. Heller and Romuald A. Janik and Przemysław Witaszczyk}, journal={Physical review letters}, year={2013}, volume={110 21}, pages={ 211602 } }

We utilize the fluid-gravity duality to investigate the large order behavior of hydrodynamic gradient expansion of the dynamics of a gauge theory plasma system. This corresponds to the inclusion of dissipative terms and transport coefficients of very high order. Using the dual gravity description, we calculate numerically the form of the stress tensor for a boost-invariant flow in a hydrodynamic expansion up to terms with 240 derivatives. We observe a factorial growth of gradient contributions…

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## References

SHOWING 1-10 OF 44 REFERENCES

Improved hydrodynamics from the AdS/CFT duality

- Physics
- 2009

We generalize (linearized) relativistic hydrodynamics by including all order gradient expansion of the energy-momentum tensor, parametrized by four momenta-dependent transport coefficients, one of…

Relativistic viscous hydrodynamics, conformal invariance, and holography

- Physics, Mathematics
- 2008

We consider second-order viscous hydrodynamics in conformal field theories at finite temperature. We show that conformal invariance imposes powerful constraints on the form of the second-order…

Nonlinear fluid dynamics from gravity

- Physics
- 2008

Black branes in AdS5 appear in a four parameter family labeled by their velocity and temperature. Promoting these parameters to Goldstone modes or collective coordinate fields—arbitrary functions of…

Asymptotic perfect fluid dynamics as a consequence of AdS/CFT correspondence

- Physics
- 2006

We study the dynamics of strongly interacting gauge-theory matter (modelling quark-gluon plasma) in a boost-invariant setting using the AdS/CFT correspondence. Using Fefferman-Graham coordinates and…

Gauge-gravity duality and thermalization of a boost-invariant perfect fluid

- Physics
- 2006

We derive the equation for the quasinormal modes corresponding to the scalar excitation of a black hole moving away in the fifth dimension. This geometry is the AdS/CFT dual of a boost-invariant…

Consistent holographic description of boost-invariant plasma.

- PhysicsPhysical review letters
- 2009

The calculations presented correctly reproduce the plasma energy-momentum tensor within the framework of second-order viscous hydrodynamics.

How much entropy is produced in strongly coupled quark-gluon plasma (sQGP) by dissipative effects?

- Physics
- 2007

We argue that estimates of dissipative effects based on first-order hydrodynamics with shear viscosity are potentially misleading because higher order terms in the gradient expansion of the…

Quasinormal modes and holography

- Physics
- 2005

Quasinormal frequencies of electromagnetic and gravitational perturbations in asymptotically anti-de Sitter spacetime can be identified with poles of the corresponding real-time Green's functions in…

Characteristics of thermalization of boost-invariant plasma from holography.

- PhysicsPhysical review letters
- 2012

A sizable anisotropy in the energy-momentum tensor at thermalization is observed, which suggests that effective thermalization in heavy-ion collisions may occur significantly earlier than true thermalization.

Boost-invariant early time dynamics from AdS/CFT

- Physics
- 2009

Boost-invariant dynamics of a strongly-coupled conformal plasma is studied in the regime of early proper-time using the AdS/CFT correspondence. It is shown, in contrast with the late-time expansion,…