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Uncoupling Coriolis Force and Rotating Buoyancy Effects on Full-Field Heat Transfer Properties of a Rotating Channel

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Kubo formulas for second-order hydrodynamic coefficients.

Guy D Moore¹, Kiyoumars A Sohrabi

¹Department of Physics, McGill University, 3600 rue University, Montréal, Quebec H3A 2T8, Canada.

Physical Review Letters

|April 27, 2011

Summary

Conformal relativistic hydrodynamics includes viscosity and five additional coefficients. This study derives Kubo relations for these coefficients and shows that λ₃ can be directly evaluated and is generally non-zero.

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Area of Science:

Theoretical physics
Fluid dynamics
Relativistic hydrodynamics

Background:

Second-order conformal relativistic hydrodynamics involves viscosity and five additional coefficients: τ(Π), κ, λ₁, λ₂, and λ₃.
Understanding these coefficients is crucial for describing fluid behavior at higher orders.

Purpose of the Study:

To derive Kubo relations for the five second-order hydrodynamical coefficients.
To relate these coefficients to equilibrium, fully retarded three-point correlation functions of the stress tensor.
To investigate the direct evaluation and general behavior of the coefficient λ₃.

Main Methods:

Derivation of Kubo relations for second-order hydrodynamical coefficients.
Calculation of equilibrium, fully retarded three-point correlation functions of the stress tensor.
Direct evaluation of the coefficient λ₃ using Euclidean methods.

Main Results:

Kubo relations were successfully derived for the coefficients τ(Π), κ, λ₁, λ₂, and λ₃.
These coefficients are shown to be related to specific three-point correlation functions.
The coefficient λ₃ was found to be directly evaluable by Euclidean means and is not generally zero.

Conclusions:

The study provides a theoretical framework for calculating second-order hydrodynamical coefficients.
The findings offer new insights into the behavior of relativistic fluids beyond first-order approximations.
The non-vanishing nature of λ₃ has implications for the transport properties of strongly interacting systems.