1206.3311 (Ayan Mukhopadhyay)

Non-equilibrium fluctuation-dissipation relation from holography    [PDF]

Ayan Mukhopadhyay

We derive non-equilibrium fluctuation-dissipation relation for bosonic correlation functions from holography in the classical gravity approximation. We also show this holds universally in any classical gravity theory which has a stable thermal background as a solution. Therefore, this can provide a strong experimental test for the applicability of the holographic framework. The fluctuation-dissipation relation gives a proportionality factor between the expectation value of the commutator i.e. the spectral function, and the expectation value of the anti-commutator, i.e. the Keldysh propagator, in an arbitrary non-equilibrium state. We show that, in the limit in which the external sources vanish and within the range of validity of perturbative hydrodynamic (derivative) and non-hydrodynamic (amplitude) expansions, the holographic non-equilibrium fluctuation-dissipation relation is fixed completely by the temperature of the final equilibrium. We argue this is consistent with locality and causality of the dual field theory. We also argue this can indeed be tested in heavy ion collision experiments. Along the way, we do new consistency checks of our holographic prescriptions including that for the non-equilibrium spectral function obtained in our previous work. Finally, we make a conjecture regarding higher point holographic non-equilibrium correlation functions.

View original: http://arxiv.org/abs/1206.3311