What is Hydrodynamics? It is just the effective field theory description of a system close to equilibrium, valid at sufficiently long times and sufficiently large distances [148]. Notice that, despite the misleading name, it can be applied to very generic systems, and not necessarily only to fluids [149]! Hydrodynamics is not the theory of fluids but it is much more general and it is simply the low energy effective description of a specific system.
It is life, I think, to watch the water. A man can learn so many things.
Again, hydrodynamic is much powerful than that and it can be applied or generalized in the case of softly broken symmetries. See, for example, [150–152].
3.
See [105, 108, 109] for review about relativistic hydrodynamics and connections with holography.
4.
In this case, the stress tensor but, for example, in presence of a U(1) symmetry, we will have also the corresponding U(1) conserved current \(J^\mu \).
5.
Remember that “faster”, or if you want higher frequency, implies higher energy.
6.
To be precise, recent works point out that hydrodynamics is at most a divergent series in position space. In momentum space and expanded around the \(\omega =k=0\) point is a legitimate series with finite radius of convergence in the sense of the Puiseux series. I thank Saso Grozdanov for this clarification.
7.
\(=\) traceless and transverse part.
8.
This is a good thought when you feel you are working under stress. To cope with it with some laughs, I suggest a visit to http://www.thegrumpyscientist.com/.
9.
Remember that the viscosity of a system is proportional to the mean free path \(l_{mfp}\). The smaller the mean free path the strongest the interactions.
10.
This criterion is now under debate as a consequence of the experimental results of [173, 174] and the theoretical discussions in [175, 176], which seem to be in agreement with what Holography suggests [177, 178].
11.
This is equivalent of fixing \(r_h=1\).
12.
There are various ways to obtain this result. One possibility is to realize that AdS\(_2\) is hiddenly a Lifzhitz spacetime with infinite dynamical exponent \(z=\infty \) and that the entropy scales like \(s\sim \, T^{d/z}\sim cost.\)! This property is recently very discussed [192], because of its relation with the SYK model [193], the strange metals phenomenology and the physics of glasses [194]. Have a look!
Author information
Authors and Affiliations
Physics Department, IFT Instituto de Fisica Teorica Madrid, Madrid, Spain
Baggioli, M. (2019). The First Big Success: \(\eta /s\) and Hydrodynamics.
In: Applied Holography. SpringerBriefs in Physics. Springer, Cham. https://doi.org/10.1007/978-3-030-35184-7_3
