• Register
PhysicsOverflow is a next-generation academic platform for physicists and astronomers, including a community peer review system and a postgraduate-level discussion forum analogous to MathOverflow.

Welcome to PhysicsOverflow! PhysicsOverflow is an open platform for community peer review and graduate-level Physics discussion.

Please help promote PhysicsOverflow ads elsewhere if you like it.


PO is now at the Physics Department of Bielefeld University!

New printer friendly PO pages!

Migration to Bielefeld University was successful!

Please vote for this year's PhysicsOverflow ads!

Please do help out in categorising submissions. Submit a paper to PhysicsOverflow!

... see more

Tools for paper authors

Submit paper
Claim Paper Authorship

Tools for SE users

Search User
Reclaim SE Account
Request Account Merger
Nativise imported posts
Claim post (deleted users)
Import SE post

Users whose questions have been imported from Physics Stack Exchange, Theoretical Physics Stack Exchange, or any other Stack Exchange site are kindly requested to reclaim their account and not to register as a new user.

Public \(\beta\) tools

Report a bug with a feature
Request a new functionality
404 page design
Send feedback


(propose a free ad)

Site Statistics

205 submissions , 163 unreviewed
5,047 questions , 2,200 unanswered
5,345 answers , 22,709 comments
1,470 users with positive rep
816 active unimported users
More ...

  Analog Hawking radiation

+ 20 like - 0 dislike

I am confused by most discussions of analog Hawking radiation in fluids (see, for example, the recent experimental result of Weinfurtner et al. Phys. Rev. Lett. 106, 021302 (2011), arXiv:1008.1911). The starting point of these discussions is the observation that the equation of motion for fluctuations around stationary solutions of the Euler equation have the same mathematical structure as the wave equation in curved space (there is a fluid metric $g_{ij}$ determined by the background flow). This background metric can have sonic horizons. The sonic horizons can be characterized by an associated surface gravity $\kappa$, and analog Hawking temperature $T_H \sim \kappa\hbar/c_s$.

My main questions is this: Why would $T_H$ be relevant? Corrections to the Euler flow are not determined by quantizing small oscillations around the classical flow. Instead, hydrodynamics is an effective theory, and corrections arise from higher order terms in the derivative expansion (the Navier-Stokes, Burnett, super-Burnett terms), and from thermal fluctuations. Thermal fluctuations are governed by a linearized hydro theory with Langevin forces, but the strength of the noise terms is governed by the physical temperature, not by Planck's constant.

A practical question is: In practice $T_H$ is very small (because it is proportional to $\hbar$). How can you claim to measure thermal radiation at a temperature $T_H << T$?

This post has been migrated from (A51.SE)
asked Jan 6, 2012 in Theoretical Physics by tmschaefer (720 points) [ no revision ]
Most voted comments show all comments
Maybe, but the temperature is proportional to $\hbar$, so I would call it quantum.

This post has been migrated from (A51.SE)
Doesn't matter what you call it --- it's still perfectly described as classical...

This post has been migrated from (A51.SE)
If you have radiation at a rate proportional to $\hbar$, how can it not be a quantum effect?

This post has been migrated from (A51.SE)
Thomas I think this effect should be noticeable when the external temperature is not very high with respect to the Hawking temperature, that is, the external temperature has to be very low. This is why I don't think it makes sense for water which cannot remain liquid at low temperatures

This post has been migrated from (A51.SE)
The sonic analogue of Unruh effect is fully classical. You can read more about it in G.E. Volovik's book, "The universe in a helium droplet". The $\hbar$ you mention is merely metaphorical.

This post has been migrated from (A51.SE)
Most recent comments show all comments
John indeed mentions a possible analogue of Hawking radiation in polariton liquid. However in this case it might actually make sense since the polariton liquid is quantum (i.e. the wavelength isn't small w.r.t. the mean free path)

This post has been migrated from (A51.SE)
Indeed, I refer to the Weinfurtner et al paper because I find this particularly puzzling (they have a water tank). But I am confused even in the case of quantum fluids: 1) Ordinary (non superfluid) quantum fluids are described by standard hydro, the only thing that is quantum is the microscopic kinetic description. 2) In superfluids, it is indeed the case that the normal components can be described (in some limit) as a gas of quantized sound waves (phonons). But even in this situation you would think that the main effect is ordinary thermal fluctuations at temperature T.

This post has been migrated from (A51.SE)

Your answer

Please use answers only to (at least partly) answer questions. To comment, discuss, or ask for clarification, leave a comment instead.
To mask links under text, please type your text, highlight it, and click the "link" button. You can then enter your link URL.
Please consult the FAQ for as to how to format your post.
This is the answer box; if you want to write a comment instead, please use the 'add comment' button.
Live preview (may slow down editor)   Preview
Your name to display (optional):
Privacy: Your email address will only be used for sending these notifications.
Anti-spam verification:
If you are a human please identify the position of the character covered by the symbol $\varnothing$ in the following word:
Then drag the red bullet below over the corresponding character of our banner. When you drop it there, the bullet changes to green (on slow internet connections after a few seconds).
Please complete the anti-spam verification

user contributions licensed under cc by-sa 3.0 with attribution required

Your rights