Comments on: A bound on the speed of sound from holography? http://www.nonequilibrium.net/bound-speed-sound-holography/#utm_source=feed&utm_medium=feed&utm_campaign=feed For physicts by physicists Tue, 31 Jan 2012 20:24:03 +0000 hourly 1 http://wordpress.org/?v=3.3.1 By: Dmitry http://www.nonequilibrium.net/bound-speed-sound-holography/comment-page-1/#comment-8420 Dmitry Wed, 20 May 2009 12:17:40 +0000 http://www.nonequilibrium.net/?p=3732#comment-8420 Dear Abhi, sorry for the tardy response, I am currently in US and my laptop does not want to work :-) EOS [tex]\epsilon=p[/tex] is what's called stiff matter EOS, it <em>only</em> holds for relativistic <em>scalar</em> field and in the regime where kinetic energy completely dominates over potential energy. If the opposite limit is true, for example, EOS is [tex]\epsilon=-p[/tex], the one of cosmological constant. Your counterexample (gas of pions, and pions are scalars) belongs to this class. Now, if you deal with relativistic plasma with many different components (the N=4 plasma you deal with in AdS/CFT belongs to this class), EOS is typically [tex]\epsilon=3p[/tex] (check out for example Landau-Lifshitz, vol. II). So, the real question is which degrees of freedom give dominating contribution into overall energy-momentum tensor of N=4 plasma - if scalars are important, then you might see deviations from [tex]\epsilon=3p[/tex], if vectors/fermions dominate, then the latter EOS is the most natural to expect. I guess what you ultimatly find is that scalars are not that important for the overall dynamics of plasma. Cheers, Dmitry. Dear Abhi,

sorry for the tardy response, I am currently in US and my laptop does not want to work :-)

EOS \epsilon=p is what’s called stiff matter EOS, it only holds for relativistic scalar field and in the regime where kinetic energy completely dominates over potential energy. If the opposite limit is true, for example, EOS is \epsilon=-p, the one of cosmological constant. Your counterexample (gas of pions, and pions are scalars) belongs to this class.

Now, if you deal with relativistic plasma with many different components (the N=4 plasma you deal with in AdS/CFT belongs to this class), EOS is typically \epsilon=3p (check out for example Landau-Lifshitz, vol. II). So, the real question is which degrees of freedom give dominating contribution into overall energy-momentum tensor of N=4 plasma – if scalars are important, then you might see deviations from \epsilon=3p, if vectors/fermions dominate, then the latter EOS is the most natural to expect. I guess what you ultimatly find is that scalars are not that important for the overall dynamics of plasma.

Cheers,
Dmitry.

]]> By: Abhinav Nellore http://www.nonequilibrium.net/bound-speed-sound-holography/comment-page-1/#comment-8370 Abhinav Nellore Thu, 14 May 2009 20:03:43 +0000 http://www.nonequilibrium.net/?p=3732#comment-8370 Hey Dmitry, Thanks for the question! It's not true that all relativistic matter has \epsilon=3p. Consider the pion gas example treated by Son and Stephanov and mentioned in the blog post Aleksey and I wrote. This is clearly a relativistic system, but it nevertheless has v_s->the speed of light, and \epsilon does not equal 3p. CFTs have \epsilon=3p because the trace of the stress-energy tensor vanishes. So CFTs trivially have v_s^2=1/3. The system treated by Hohler, Stephanov, and my collaborators and me is conformal in the limit T->\infty. What's not clear is whether 1/3 is approached from above or from below as T->\infty. What we show is that it is approached from below for a wide class of theories. Abhi Hey Dmitry,

Thanks for the question! It’s not true that all relativistic matter has \epsilon=3p. Consider the pion gas example treated by Son and Stephanov and mentioned in the blog post Aleksey and I wrote. This is clearly a relativistic system, but it nevertheless has v_s->the speed of light, and \epsilon does not equal 3p. CFTs have \epsilon=3p because the trace of the stress-energy tensor vanishes. So CFTs trivially have v_s^2=1/3. The system treated by Hohler, Stephanov, and my collaborators and me is conformal in the limit T->\infty. What’s not clear is whether 1/3 is approached from above or from below as T->\infty. What we show is that it is approached from below for a wide class of theories.

Abhi

]]> By: Dmitry http://www.nonequilibrium.net/bound-speed-sound-holography/comment-page-1/#comment-8369 Dmitry Thu, 14 May 2009 13:02:10 +0000 http://www.nonequilibrium.net/?p=3732#comment-8369 Dear Aleksey and Abhi, thanks for the nice post! I would like to ask a somewhat arrogant question: why this bound seems surprising to you (and Stephanov)? First of all, <em>any relativistic matter</em> has an equation of state [tex]\epsilon=3p[/tex]. I think there is no surprise that any plasma becomes ultrarelativistic at high temperatures (that is, [tex]T\gg{}m_{\rm eff}[/tex]), where [tex]m_{\rm eff}[/tex] is the largest among effective masses of degrees of freedom of the theory. Bare [tex]m[/tex] is of course zero, since you consider CFTs, but due to interactions between different degrees of freedom their effective masses can be non-zero. If this is so, I guess, there is also no surprise why this bound is upper bound since at lower temperatures plasma should become non-relativistic. What do you think? Cheers, Dmitry. Dear Aleksey and Abhi,

thanks for the nice post! I would like to ask a somewhat arrogant question: why this bound seems surprising to you (and Stephanov)?

First of all, any relativistic matter has an equation of state \epsilon=3p. I think there is no surprise that any plasma becomes ultrarelativistic at high temperatures (that is, T\gg{}m_{\rm eff}), where m_{\rm eff} is the largest among effective masses of degrees of freedom of the theory.

Bare m is of course zero, since you consider CFTs, but due to interactions between different degrees of freedom their effective masses can be non-zero.

If this is so, I guess, there is also no surprise why this bound is upper bound since at lower temperatures plasma should become non-relativistic. What do you think?

Cheers,
Dmitry.

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