NEQNET: non-equilibrium phenomena in physics, social dynamics, markets and much more. No nonsense, just science.

376. A GRB detected at z=8.3

Posted by Dmitry

at April 28, 2009

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… which makes it, as it seems, the most distant object in the Universe observed so far – see the Swift page (that’s the spacecraft that originally detected the GRB on Apr 23) on the NASA site for technical details or this article on New Scientist site for general discussion.

Swift detects GRB at redshift 8.3

That’s the guy.

Do you find it ironic that we can detect CMB photons from the last scattering surface (400000 years after the Big Bang, $z\sim{}1000$ ) and photons from objects like GRB 090423 at $z\sim{}10$ (640 million years after the Big Bang) but not so much in between? (The only radiation emitted during those Dark Ages is 21 cm neutral H line.) Is it really true that nothing interesting happened in the Universe for those 600 million years? Deep in my heart I seriously doubt that.

Astrophysics, Cosmology, Entered Apprentice

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375. Inertial confinement: concluding part on lasers

Posted by Dmitry

at April 28, 2009

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The previous parts on interaction between laser emission and material of fuel capsule are “Inertial confinement – using lasers for compression” and “Inertial confinement: more on interaction of laser emission with matter“. I hope to finish with discussion of laser-target interaction today and proceed to instabilities (the most interesting part of the physics of inertial confinement reactors from my point of view).

So, as we discussed previous time, the outer shell of the capsule (ablator) rapidly evaporates due to the interaction with laser emission. A so called ablative pressure impulse is formed near the boundary of the evaporating region: the main contribution into this pressure comes from heat pressure and reactive pressure of plasma (if plasma temperature is around 1 keV, plasma moves towards the center of the capsule with characteristic velocities as high as $\approx 300 {\rm km}/{\rm s}$ , corresponding to reactive pressure around 10^6 atm).

Due to ablative pressure the part of the capsule that did not evaporate is getting collapsed towards the center of the capsule (typically, the characteristic time of collapse is of the same order of magnitude as the length of the laser impulse). The collapse itself can be described as follows.

Let us consider for simplicity that the target (fuel capsule) is almost a sphere, with thin ablator (outer layer) and empty inside. If so, we can write

$M\frac{du}{dt}=4\pi{}R^22\rho{}v^2$ , (1)

$\frac{dM}{dt}=-4\pi{}R^2\rho{}v$ , (2)

where $M=4\pi{}R^2\delta{}R\rho_0$ is the mass of abalator layer, – “current radius” of the compressed target, – is the compression velocity and is the velocity of target corona. The solution of the Eqs. (1) and (2) depends only on a single parameter

$\beta=\frac{\rho{}R}{\Delta{}R\rho_0}$ .

The compression velocity (it is of the same order of magnitude as the speed of sound in plasma) and kinetic energy of the ablator Mu^2/2 are other two important parameters.

One more important parameter is a quantity

$\gamma=\frac{Mu^2}{2\int{}Qdt}$

called hydrodynamic efficiency. It determines how much absorbed energy goes into kinetic energy of collapsing ablator layer. In spherical targets, $\gamma$ depends on $\beta$ and varies from 3% to 15%.

Rayliegh-Taylor instabilities in fuel capsule

Rayleigh-Taylor instabilities in fuel capsule. Computer simulations by LLNL.

Apart from transformation of absorbed energy and kinetic energy of collapsing ablator (the outer layer acts as a forcer adiabatically compressing the fuel inside the capsule), there is another important mechanism that leads to compression of the fuel – shock waves. Simultaneously, shock waves are the big problem for the whole idea since they lead to inhomogeneous heating of the fuel. Fast electrons created due to the interaction of target material with the laser impulse and X-rays as well as development of Rayleigh-Taylor instabilities also lead to inhomogeneous heating of the fuel. In overall, we do have freedom to resolve these issues to some extent since we can set the flux in the laser impulse ( $10^{14}-10^{16}\frac{\rm W}{{\rm cm}^2}$ ), its wavelength ( $(0.3-0.6)\times{}10^{-6}{\rm m}$ ), the form of the impulse and the capsule.

If we are able to relatively precisely control the form of the capsule and the homogeneity of the laser impulse, theory shows that the peripheral part of the target can be compressed up to the densities of the order $10^2-10^3 \frac{\rm g}{{\rm cm}^3}$ and temperatures around 0.5-1 keV, while the central part of the capsule can be heated up to 10 keV (the density there will be much smaller though – about $5-50\frac{\rm g}{{\rm cm}^3}$ ). In principle, this is enough for a self-sustained thermonuclear reaction to take off. The reaction will start in the center of the capsule and capture the outer layers of the target.

Entered Apprentice, Nuclear physics

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365. Inertial confinement – using lasers for compression

368. Inertial confinement: more on interaction of laser emission with matter

364. Thermonuclear reactors. More on inertial confinement

374. How big is the Universe: video of the day

Posted by Dmitry

at April 27, 2009

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Well, if you recall that it takes more than 3 years for a photon emitted by the Sun to reach the nearest star… the size of the causal patch, 14 billion light years, should impress you If words did not really impress you, then maybe this nice video will -

Update: Daniel also liked this video, although the scales expressed there are astrophysical rather than cosmological

Cosmology, Entered Apprentice

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373. Some musings about Unruh effect

Posted by Dmitry

at April 27, 2009

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Good new long work week, science geeks! I’ve just finished reading a recent paper by Ugo Moschella and Richard Schaeffer “Quantum fields on curved space times and a new look at the Unruh effect” and wanted to share some of my thoughts with you…

1. Unruh effect. Gravitation and thermodynamics

The subject of the paper – Unruh effect in particular and relation between gravitation and thermodynamics in general is not, I think, yet really well understood by us at the fundamental level (albeit it is for more than 20 years on the market). Probably, it would be fair to say that fresh graduate students facing with this subject on the path of their “scientific career” always find it somewhat puzzling and counter-intuitive , so before turning to the paper let me discuss basics a bit…

What is Unruh effect? We live in the Universe filled with matter: scalars, spinors, gauge fields, etc. Suppose for fun that our home is Apollo spacecraft with its engine turned off. Somehow we managed to fly to the point somewhere in intergalactic space. The gravitational field of Sun, other stars and planets is negligibly small – we can say that the metric of the spacetime around us is approximately Minkowski metric of the flat spacetime. We might start trying to detect particles from space: quanta of scalar fields, for simplicity. If we are really far from the strong sources of radiation (AGNs, stars, etc.), we won’t detect any and conclude that matter fields are in the vacuum state.

Imagine now that we turn the engine of the spacecraft on and start moving with constant acceleration . If we again start looking for particles coming from the outer space, we find that there are two major new effects compared to the previous situation. First of all, we find that spacetime around us now has an (apparent) horizon. The reason for its appearance is simple: since we are moving with constant acceleration now, it becomes harder and harder for distant particles travelling somewhere in the space to reach us. Actually, if some particles are relatively far from us, they will never be able to reach us even if they have an infinite time to do so..

The second effect is that we can observe a thermal radiation of quanta of various fields from the horizon, with the temperature of the thermal flux being related to the acceleration: $T\sim a$ – that is, the larger is our acceleration, the warmer is radiation we detect.

These two facts are combined into surprising relation of gravity (because accelerated frame of reference is equivalent to the presence of constant gravitational field!) and thermodynamics (see for example recent paper by Brustein and Hadad), that can be formulated as follows. The presence of apparent horizon means that there are regions of the global spacetime which will never be observer by us, so there should be a certain entropy associated to the lack of our knowledge about the physics behind the apparent horizon. If we calculate the energy flux dE from the horizon, we find that

dE=TdS ,

i.e., the second law of thermodynamics that appears in a rather interesting context: we need a) a curved spacetime (or an accelerated observer) and b) quantum fields living in this curved spacetime. I don’t know about you, but I certainly feel that something really deep is covered behind these formal considerations.

2. What’s the paper about?

If we are trying to construct quantum field theory in a curved spacetime (with invariance $\Gamma$ ) from the scratch, what you should do in the first place is to pick a coordinate patch. Typically, this patch won’t cover the whole spacetime, so the Cauchy surface in the patch under consideration will not necessarily correspond to a Cauchy surface for the whole spacetime. If so, after contructing the appropriate Fock space you’ll find that the vacuum state is not necessarily invariant w.r.t. the transformations from \Gamma: take for example Rindler patch of Minkowski space or planar patch of de Sitter space – corresponding vacua are not Minkowski- and de Sitter-invariant. In we want to find a $\Gamma$ -invarant vacuum, we need to find a coordinate system that covers the whole manifold. This can be quite hard – for example, it took about 50 years to discover Kruskal coordinate system covering the whole Schwartschild spacetime.

What authors suggest is a relatively simple algorithm for constructing an $\Gamma$ invariant vacuum starting from a QFT defined in the patch that does not cover the whole spacetime. What one has to do is to find the complete set of modes u_{i}(x) as usual and then combine them into generic quadratic form

$W(x,x')=\sum(\delta_{ij}+B_{ji})u_{i}(x)u_{j}^{*}(x')+\sum B_{ij}u_{i}^{*}(x)u_{j}(x')+$
$+{\rm Re}\sum C_{ij}(u_{i}(x)u_{j}(x')+u_{i}(x')u_{j}(x))+S(x,x')$ . (1)

where $B_{ij}$ is a Hermitean matrix, while $C_{ij}$ is a complex matrix satisfying the condition $C_{ij}=C_{ji}$ . This form defines the Wightman pair Green fuction in a quantum state (not necessarily vacuum state for the modes $u_{k}$ ). Only the first term in the r.h.s. of (1) contributes to the uniqual time commutator $[\phi(x),\phi(x')]$ , the other terms basically determine how much is the given state deviates from the vacuum state (or the states related to vacuum by Bogolyubov transformations).

After you write this form, you need to put additional requirement that the form should be invariant w.r.t. the group $\Gamma$ and tune the free functions B and C correspondingly. The resulting W will give you the desired Wightman function for the $\Gamma$ -invarant state.

3. The question of interaction

Typically, when we discuss the Unruh effect and relation between gravity and thermodynamics, we stay focused on a free field theory. While it would be fair to say that physics of free field theories in curved spacetimes is understood at the formal level very well, what remains to be understood is the physics of interacting field theories in curved spacetimes.That’s where a lot of interesting things remains to be discovered… As an example, take de Sitter space. De Sitter invariant Bunch-Davies state for massive free scalar field is known for decades, and I don’t think that the author’s construction does not really bring anything new for deeper understanding of physics of quantum field theory in dS space (basically, following authors’ prescription you can start from QFT in planar patch and find dS-invariant BD state, that’s all). What’s interesting is that turning interactions on will actually show you which states are relevant for physics, and which are not. For example, as it turns out, if the BD state is the initial state of your scalar field, you are not able to turn the interaction term adiabatically – i.e., BD state is associated with adiabatic catastrophe in the theory… In other words, if we turn ineraction, dynamics on, the prefactors B and C in the expression (1) above will become the function of time (and coordinate) – it is clear from the fact that the expression (1) describes Wightman function for a generic mixed state, i.e., carries information about occupation numbers, and occupation numbers are the functions of time if interaction is turned on. What happens with and in the dynamical, ineracting problem? Does dynamics decide which and I can actually choose? This is a problem for the future…

Some literature
1. N. Birrell, P. Davies, Quantum fields in curved space. Very good (if not the best) introduction into the subject. Everything you need to know about QFTs in curved spacetimes.
2. J. Kapusta. Finite temperature field theory. A fundamental textbook on Matsubara diagrammatics as well as canonical treatment of finite temperature QFTs.
3. R. Wald, Quantum field theory in curved spacetime and black hole thermodynamics. Much shorter than Birrell and Davies, nice discussion of the Unruh effect.

Cosmology, Fellow Craft, Journal club, Quantum field theory

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372. On science (in Russia)

Posted by Dmitry

at April 26, 2009

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As I believe, in the long run the most painful hit that Russia got in final rounds of Cold War wasn’t a decrease of its military might or loss of political influence. It should be rather clear that those who suffer in war the most are the ones who cannot really defend themselves. The most affected by the loss in Cold War was science in Russia.

Below is a famous plot showing how the overall number of publications in refereed journals, papers written in Russia behaved with time:

Number of publications in refereed journals (Russia)

Tremendous drop of 1992/93 is related to three factors: a) almost complete loss of funding of science after decay of USSR, b) the fact that almost all top scientists (including of course best teachers and leaders of scientific schools) from the former USSR were offered jobs on the West and c) the fact that so many people have left science during hard times. While (b) and (c) together meant the loss of quantity, (b) alone also meant the loss of quality. The latter, as you know, is measured in “scientific impact” Before 1992 Russia was among first 10 countries with the most impact in science. Nowadays the top 10 list looks like this:

Scientific impact: top 20 countries

The list probably only shows inadequacy of impact estimations and impact as a parameter that really characterizes science (Switzerland is the 1st and Denmark is the 3rd? and Japan is 19th?? WTF?), but the most important fact for me that follows from this list is that Russia is no longer in the top 20. Actually, as for the scientific impact, it is next to China:

Russia and China: scientific impact

I think, the situation might have changed would the funding of science in Russia be dramatically increased somewhere around 2000 (the earlier-the better). To my knowledge, no drastic changes in funding policy are observed even today, 10 years later. Quite the opposite, it seems that the number of professionals in science working in Russia continues to decrease.

Update: Rafael asked for links to statistics used in the post – here you go. The first plot (number of publications in refereed papers) is based on data from the portal scientific.ru and was first published in Lenta.ru. The impact factor data are taken from Thomson Scientific?s Essential Science Indicators database (1.01.98-30.04.08).

Entered Apprentice, Rants