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366. Some interesting recent papers in Arxiv

Posted by Dmitry

at April 23, 2009

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Just wanted to acknowledge their existence, although I’ll not be really able to review them due to the lack of time…

1. Quantum field theory

1.1. “Non-Abelian Duality and Confinement in N=2 Supersymmetric QCD” by Michail Shifman and Alesha Yung. The authors study transitions from weak to strong coupling in N = 2 SQCD that happen when you change parameters of the theory – that is, the coefficient $\xi$ in front of Fayet?Iliopoulos term and quark mass differences. Here the authors are interested in the case N<N_f<2N and study phases of the theory at different values of $\xi$ .

1.2. “Deconfinement phase transition in mirror of symmetries” by M.N. Chernodub, Atsushi Nakamura and V.I.Zakharov. The idea is that the 4d magnetic vortices get reduced to their 3d projection in the deconfining phase. Behavior of the latter can be described by a 3d Higgs field, which is condensed.

2. Quantum computations

2.1. “Topological phases and quantum computation” by Alexei Kitaev and Chris Laumann. If you follow NEQNET really carefully, you should remember Kitaev (he is a master mind of topological quantum computation). This paper contains the set of his lectures on the subject – in particular, topological effects in 1d superconductors and honeycomb model (which features non-abelian anyons).

3. Cosmology

3.1. “Non-Gaussianity as a Probe of the Physics of the Primordial Universe and the Astrophysics of the Low Redshift Universe“, a white paper by a huge number of co-authors (there are so many of them, that one may start wondering who really wrote the paper ) If you are, say, a curious condensed matter theorist (or experimentalist) and always wanted to learn what is the non-gaussianity buzz in cosmology about, that’s the paper you want to go through – it is short (8 pages) and it does not really contain a single formula.

3.2. “Levitating Dark Matter” by Nemanja Kaloper and Antonio Padilla. The basic idea of the paper is that dark matter can be realized in the form of quanta of heavy fields satisfying BPS condition (mass of the particle is equal to its charge). In this case, gauge repulsion may effectively look like an “antigravity”, and one has to take it into account when studying flows of dark matter agglomerates.

3.3. “Dynamical compactification from de Sitter space” by Sean M. Carroll, Matthew C. Johnson and Lisa Randall. The authors argue that dS space “is unstable to the nucleation of non-singular geometries containing spacetime regions with different numbers of macroscopic dimensions”. The setup they discuss is D-dimensional space with cosmological constant (so, background is supposed to be dS_D initially) and q-form gauge fields. The claim is that this setup is unstable w.r.t. the nucleation of D-q -dimensional regions stabilized by flux.

4. Condensed matter theory

4.1. “Introduction to superconductivity in metals without inversion center“ by Vladimir Mineev and M. Sigrist. Both authors are well-known experts in unconventional superconductivity and, as I understood, this paper is a single chapter from the forthcoming book on the subject.

That’s pretty much all that caught my eye… Did I miss anything exciting that happened during the last week?

Condensed Matter, Cosmology, Journal club, Master Postdoc, Quantum computation, Quantum field theory

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This and that in ArXiv on Monday

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365. Inertial confinement – using lasers for compression

Posted by Dmitry

at April 22, 2009

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I hope you are not getting bored too much by my discussion of thermonuclear fusion in inertial confinement reactors, because today I’m going to continue and finally start explaining why do they want to use lasers in HiPER to compress plasma.

Basically, the main bonus of using lasers is their ability to concentrate huge energy in a very small volume ( $<10^{-6}{\rm cm}^{-3}$ ) during tiny amounts of time ( $<10^{-10}\div{}10^{-9}{\rm sec}$ ), so that the very phenomenon of inertial confinement becomes possible. Actually, nowadays laser technology is the only technology available that allows us to build up energy densities as high as $10^{20}{\rm W}/{\rm cm}^3$ , matter densities of the order $10^{26}{\rm cm}^{-3}$ and temperatures about 10 keV at which fusion reactions start.

The time scale during which plasma is confined in inertial confinement devices is of the order $10^{-11}\div{}10^{-10}{\rm sec}$ , so devices can clearly only work in impulse regime.

Last time I presented a photo of fuel capsule for inertial confinement reactor (naturally, it should be a sphere since sphere compresses the best). Actually, such fuel cell may have a rather complicated structure. The outer layer of the capsule is called ablator (one can show that it is energetically favourable to make ablator from the material with large ). Its main purpose is to hold the form of the capsule and evaporate as fast as possible after the laser starts to heat the microcapsule. In the simplest case, below the ablator lays fuel – d+t ice or gas (at normal or high pressure). In more complicated cases additional insulating layers may be present that, say, protect d+t ice from melting.

In indirect drive thermonuclear fusion reactors, capsule is placed inside this NIF hohlraum…

HiPER - laser heats up the capsula

… and then the laser is turned on. The beam heats up the material of hohlraum, and the latter emits X-rays heating the capsule in turn.

Laser emission is focused on the capsule in a spherically symmetric way (and least, we try to focus it this way – why? see discussion in the previous post). If the power of the beam is about $10^{14}{\rm W}/{cm}^3$ , ablator is evaporated and ionized at time scales $\ll{}10^{-9}{\rm sec}$ . Its material becomes plasma with characteristic temperature of the order $1{\rm keV}\approx{}10^7{\rm K}$ and density around $10^{18}\div{}10^{22}{\rm cm}^{-3}$ . This plasma blows off, with typical velocities being around 300-1000 km/s, while laser emission continues to heat the lower layers of the capsule up – laser emission strongly interacts with plasma.

To be continued.

Entered Apprentice, Nuclear physics

375. Inertial confinement: concluding part on lasers

385. NEQNET: Last two weeks of April

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

364. Thermonuclear reactors. More on inertial confinement

Posted by Dmitry

at April 21, 2009

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Last time I did not quite finish with the discussion of physics of inertial confinement, so let me continue…

An important parameter that characterizes plasma in reactors with inertial confinement is the ratio between the geometric size of the region where reactions take place and the mean free path $l_\alpha$ of $\alpha$ -particles. It basically determines the ability of thermonuclear reactions in the plasma to self-sustain – if $\alpha$ particles are adsorbed faster, plasma is getting warmed up more effectively. In other words, one naturally would want to increase or decrease $l_\alpha$ . How to do that?

We have:

$\frac{R}{l_\alpha}\sim \rho_0 R$ ,

i.e., the ratio depends on the density of plasma in the beginning of the experiment and the characteristic size of the plasma (prefactor that we omitted also depends on temperature of the plasma non-trivially). Basically, at $T\sim{}1\div{}10{\rm keV}$ characteristic velocity of particles in plasma is about $10^7\div{}10^8{\rm cm/s}$ , and the fusion can be only effective at plasma densities of the order $10^{23}{\rm cm^{-3}}$ or larger. Such densities greatly exceed the ones we deal with in solid state physics, so one needs to really strongly compress plasma to make fusion possible.

Geometrically, the most convenient way to compress plasma is to deal with spherical samples. In this case, we have $\rho{}R^3={\rm Const.}$ , so $\rho\sim{}R^{-3}$ (geometrically, the fastest decrease with which is possible) and $\rho{}R\sim{}R^{-2}$ .

Inertial confinement reactor microcapsule

And that’s how a corresponding fuel microcapsule looks like (inside this capsule is d+t fuel)

It is also clear from the considerations above that we really want to keep the spherical symmetry intact during the whole compression stage – otherwise, the density of the fuel will not achieve maximal possible values. As it turns out, that is the main technical difficulty we face with when we try to start reaction of fusion in an inertial confinement reactor – Rayleigh-Taylor instabilities in the heated fuel lead to breakdown of spherical symmetry. That’s how the problem of thermonuclear fusion is related to the problem of turbulence, but let me leave the discussion of hydrodynamic instabilities to another post…

Entered Apprentice, Nuclear physics

358. Thermonuclear reactors. Inertial confinement

365. Inertial confinement – using lasers for compression

385. NEQNET: Last two weeks of April

355. Introduction into thermonuclear reactors

363. Vector inflation

Posted by Alexey Golovnev

at April 20, 2009

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Alexey Golovnev is a research associate in the Arnold Sommerfeld Center for Theoretical Physics , U. of Munich. Dmitry.

I would like to blog about the recently proposed model of vector inflation, Golovnev, Mukhanov, Vanchurin, arXiv:0802.2068. (See also Golovnev, Mukhanov, Vanchurin, arXiv:0810.4304 and Golovnev, Vanchurin, arXiv:0903.2977 for further developments.) Inflation is one of the basic concepts in cosmology, it solves the well-known cosmological problems (for which I refer the reader to any modern textbook on cosmology, see below) by a period of very rapid (nearly exponential) increase of the size of the Universe. By a straightforward inspection of the Friedman equations, this period of accelerated expansion can be achieved with a matter content of negative pressure. As calculating the pressure basically amounts to taking the difference of kinetic and potential energies, the most natural idea to realize this type of equation of state is to “freeze” an inflaton field at a high value of its potential energy.

Successful models of inflation usually invoke a scalar inflaton field which rolls slowly down the hill of potential energy. The Universe expansion provides a viscous friction term making the slow roll regime possible. Indeed, if we assume chaotic inflation on a mass term, the equation of motion reads $(\square + m^2)\phi=0$ and the D’Alambert operator can be calculated as the divergence of the gradient: $\square \phi=\bigtriangledown_{\mu} \bigtriangledown^{\mu} \phi=\frac{1}{\sqrt{-g}} \partial_{\mu} g^{\mu \nu} \sqrt{-g} \partial_{\nu} \phi$ . In the physical time with the metric element $ds^2=dt^2-a^2(t){ \overrightarrow{dx}}^2$ we get $\ddot{\phi}+3H \dot{\phi}+m^2 \phi=0$ where $H \equiv \frac{\dot{a}}{a}$ stands for the Hubble parameter. The coefficient refers to the Universe expansion. More physically it can be understood if we consider taking divergence of some conserved vector current $j^{\mu}$ . In this case the 3Hj^0 term shows that the charge density exponentially decays because the physical volume grows at the relative rate of . For cosmology it means that the highly excited scalar field does not relax fast, but rather rolls down slowly providing a large enough period of inflation.

Vector fields have not received that much attention in the cosmological context due to several reasons. First of all, vector fields induce anisotropy. We resolve this problem either exactly by taking a triad of vector fields or approximately by introducing a large random collection of them. (The former solution was known before, stemming from some specific Einstein-Yang-Mills configurations, see the reference list in our article.) After that one can deduce the equations of motion in an inflationary background. Everything proceeds exactly along the lines indicated above, and the final result for a massive vector field shows that in the homogeneous test field approximation we have A_0=0 and for the spatial components A_i the slow-roll regime is possible. Clearly, it is not what we want to have. The potential energy rapidly decays as $A^2 \equiv A_{\mu}A^{\mu}=-\frac{A_i A^i}{a^2}$ . These vector fields can not source the inflation. There is no surprise in that. Neglecting the potential term, the vector fields are conformal invariant and shouldn’t really care about the relevant length scale.

A better choice of variables is $B_i=\frac{A_i}{a}$ ; it is these quantities which have to change slowly during inflation. One can easily find the following equation of motion for them: $\ddot{B}_i+3H \dot{B}_i+(\dot{H}+2H^2+m^2)B_i=0$ . During inflation it implies a very large effective mass of order 2H^2 which renders the friction term inefficient and the slow roll impossible. But note that $\frac{R}{6}=-\dot{H}-2H^2$ where is the scalar curvature; it shows that this unfortunate contribution can be compensated exactly by a suitable non-minimal coupling of the vector fields to gravity.

It brings us to original Lagrangian of the vector inflaton fields from 0802.2068 arXiv paper: ${\cal{L}}=-\frac{1}{4}F^2+\frac{1}{2}(m^2+\frac{R}{6})A^2$ with $F_{\mu \nu}=\bigtriangledown_{\mu}A_{\nu}-\bigtriangledown_{\nu}A_{\mu}$ and $A^2 \equiv A_{\mu}A^{\mu}$ . We also take the standard Einstein-Hilbert action for gravity and sum over a large number of independent randomly oriented vector fields. At the background level the solution is basically the same as for scalar inflaton fields but we can have some anisotropy for free. And one would like to consider also a more general proposal ${\cal{L}}=-\frac{1}{4}F^2-V(A^2)+\frac{R}{12}A^2$ before proceeding with the perturbation analysis.

Being that simple for inferring the background evolution, the vector fields turn into a real disaster already at the linear level in perturbations. The reason is very simple. Different types of perturbations (scalar, vector and tensor) do not decouple even for perfectly isotropic backgrounds because, for example, terms like $h_{\mu \nu}A^{\mu}A^{\nu}$ couple tensor (transverse and traceless) metric perturbations $h_{\mu \nu}$ to the scalar part of the linear perturbation equations. Due to this problem, we don’t have at the moment a full rigorous analysis of linear perturbations in vector inflation. Nevertheless, we were able to provide some approximate consideration in our paper 0903.2977 which strongly suggests that, most probably, there should be some considerable correlations between scalar and tensor modes in CMB. And, of course, another very important consequence is that we expect some anisotropy. It is very important in view of the current observational progress in cosmology. See D. Wands, Nature Physics, Volume 5, Issue 2, pp. 89-90 (2009) for an interesting expert opinion.

A better analysis is needed to have more detailed predictions and to choose a proper form of inflationary potential V(A^2) . As I’ve stated above, it is not available yet. However, a simple consideration of gravitational waves only allowed us to exclude a large class of models in arXiv:0810.4304. A catastrophic growth of gravitational waves in most of the models with large values of vector fields can be seen directly in the equations of motion, but an easier way of doing this is to expand the action of the theory up to the second order in the tensor metric perturbation neglecting variations of all the other variables. It shows that the gravitons acquire an effective mass because we have quadratic in $h_{\mu \nu}$ terms in the action which depend on background values of the vector fields and come about due to raising the indices in A^2 and F^2 . (Of course, it is of crucial importance here that the fields are in the slow-roll regime which makes the mass approximately constant.) It is clear that for models with large vector fields the mass should also be large. And in fact, it is usually tachyonic and makes the large fields vector inflationary models badly unstable. (There are some weird exceptions like $V \sim B^{600}$ ). On the other hand, the small fields models are generically stable in this respect. For example, one can use the Coleman-Weinberg type of potential for vector inflaton fields.

I have to mention here that in D. Lyth et al., arXiv:0809.1055 it was claimed that gravitational waves are stable in vector inflation. The authors have moved to the Einstein frame without finding it explicitly and then they have made some arguments of slightly philosophical nature for rather tame behaviour of the gravity waves. This statement can’t be trusted because the raising of indices occurs in any frame and, after all, there is no reason for such a striking difference between results obtained in different frames (unless some wild instability of the conformal factor takes place).

There is also one more controversy about vector inflation in the literature. It is the problem of stability raised in B. Himmetoglu, C. Contaldi, M. Peloso, Physical Review D79, 063517 (2009). It was noticed that the longitudinal component of a tachyonic vector field looks like a ghost making the quantum theory problematic. (I remind to the reader that a large tachyonic contribution to the effective mass is absolutely crucial to insure the slow roll.) At the classical level we don’t see this instability. The tricky point here is that $\delta A_i$ can be allowed to grow (even exponentially), but what should be stable is $\delta B_i=\frac{\delta A_i}{a}$ . Any theory in terms of the A_i components should be in a sense unstable. The tachyonic mass (at least for the large fields models) translates exactly to this purely coordinate effect. The more physical fields B_i behave like if there were no tachyonic mass. If there is no way to construct a stable quantum theory in this case, then this translation of the purely coordinate growth to a fundamental catastrophic instability sounds very unsatisfactory for me. Actually, some arguments in favour of quantum stability are given in D. Lyth et al., arXiv:0809.1055 although they are not very conclusive. Ghost instabilities present a very serious issue for quantum field theory and deserve somewhat more serious attitude than just counting the total energy of a state with a very small occupation number.

So, I have to admit that I have no answers to many perfectly legal questions. But I think, at the very least, it is important to understand the possibility of playing with vector fields too instead of restricting oneself to a purely scalar world of inflation. Moreover, higher spin fields are also possible, see T. Kobayashi, S. Yokoyama, arXiv:0903.2769 and T.Koivisto, D. Mota, C. Pitrou, arXiv:0903.4158.

Some literature

1. V. Mukhanov, Physical foundations of cosmology.
2. A. Liddle, D. Lyth, Cosmological inflation and large-scale structure.
3. A. Linde, Particle physics and inflationary cosmology.

Cosmology, Journal club, Master Mason

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362. Kepler sees first light

Posted by Dmitry

at April 19, 2009

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Star cluster NGC6791

Star cluster NGC6791 from the Kepler’s first light image

Tres-2

Just a small part of Kepler’s field of view. The star in the center of the field is known to have large Jupiter-like planet called TrES-2.

Just wanted to let you know (if you did not hear about that already), that Kepler has just seen the first light (on Apr – the official NASA press-release came out on Apr 16.

The ultimate goal of the mission is to estimate the average number of large planets per cubic kPc in our galaxy. To achieve this goal, Kepler will be pointed at large star field in Cygnus constellation to watch the small drops of brightness of stars (in particular, we are interested in dwarfs) in the field, which presumably would correspond to a planet’s transit in front of the star. Cygnus constellation was chosen since it’s far north of the ecliptics, so that the Sun cannot get in the way of the Kepler’s view for the entire orbit. Kepler is good enough to detect a Earth-size planet orbiting Sun-like star of the magnitude of 14. Changes in brightness of the field have to be measured continuously (planet’s transit is a relatively rare event, and we don’t know where exactly it can happen, so we can only detect them statistically – looking at a large field full of stars), so HST is of no good for planet detection mission.

Astrophysics, Cosmology, Entered Apprentice

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