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Apr
27
comment Have we ever seen an atom? If not, how do we know they exists?
Google STM (scanning tunneling microscope) or AFM (atomic force microscopy). And how do we know they exist... well the answer is physics...
Feb
16
comment How would one experimentally prove AdS/CFT correspondence?
Yeah, but that's only for string theory. AdS/CFT doesn't necessary need string theory in some cases (Kerr/CFT and AdS${}_3$/CFT${}_2$ where you work within the framework of asymptotic symmetries).
Feb
15
comment Wald General Relativity, Chap 7.1
Well, I think you need to just write it out. (7.1.19) is the metric in ($t,\phi,\rho,z$) basis, and V,X and W are defined on a page before. So you need to calculate (you can always use Mathematica and GRTensor for checking your result) the first equation, and then the second equation, and they should be the same.
Feb
7
comment Warped AdS${}_3$ and symmetry breaking
Oh, cool :D I was worried for a bit that I did something wrong :D
Feb
7
comment Warped AdS${}_3$ and symmetry breaking
Really? Because when I compare it to the near horizon extreme Kerr, with the $\Lambda(\theta)=1$ factor, I get the AdS${}_3$, where by just comparing I have $r\to\sinh\omega$ and $\varphi\to\sigma$ :S Plus I solved the Killing equation and got that for warped metric only $2\partial_\sigma$ is a Killing vector, and of all three of $SL(2,\mathbb{R})_R$ are too :S
Feb
7
comment Warped AdS${}_3$ and symmetry breaking
Thanks for the explanation :)
Feb
6
comment Warped AdS${}_3$ and symmetry breaking
So it's just putting them in Killing equation and seeing that they're no longer Killing vectors. I was thinking that there is some more profound way than that. How did they know that the warping will break the symmetry of $SL(2,\mathbb{R})$ to $U(1)$? Is it because the $\sigma$ part represents the rotation, and the wrapping factor is in front of that part of the metric which contains it?
Feb
6
comment Changing vector basis in AdS$_3$
I should be able to change the basis with: $V^{\mu\prime}=V^\mu g_{\mu\nu} \frac{\partial x^\nu}{\partial x^{\nu\prime}} g^{\mu\prime \nu\prime}$, where primed are new coordinates ($\tau,\sigma,\phi$), and not primed are old ($x,y,u,v$), but I'm not getting a good result :\
Feb
5
comment Changing vector basis in AdS$_3$
I'll try this and see the result.
Feb
5
comment Changing vector basis in AdS$_3$
I can make $\partial_\tau=\frac{\partial x}{\partial \tau}\partial_x+\frac{\partial y}{\partial \tau}\partial_y+\frac{\partial u}{\partial \tau}\partial_u+\frac{\partial v}{\partial \tau}\partial_v$, but that doesn't help much :\
Feb
4
comment Changing vector basis in AdS$_3$
I did this on paper, for which I get: $\partial_x=\frac{\partial \tau}{\partial x}\partial_\tau+\frac{\partial \sigma}{\partial x}\partial_\sigma+\frac{\partial \omega}{\partial x}\partial_\omega$, but I kinda got stuck there :S Should I express $\tau,\sigma,\omega$ in terms of $x,y,u,v$ then? Is that even possible? :\
Jan
25
comment Measuring background radiation
The water in the nuclear power plants has boron in it that absorb neutrons if I recall correctly ;)
Jan
13
comment Squashed 3-sphere?
Yeah, that was what I was thinking. It's not really intuitive. I would expect something that was more standard 3 sphere metric looking... But thanks nonetheless :)
Jan
13
comment Squashed 3-sphere?
Oh, so that's where all the similarity with warped AdS${}_3$ comes from. Just a warped sphere in a sense...
Jan
10
comment Different definition of SL(2,R) algebra?
I was just reading something about structure constants and thought that that might be the answer! So it is only difference in the given representation after all.
Jan
10
comment How do I correctly choose signs for a falling particle?
Have you tried setting up a coordinate system? That should help...
Jan
10
comment Different definition of SL(2,R) algebra?
Sorry, forgot about that, corrected it now.
Jan
7
comment Energy dispersion in graphene
See this: en.wikipedia.org/wiki/Density_of_states It has basically all you need ;)
Jan
6
comment Energy dispersion in graphene
If I'm not mistaken, there are two carbon atoms per primitive cell, and each has 3 nearest neighbors, so that should be correct. For DoS you need the expression: $g_{2d}(E)=\frac{1}{A}\sum_k\delta(E-E(k))$ if I recall correctly. Then you assume that you have a large volume and go to continuous limit, from sum to integral. Then it's just solving the integral (transform the integral from $k$ to $E$ to integrate and that should be it)
Jan
6
comment Energy dispersion in graphene
Well you need to draw the crystal structure of graphene, then you can find the unit cell, primitive cell, all the info about Bravais lattice. Then you can see the number of nearest neighbors. For DoS you can search the google density of states for graphene, and 4th pdf has about this. Also look your literature: Kittle, Ashcroft Mermin... graphene is really popular and there is a lot of info on it.