Good Monday evening all, and welcome to another edition of Your Week in Seminars. Last week was a half week here in Cornell, but we still managed two talks, the general colloquium and the Wednseday-talk-on-Tuesday. Monday we had Charles Marcus of Harvard talk about Building Schrödinger's Chip. This was a quantum computing talk. We don't actually have a quantum computing group in Cornell, but I've taken a couple of courses on it back home, and it's an interesting subject, although I've been a bit disillusion by the notable lack of problems solvable by quantum computers. Marcus started by talking about the wonders and insanities of quantum mechanics - the usual spiel about the two slit experiment, electrons passing through walls, and Schrödinger's cat. He said he dubbed the talk Schrödinger's chip because unlike cats, that appear to break when we put them in the kind of low-temperature vacuum conditions we like to do quantum experiments in, chips keep working pretty well. Next he introduced the concept of entanglement, which is at the basis of the whole concept of quantum computing. Entangled particles are two or more particles that do not have a definite quantum state, but are definitely in the same quantum state. If I take them apart and measure their state - say, spin up or down - then I do not know the answer, but as soon one turns up, the other is up as well, and if one is down the other is immediately down as well. The experimental side of quantum computing is all about making little quantum boxes that contain a small number of states (like up or down) and then making it possible to entangle two of those boxes together. Add up enough boxes, under some criteria that were posited a decade ago but still not achieved, and you have a quantum computer. The majority of the talk was a survey of the various state of the art boxes and the methods used to make them. For those keeping track, 15 is still the largest number factored by a quantum computer. On Tuesday, I came in just in time for the second half of John Terning's talk on Monopoles, Anomalies, and Electroweak Symmetry Breaking. It's not really ideal to go into the second half of a talk in Newman 311, and this one actually sounded like I missed some interesting stuff. The part that I heard was about adding magnetic monopoles to the standard model., Those lovely magnetic equivalents of the electric point charge that we all heard about in our undergraduate E&M course turn out to be surprisingly hard to integrate into basic particle theories, which is perhaps for the best as we have not detected them so far. The gist of what I got from the second half of the talk was that it is not enough to add a magnetic counterpart to the electric part of the standard model, but in fact one needs a magnetic QCD and Weak force as well. Under some conditions, this kind of configuration can work, and predict magnetic monopoles with TeV-scale masses - the kind we might see in the LHC. Terning also talked about how these could be detected in the LHC. It turns out this isn't simple, because at TeV we would be producing monopole-anti-monopole pairs just barely, and so without a lot of kinetic energy they would tend to collapse back on themselves and annihilate, creating what is essentially an omnidirectional shower of photons. He mentioned that one of the big detectors at the LHC - the CMS - was equipped to detect these kind of photon bursts, and so this another prediction or possibility that we can look forward to seeing or not seeing soon. That's it for last week, kind of on the short side due to the holiday and so on. This week is our last normal one, as the semester ends, but I'll have a couple more particle talks the week after that, as well.

Thanks to all who sent in solutions! We are very happy with the vast number of responses, and we will put up a leader board shortly! Solution Let A be the fraction of the rubber band that the ant has traversed. $$A\left(t\right)=\frac{x\left(t\right)}{L+vt}.$$ The ant's velocity relative to any point along the rubber band is equal to the length of the rubber band times the first time derivative of A: $$u=\left(L+vt\right)\frac{dA}{dt}=\left(L+vt\right)\left[\frac{\dot{x}}{L+vt}-\frac{vx}{\left(L+vt\right)^{2}}\right]=\dot{x}-\frac{vx}{L+vt}.$$ This gives us an inseparable, first-order differential equation for x(t). The general differential equation of this type, $$\dot{x}+p\left(t\right)x=q\left(t\right),$$ has the general solution $$x\left(t\right)=e^{-\int_{0}^{t} p\left(t\right)dt}\int_{0}^{t} q\left(t\right)e^{\int_{0}^{t} p\left(t\right)dt}dt.$$ In our case, $$p\left(t\right)=-\frac{v}{L+vt},\quad q\left(t\right)=u.$$ Therefore, $$x\left(t\right)&=&e^{\int\frac{v}{L+vt}dt}\int ue^{-\int\frac{v}{L+vt}dt}dt=\frac{u}{v}\left(L+vt\right)\ln\left(1+\frac{vt}{L}\right).$$ When the ant has reached the other side, x(t) = L + vt, so $$x\left(t\right)=L+vt=\frac{u}{v}\left(L+vt\right)\ln\left(1+\frac{vt}{L}\right).$$ Solving for t, we get $$t=\frac{L}{v}\left(e^{v/u}-1\right).$$ So the ant always makes it to the other side (unless u = 0)! In the limit as v -> 0, we get $$t\approx\frac{L}{u},$$ which is exactly what we would expect. We can show that the ant will reach the other side without doing any calculations. As the ant moves across the rubber band, the velocity of the point on the rubber band that the ant is currently walking on increases from 0 to v. Therefore, the ant is accelerating. Since the other end of the rubber band is moving at a constant velocity, the accelerating ant will always eventually catch up to the far end. Another way to see this is that since the ant is accelerating, if it makes it halfway, it will make it all the way to the other side; if it makes it one-quarter of the way, it will make it halfway, and so on. We know that since the ant is traveling at some nonzero velocity, it must make it some nonzero fraction of the way to the other side. Therefore, it must make it twice that far, and so on, all the way to the other side. Thanks to Frank for pointing this out!

Hello everyone and welcome to another week of talks here at the physics department. I was out of Ithaca for a bit this past week, so in this very special edition I'm going to present a full week's worth of seminars (one from last week and two from the previous week) in one post covering two weeks. The Colloquium two weeks ago was given by our own Csaba Csaki, who talked about Electroweak Symmetry Breaking and the Physics of the TeV Scale. This was essentially an overview of beyond-the-standard-model physics and the kind of things we expect out of the LHC. Csaba started off by reminding us of the Standard Model, our very successful model of particle physics that's withstood nearly every test over the last thirty or forty years. The Standard Model is a set of three gauge theories - three forces that a relayed by massless particles - along with the theory of electroweak symmetry breaking that explains why one of these powers, the Weak one, is relayed by massive particles. This theory is well-backed by experiment, with the exception of the crucial Higgs boson, the one that gives mass to those previously massless W and Z, which we hope to see soon in the LHC. There are a few problems with the Standard Model, and the big one is the Hierarchy problem. Given what we know of symmetry breaking and how the W and Z get their masses, we expect elementary particles to have masses that correlate with the energy scale of the interaction that gives them this mass. Since that interaction is not one we see at low energies, we expect the elementary particles to be very massive. Since they are not, we conclude that there must be some symmetry that keeps them massless or nearly so. Some solutions to this was mentioned, beginning with current-favorite supersymmetry. This extra symmetry relation bosons to fermions and vice versa works well to solve the original problem, but creates a few of its own, like the Little Hierarchy Problem - if there's all this new physics at energies just a little higher than we've been exploring, why don't we see its effects on the low energy physics? In other words, why does the non-sypersymmetry Standard Model work so well? Csaba went on to mention some ways of solving these problems, such as burying the Higgs by allowing it to decay only in very specific ways. He also talked about a few more, like no-Higgs theories that accomplish electroweak symmetry breaking by different means, and extra-dimensional theories that allow us to give different energy scales to different forces. And the exciting thing about all of this is that we are likely to know a great deal of the answers soon, within the next few years, once the LHC starts giving data. On Wednesday after it we had Sven Krippendorf from Cambridge talk about Particle Physics from local D-brane models at toric singularities. This was a heavy string theory talk and I couldn't follow much of it. The question at hand was how to get the Standard Model, or parts of it, out of string theory models, and the gist of the talk revolved around toric singularities in the spacetime that the string theory lives in. No, I'm not entirely sure what makes a singularity toric. There were a lot of colorful graphs and some explanations. At the end there seemed to be some analogy made between different types of singularities on the manifold in string theory language and different gauge theories in the quantum field theory language, with a way to map them to each other. Possibly exciting, but you'd have to ask a proper string theorist about it. Then just this last Friday, we had Rachel Rosen from Stockholm University talk about Phase Transitions of Charged Scalars and White Dwarf Stars. This was a blackboard talk, which is always exciting and is usually more illustrative than Power Point ones. The subject was the thermodynamics of white dwarf stars - stars that are very dense and old, where fusion has mostly stopped and the only thing preventing the collapse of the star upon itself is the fermionic pressure of the electrons, that cannot fall into the same quantum states. The physical description of these stars is one of relatively free positive ions, specifically helium ions in this case, floating through a background of fermions. They are described by a quantum condensate, which has a good theory explaining it, but with the addition of Coulombic interaction between the ions. This state applies, specifically, to a subgroup of these stars that are mostly made of helium. This kind of ion condensate tends to crystallize depending on the ratio between the kinetic and potential Coulombic energy. Quantum effects, on the other hand, depend on some ratios of mass and charge between the ions. The only material where this applies turns to be helium, but luckily there are plenty of these helium-made white dwarfs. The derivation, as Rosen showed it, starts with a neutral Bose-Einstein condensate, which has a simple phase diagram - uncondensed above some critical temperature, and increasing condensation as the temperature is lowered to zero. The charged condensate introduces photons as it is usually done in field theory and follows the consequences. The result is a more complicated phase diagram. Under the old Tc, the ions still condense, but things change above it. There is now some higher temperature above which there is no condensation, but in between there are two solutions to the equations of motions, a condensate and a non-condensed state, and both a local energy minima. This means that the transition into a condensate is not continuous, and this is a first order phase transition. The nice thing here is that we have such white dwarf stars to observe and we can compare this theory to observations. That's it for these last two weeks. All you Americans out there have a good Thanksgiving, and I'll see you next week with two new seminars.

We welcome you to send in solutions, or even any ideas you have about how to solve the problems tothe.physics.virtuosi@gmail.comwith “problem of the week” in the subject line. We will keep track of the top Virtuosi problem solvers. Welcome to the third installment of Problem of the Week! We are very pleased with the number of responses we have gotten so far and we super duper promise to put up some kind of leader board soon. In fact, I super duper promise to relegate that assignment to Alemi. We intend to keep this up as long as we can and give out prizes for high scores maybe...? They will be lame internet prizes...? The solution to the last problem of the week will be up shortly. Adam is the only one who knows the answer and he was busy all weekend taking a magic ring to Mordor. One more housekeeping note. Since we want everyone to have a clean shot at answering the question, we would prefer the solutions to be sent by email instead of posted in the comments. However, we certainly don't want to stop discussion on the problem, so if you don't want any hints you might want to avoid the comments! Now for the problem... ** James Bond has been captured by the evil mastermind Dr. Vontavious Cherrycoke, who is trying to take over the world's ice cube supply. The minions of Dr. Cherrycoke have placed Mr. Bond in an elaborate and unnecessary death contraption that, if triggered, would drop our hero into a pit of ravenous killer koalas. In other words, certain death! Dr. Cherrycoke has constructed a fitting trigger for his death machine / koala feeder. A single ice cube is placed in a glass of water so that the water is completely filling the glass up to the brim. The glass of water is then placed on a very sensitive detector. If even a single drop of water spills out of the glass as the ice cube melts, James Bond will find himself on the wrong end of a murderous marsupial mauling. Vontavious exits the room with his minions, confident that his death trap will be triggered and Bond will be vanquished once and for all. Does Mr. Bond survive? If not, roughly how long does it take until he checks in to the big MI6 in the sky? Be sure to back up your answer!

As always, we welcome you to send in solutions, or even any ideas you have about how to solve the problems tothe.physics.virtuosi@gmail.comwith “problem of the week” in the subject line. We will keep track of the top Virtuosi problem solvers.Why did the ant cross the rubber band?** A rubber band is held fixed at one end. The other end is pulled at a velocity v. At time t = 0, the rubber band has a length of L, and an ant starts crawling from one end to the other at velocity u. Does the ant reach the other side? If so, how long does it take to get there? Assume that the rubber band is able to be stretched indefinitely without breaking.

Good afternoon everyone, and welcome to another week of seminars here in the physics department. Our theme of the week is dark matter - where does it come from, how do we see it, and why is there so much of it. Along with that we have a little more AdS/CFT, seemingly continuing last week's subjects theme. All in all, it looks like seminars on similar subjects tend to condense here in the department. We start with the Monday Colloquium, where Richard Schnee from Syracuse University told us about What's the Matter in the Universe? Direct Searches for WIMP Dark Matter. Dark matter, we'll recall, is the astrophysics name for any kind of matter that doesn't emit light - one that is not inside stars. Our knowledge of our own solar system, which has its mass concentrated almost entirely inside the sun, led us to expect that mass in the universe in general would behave similarly. It turns out that the motion of observed galaxies is not consistent with the mass we measure them to have, and so we hypothesize the existence of non-luminary matter around us. These days dark matter is an object of interest not only for astrophysicists but for particle theorists as well. With our variety of beyond-the-standard models of the universe we try to account for dark matter, guess at its properties and explains why it is dark. That last quality is rather easy to explain, in fact. Our expectation of dark matter is simply that it does not interact electromagnetically, and so does not emit photons. If we also posit that it does not interact strongly, we are left with a particle that can only decay weakly, and so we might expect a lot of it to stick around. Of course, the particle must also have a mass, which is the original property we postulated for it, and so we are looking for the WIMP, the Weakly Interacting Massive Particle. Schnee talked about the various ways we hope to see WIMPs in the coming decade, focusing on two avenues, the LHC and passive detectors trying to pick up cosmic particles passing through the Earth. WIMPs are by definitions hard to detect, because they interact only Weakly and thus only weakly. This means that we can't actually see them directly in our detectors, and we have to look for either missing energy in accelerator results, which we deduce has gone to them, or their effects on detectable particles in large particle reservoir, much as we would detect neutrinos. Of course, when we have such weak signals the art is in reducing the background noise, by putting them underground, using the least radioactive materials we can find, and so on. The last part of the talk revolved around two events in his own detector that seemed to be far enough above background level to be WIMPs . Schnee then explained how statistical analysis proved in fact these many statistical outliers were, well, statistically expected, which I found very interesting. There was also a mention at the very end, of another experiment called DAMA, which is looking for a "WIMP wind", checking for signals as the Earth moves through space in opposite directions, in a kind of modern parallel of the Michelson-Morley experiment. This one has actually shown a positive signal, though this is of course still controversial. On Wednesday we had a local postdoc, Enrico Pajer, talk about Striped holographic superonductor. I mentioned AdS/CFT last week, and how it's induced some crossover between the condensed matter study of high-temperature superconductors and particle physics. This was one of those crossover seminars, with a few CM people in the audience. Enrico spent about half of the talk introducing the audience to the basics of superconductors - there were a lot of discontent as people asked questions or had objections to statements which I imagine would have gone over more smoothly with a condensed matter crowd . The bottom line of the first half were three important attributes of high-temperature superconductors, being a strong coupling between the electrons, the existence of a quantum critical point and an inhomogeneity of the material. There was then another general introduction of the AdS/CFT duality, and I'll send you to last week's summary (or the rest of the internet) if you want to hear more about that. Enrico was working on a field theory in AdS space and trying to apply the results to superconductors through the duality. In particular, strong coupling and quantum criticalities are known features of the AdS theory, and the addition here was of striped inhomogeneity, where things change alone one axis only. This is incorporated into the AdS space by applying boundary conditions, in particularl to the gauge field in the relevant field theory, and reading the results by applying Einstein's, Maxwells and the Klein-Gordon equations, in the bulk of the theory. One interesting feature that was reproduced from other, non-AdS theories, was the dependence of the critical temperature Tc on the inhomogeneity. This is the temperature where superconductors turn into normal conductors, and previous work had shown that it would to drop as the scale of the inhomogeneity grows either very large or very small, and have some maximum point for a finite scale of inhomogeneity. Enrico's work showed a dropoff in Tc for inhomogeneity on very small scales, giving the same qualitative behavior albeit with an exponential rather than logarithmic dropoff. There were more details and math then, as they studied these inhomogeneities in the AdS model, trying to determine the conductivity along the stripes and perpendicular to them and so on, producing some promising results and promising to produce some more. Finally on Friday we had Kuver Sinha of Texas A&M talk about The Cosmological Moduli Problem and Non-thermal Histories of the Universe. As mentioned above, this talk revolved around dark matter as well, though from a particle theory perspective. The trick in particle physics is always making sure that your solution to one problem, in this case dark matter, does not interfere with our solution to another problem. The other problem here was the baryon asymmetry, or the overabundance of matter compared with antimatter in the universe. In particle physics the two are generally sides of the same coin and we have no reason to prefer one or the other, and so we must have some reason that we only observe regular matter in the universe. There is a well-established model for this, called nucleosynthesis, and now when we explain the amount of dark matter in the universe we have to keep from interfering with it. And while we're at it, we might solve a third problem - why is the density of dark matter and regular matter in the universe on the same order of magnitude? Sinha went through this, presenting two models of baryon genesis, occurring at different times in the history of the universe, each with their own features problems. Finally, he suggested one solution to the coincidence problem that is non-thermal - that is, rather than configuring the equilibrium point of matter and dark matter to be similar separately, we have them coming from the same source with similar decay rate. And that was that for last week, as dark matter obscures the better-lit one. This week have a sweeping overview of particle physics, toric singularities on branes, and possibly some news from the LHC. See you in seven.

I thought we could spice things up a bit with a more interactive post on The Virtuosi. Starting this week, a new problem of the week will be posted each week. Solutions will be posted the following week. These problems will be a collection of physics and math problems and riddles, and although hopefully challenging enough to be fun and interesting, they should mostly be solvable using concepts from introductory undergraduate physics and math classes. We welcome you to ponder these problems, and send in solutions, or even any ideas you have about how to solve the problems tothe.physics.virtuosi@gmail.comwith “problem of the week” in the subject line. We will keep track of the top Virtuosi problem solvers. Here it goes…Maximizing Gravity* You are given a blob of Play-Doh (with a fixed mass and uniform density) that you can shape however you choose. How can you shape it to maximize the gravitational force at a given point P* on the surface of the Play-Doh? Solution In cylindrical coordinates, where the point P is taken to be the origin, the z-component of the gravitational field due to any point (s, z) felt at the origin, is proportional to $$\frac{1}{s^{2}+z^{2}}\frac{z}{\sqrt{s^{2}+z^{2}}},$$ where the second factor is necessary to take the z-component. If we have azimuthal symmetry, the magnitude of the gravitational field is given by the sum of all the z-components of the forces due to all points in the planet. For a given contour $$\frac{z}{\left(s^{2}+z^{2}\right)^{3/2}}=C,$$ for some constant C, each point on the interior contributes more to the total gravitational field than each point on the exterior. Thus, the gravitational field is maximized if the surface of the planet takes the shape of one of these contours. Solving for s(z), we get$$s\left(z\right)=\sqrt{\left(\frac{z}{C}\right)^{2/3}-z^{2}}.$$ If the length of the planet in the z-direction is $$z_0,$$ we can replace C in the above expression to get $$s\left(z\right)=\sqrt{\left(z_{0}^{4}z^{2}\right)^{1/3}-z^{2}}.$$ As can be seen by the plot above, this shape looks a lot like a sphere, but slightly smushed toward the point of interest P. We can rigorously compare the field of the maximal gravity solid to that of a sphere with the same volume. The volume of the maximal solid is given by $$V=\pi\int_{0}^{z_{0}}s^{2}\left(z\right)dz=\pi\int_{0}^{z_{0}}\left[\left(z_{0}^{4}z^{2}\right)^{1/3}-z^{2}\right]dz=\frac{4\pi}{15}z_{0}^{3}$$ The volume of a sphere of radius r is of course $$V=\frac{4}{3}\pi r^{3},$$ so in order for the volumes to be the same, the sphere must have a radius of $$r=z_{0}/5^{1/3}.$$ The acceleration due to the maximal solid is proportional to $$a_{max}=\int dVa_{z}=2\pi G\rho\int_{0}^{z_{0}}dz\int_{0}^{s\left(z\right)}sds\frac{z}{\left(s^{2}+z^{2}\right)^{3/2}}=\frac{4\pi G\rho z_{0}}{5},$$ while the acceleration due to the sphere is just $$a_{sphere}=\frac{G\rho\frac{4}{3}\pi r^{3}}{r^{2}}=\frac{4\pi G\rho z_{0}}{3\cdot5^{1/3}}.$$ Thus, we have $$\frac{F_{max}}{F_{sphere}}=\frac{4\pi G\rho z_{0}/5}{4\pi G\rho z_{0}/\left(3\cdot5^{1/3}\right)}=\frac{3}{5^{2/3}}\approx1.026.$$ So the solid that gives the maximum gravitational field at a point is only about 3% better than a sphere. For a more detailed discussion, see Alemi's solution.