I don't know what's more mortifying: this story, or the possibility that the Senate will strip NSF funding out of the stimulus bill because of the actions of a small number of idiots.
Wednesday, January 28, 2009
Tuesday, January 27, 2009
Colbert on science policy
This was very funny. For those not in the US, my apologies that the video doesn't work. It's Stephen Colbert talking about science policy under the Bush administration and then interviewing Chris Mooney.
This article in the NY Times was also very good.
This article in the NY Times was also very good.
Saturday, January 24, 2009
What is a polaron?
This is another attempt to explain a condensed matter physics concept in comparatively nontechnical language. Comments are, as always, appreciated.
One common example of a quasiparticle is the polaron. When a charge carrier (an electron or hole) is placed into a solid, the surrounding ions can interact with it (e.g., positive ions will be slightly attracted to a negatively charged carrier). The ions can adjust their positions slightly, balancing their interactions with the charge carrier and the forces that hold the ions in their regular places. This adjustment of positions leads to a polarization locally centered on the charge carrier. The combo of the carrier + the surrounding polarization is a polaron. There are "large" and "small" polarons, defined by whether or not the polarization cloud is much larger than the atomic spacing in the material. Polarons are a useful way of thinking about carriers in ionic crystals, materials with "soft" vibrational modes (such as the manganites), and organic semiconductors (very squishy, deformable systems held together by van der Waals rather than covalent bonding).
Not content to let the general relativity fans have all the fun, I can describe this with a ball-rolling-on-a-rubber-sheet analogy. The ball is the charge carrier; the deformation of the rubber sheet is the polarization "cloud". Consider tilting the rubber sheet - this is analogous to applying an electric field to the material. The ball will roll in response to the tilt, but it will be slowed down compared to how it would roll on a hard tilted surface, since it has to put energy into deforming the sheet. In real materials, this shows up as a correction to the effective mass of the charge carrier. All other things being equal, polarons are heavy compared to bare quasiparticles.
We can carry this analogy further. Suppose we have two balls on the rubber sheet. In this classical picture, if the balls are so close together that their sheet deformations touch, the balls will be attracted together and end up in one deformation, held apart by their mutual hard-core repulsion. This is a crude analogy for bipolaron formation, which does happen in real materials. (Though, in real bipolarons the (purely quantum mechanical) spins of the individual polarons are important to stabilizing the bipolaron. The spins form a singlet....) Furthermore, suppose the rubber sheet takes some time to respond to the balls, and takes some time to restore itself to its undeformed state once a ball passes by. You can picture a ball rolling in some direction, leaving behind itself a little groove in the sheet that "fills in" at some rate. This would lower the energy of some other ball if that other ball were traveling in, say, the exact opposite direction of the first ball. This is a very crude way of thinking about the attractive pairing interaction between electrons in low temperature superconductors.
Finally, suppose the rubber sheet is really stretchy. A ball dropped on the sheet will pull the sheet down so far that it'll look like a little punching bag. Now if you try to tilt the sheet, the sheet will have stretched so tightly that the ball won't want to roll at all. Instead, the little punching bag will hang there at an angle relative to the sheet. Something analogous to this can happen in real materials, too - polarons can self-trap. That is, the charge carrier deforms the local environment so much that it basically digs itself such a deep potential well that it can't move anymore. Chemists have their own name for this, by the way. A molecule that deforms to self-trap an extra electron is a radical anion, and a molecule that deforms to self-trap a hole is a radical cation.
One common example of a quasiparticle is the polaron. When a charge carrier (an electron or hole) is placed into a solid, the surrounding ions can interact with it (e.g., positive ions will be slightly attracted to a negatively charged carrier). The ions can adjust their positions slightly, balancing their interactions with the charge carrier and the forces that hold the ions in their regular places. This adjustment of positions leads to a polarization locally centered on the charge carrier. The combo of the carrier + the surrounding polarization is a polaron. There are "large" and "small" polarons, defined by whether or not the polarization cloud is much larger than the atomic spacing in the material. Polarons are a useful way of thinking about carriers in ionic crystals, materials with "soft" vibrational modes (such as the manganites), and organic semiconductors (very squishy, deformable systems held together by van der Waals rather than covalent bonding).
Not content to let the general relativity fans have all the fun, I can describe this with a ball-rolling-on-a-rubber-sheet analogy. The ball is the charge carrier; the deformation of the rubber sheet is the polarization "cloud". Consider tilting the rubber sheet - this is analogous to applying an electric field to the material. The ball will roll in response to the tilt, but it will be slowed down compared to how it would roll on a hard tilted surface, since it has to put energy into deforming the sheet. In real materials, this shows up as a correction to the effective mass of the charge carrier. All other things being equal, polarons are heavy compared to bare quasiparticles.
We can carry this analogy further. Suppose we have two balls on the rubber sheet. In this classical picture, if the balls are so close together that their sheet deformations touch, the balls will be attracted together and end up in one deformation, held apart by their mutual hard-core repulsion. This is a crude analogy for bipolaron formation, which does happen in real materials. (Though, in real bipolarons the (purely quantum mechanical) spins of the individual polarons are important to stabilizing the bipolaron. The spins form a singlet....) Furthermore, suppose the rubber sheet takes some time to respond to the balls, and takes some time to restore itself to its undeformed state once a ball passes by. You can picture a ball rolling in some direction, leaving behind itself a little groove in the sheet that "fills in" at some rate. This would lower the energy of some other ball if that other ball were traveling in, say, the exact opposite direction of the first ball. This is a very crude way of thinking about the attractive pairing interaction between electrons in low temperature superconductors.
Finally, suppose the rubber sheet is really stretchy. A ball dropped on the sheet will pull the sheet down so far that it'll look like a little punching bag. Now if you try to tilt the sheet, the sheet will have stretched so tightly that the ball won't want to roll at all. Instead, the little punching bag will hang there at an angle relative to the sheet. Something analogous to this can happen in real materials, too - polarons can self-trap. That is, the charge carrier deforms the local environment so much that it basically digs itself such a deep potential well that it can't move anymore. Chemists have their own name for this, by the way. A molecule that deforms to self-trap an extra electron is a radical anion, and a molecule that deforms to self-trap a hole is a radical cation.
Wednesday, January 21, 2009
"Science" and inaugural addresses
Yesterday, as a bunch of us gathered in an office to watch the Inauguration, after President Obama's line about science ("We will restore science to its rightful place...."), I said that I'd bet that was the only time science had been mentioned in an inaugural address. Well, thanks to this impressive website, I now know that I was quite wrong. The word "science" has appeared 22 times in 15 different inaugural addresses. These uses include John Adams back in 1797 (in one of the biggest run-on sentences I've seen since the last time I read a Virginia Woolf novel) encouraging the founding of universities, FDR worrying about science run amok ("For, without [government aid], we had been unable to create those moral controls over the services of science which are necessary to make science a useful servant instead of a ruthless master of mankind."), and Kennedy wanting to use science to thaw US-Soviet relations ("Let both sides seek to invoke the wonders of science instead of its terrors") and forestall nuclear war ("the dark powers of destruction unleashed by science"). Interesting stuff. By the way, I'll save you the trouble of looking. No president has ever said "physics" in an inaugural address.
Thursday, January 15, 2009
Science in the stimulus.
For those interested, here is a link to the executive summary of the (Democratic draft of the House version) of the forthcoming economic stimulus bill. The science portions are easy to find in there, and I like what I see.
Update. The science policy bloggers for Science have an article that basically points to this analysis of the proposed stimulus by the AAAS. The two big questions that come to mind are, (1) will there be sustained support for science to follow up on this investment of resources?; and (2) how will the details work regarding the requirements that the funds be allocated quickly?
Update. The science policy bloggers for Science have an article that basically points to this analysis of the proposed stimulus by the AAAS. The two big questions that come to mind are, (1) will there be sustained support for science to follow up on this investment of resources?; and (2) how will the details work regarding the requirements that the funds be allocated quickly?
Saturday, January 10, 2009
What are quasiparticles?
The word quasiparticle is a term of art that condensed matter physics types throw around quite a bit. What does is it really mean? I'll describe one analogy that may be useful, and then give a more rigorous definition. Suppose you had a bin filled up to some height with rubber balls of uniform size. The lowest energy ("ground") state of this would be the one with the balls pretty much forming a close-packed structure, all stacked up. If you took one ball from somewhere and set it on top of the others, that would cost a little bit of energy, because the ball has some mass acted on by gravity and it takes work to lift it up. This one ball popped up above the rest is not exactly a quasiparticle. Notice that it's not really the same as an isolated ball. It's a bit deformed from interactions with the balls underneath it, since it has weight and the balls are all a little squishy. Similarly, if you took a step back and looked really carefully, you'd see that the balls right under that one have all had to rearrange themselves a little. The whole package (popped-up ball + deformations + rearrangement of the positions of the neighboring balls) is analogous to a quasiparticle, since you can't really have some parts without the others. In condensed matter physics, a fancier scientific definition would be: "a low energy excitation of a system, possessing a set of quantum numbers and/or well-defined expectation values of certain operators (position, charge, momentum, angular momentum, energy) often associated with isolated particles."
More postings soon, but looming deadlines may mean a slow-down.
More postings soon, but looming deadlines may mean a slow-down.
Monday, January 05, 2009
What does it mean for a material to be a "metal"?
Continuing on from my earlier posts about insulators, it's worth thinking about what we mean by a "metallic" state. Colloquially, people have an image of what they think is a metal: a material that is shiny, electrically conducting, and probably relatively ductile and malleable. Let's not discuss the elastic properties at the moment, since their origin is rather subtle. The electrical conduction is what really stands in contrast to insulators, and the shiny surface is a consequence of the electrical conduction at high frequencies (optical, ~ 1015 Hz). (By the way, for those interested in why some metals have color to them, this site has a pretty nice explanation. The short answer: interband transitions alter the absorption at short wavelengths.)
It's important to understand that, from the condensed matter physicist's perspective, there's a big difference between a substance that is merely electrically conductive and one that is a "real" metal. In a real metal, the electrical resistivity decreases as temperature is decreased. There are conduction mechanisms (e.g., ionic conduction in glasses; hopping conduction in doped organic semiconductors) that become much less effective at lower temperatures - those systems are not metals, just moderately conducting at room temperature. Similarly, lightly doped semiconductors aren't metals either; as T approaches 0 they have no mobile charge carriers. It would be nice to be able to find a ground state property that lets us decide whether something is a metal or an insulator rather than worrying about temperature dependences. Fortunately, there is. As discussed here (a nice pdf that I found while learning more about what Peter had written in the comments to the previous post), when placed between capacitor plates at T = 0, a metal develops only a surface charge, while an insulator develops a bulk dielectric polarization (dipole moment per unit volume) throughout itself.
There are different types of metals. Conventional metals are Landau Fermi liquids. The low energy electronic excitations of Fermi liquids are "quasiparticles" that act very much like non-interacting electrons - they have spin-1/2, charge -e, and have a lifetime much longer than h/kBT. In bulk Fermi liquids, electronic excitations can have arbitrarily low energies. The spectrum of these excitations is said to be gapless. The hallmark of Fermi liquids is that they have properties that look much like those we find in undergrad statistical mechanics treatments of noninteracting Fermi gases. For example, their heat capacities vary at low temperatures as T, and their resistivities vary at low temperatures as T2.
There are other metallic states known variously as bad metals or strange metals. The classic example of a bad metal is the normal state of optimally doped high temperature superconductors. These systems have a metallic ground state, but near T = 0, their resistivities vary linearly in T rather than quadratically. This may not seem like a big deal, but it has major implications. It implies that the low energy electronic excitations of these materials are not well described as quasiparticles; they must somehow involve collective excitations of many correlated electrons, and may not have easily intuitive quantum numbers. That is, they're non-Fermi liquids. Trying to understand these systems and their excitations is a major outstanding challenge in condensed matter physics today. It's hard because it involves understanding excitations of a system of many strongly interacting quantum particles, and also because our intuition has been shaped by our classical ideas about simple quasiparticles. By the way, this idea of excitations that are complicated and lack particle-like quantum numbers has come into vogue in high energy physics in the form of "unparticles".
It's important to understand that, from the condensed matter physicist's perspective, there's a big difference between a substance that is merely electrically conductive and one that is a "real" metal. In a real metal, the electrical resistivity decreases as temperature is decreased. There are conduction mechanisms (e.g., ionic conduction in glasses; hopping conduction in doped organic semiconductors) that become much less effective at lower temperatures - those systems are not metals, just moderately conducting at room temperature. Similarly, lightly doped semiconductors aren't metals either; as T approaches 0 they have no mobile charge carriers. It would be nice to be able to find a ground state property that lets us decide whether something is a metal or an insulator rather than worrying about temperature dependences. Fortunately, there is. As discussed here (a nice pdf that I found while learning more about what Peter had written in the comments to the previous post), when placed between capacitor plates at T = 0, a metal develops only a surface charge, while an insulator develops a bulk dielectric polarization (dipole moment per unit volume) throughout itself.
There are different types of metals. Conventional metals are Landau Fermi liquids. The low energy electronic excitations of Fermi liquids are "quasiparticles" that act very much like non-interacting electrons - they have spin-1/2, charge -e, and have a lifetime much longer than h/kBT. In bulk Fermi liquids, electronic excitations can have arbitrarily low energies. The spectrum of these excitations is said to be gapless. The hallmark of Fermi liquids is that they have properties that look much like those we find in undergrad statistical mechanics treatments of noninteracting Fermi gases. For example, their heat capacities vary at low temperatures as T, and their resistivities vary at low temperatures as T2.
There are other metallic states known variously as bad metals or strange metals. The classic example of a bad metal is the normal state of optimally doped high temperature superconductors. These systems have a metallic ground state, but near T = 0, their resistivities vary linearly in T rather than quadratically. This may not seem like a big deal, but it has major implications. It implies that the low energy electronic excitations of these materials are not well described as quasiparticles; they must somehow involve collective excitations of many correlated electrons, and may not have easily intuitive quantum numbers. That is, they're non-Fermi liquids. Trying to understand these systems and their excitations is a major outstanding challenge in condensed matter physics today. It's hard because it involves understanding excitations of a system of many strongly interacting quantum particles, and also because our intuition has been shaped by our classical ideas about simple quasiparticles. By the way, this idea of excitations that are complicated and lack particle-like quantum numbers has come into vogue in high energy physics in the form of "unparticles".
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