Coming attractions and short items

Here are a few items of interest. 

I am planning to write a couple of posts about why solids are rigid, and in the course of thinking about this, I made a couple of discoveries:

• When you google "why are solids rigid?", you find a large number of websites that all have exactly the same wording:  "Solids are rigid because the intermolecular forces of attraction that are present in solids are very strong. The constituent particles of solids cannot move from their positions they can only vibrate from their mean positions."  Note that this is (1) not correct, and (2) also not much of an answer.  It seems that the wording is popular because it's an answer that has appeared on the IIT entrance examinations in India.
• I came across an absolutely wonderful paper by Victor Weisskopf, "Of Atoms, Mountains, and Stars:  A Study in Qualitative Physics", Science 187, 605-612 (1975).  Here is the only link I could find that might be reachable without a subscription.  It is a great example of "thinking like a physicist", showing how far one can get by starting from simple ideas and using order-of-magnitude estimates.  This seems like something that should be required reading of most undergrad physics majors, and more besides.

In politics-of-science news:

• There is an amendment pending in the US Congress on the big annual defense bill that has the potential to penalize US researchers who have received any (presently not well-defined) resources from Chinese talent recruitment efforts.  (Russia, Iran, and North Korea are also mentioned, but they're irrelevant here, since they are not running such programs.)  The amendment would allow the DOD to deny these folks research funding.  The idea seems to be that such people are perceived by some as a risk in terms of taking DOD-relevant knowledge and giving China an economic or strategic benefit.  Many major US research universities have been encouraging closer ties with China and Chinese universities in the last 15 years.  Makes you wonder how many people would be affected.
• The present US administration, according to AP, is apparently about to put in place (June 11?) new limitations on Chinese graduate student visas, for those working in STEM (and especially in fields mentioned explicitly in the Chinese government's big economic plan).   It would make relevant student visas one year in duration.  Given that the current visa renewal process can already barely keep up with the demand, it seems like this could become an enormous headache.  I could go on at length about why I think this is a bad idea.  Given that it's just AP that is reporting this so far, perhaps it won't happen or will be more narrowly construed.  We'll see.

What is tunneling?

I first learned about quantum tunneling from science fiction, specifically a short story by Larry Niven.  The idea is often tossed out there as one of those "quantum is weird and almost magical!" concepts.  It is surely far from our daily experience.

Imagine a car of mass \(m\) rolling along a road toward a small hill.  Let’s make the car and the road ideal – we’re not going to worry about friction or drag from the air or anything like that.   You know from everyday experience that the car will roll up the hill and slow down.  This ideal car’s total energy is conserved, and it has (conventionally) two pieces, the kinetic energy \(p^2/2m\) (where \(p\) is the momentum; here I’m leaving out the rotational contribution of the tires), and the gravitational potential energy, \(mgz\), where \(g\) is the gravitational acceleration and \(z\) is the height of the center of mass above some reference level.  As the car goes up, so does its potential energy, meaning its kinetic energy has to fall.  When the kinetic energy hits zero, the car stops momentarily before starting to roll backward down the hill.  The spot where the car stops is called a classical turning point.  Without some additional contribution to the energy, you won’t ever find the car on the other side of that hill, because the shaded region is “classically forbidden”.  We’d either have to sacrifice conservation of energy, or the car would have to have negative kinetic energy to exist in the forbidden region.  Since the kinetic piece is proportional to \(p^2\), to have negative kinetic energy would require \(p\) to be imaginary (!).

However, we know that the car is really a quantum object, built out of a huge number (more than \(10^27\)) other quantum objects.  The spatial locations of quantum objects can be described with “wavefunctions”, and you need to know a couple of things about these to get a feel for tunneling.  For the ideal case of a free particle with a definite momentum, the wavefunction really looks like a wave with a wavelength \(h/p\), where \(h\) is Planck’s constant.  Because a wave extends throughout all space, the probability of finding the ideal free particle anywhere is equal, in agreement with the oft-quoted uncertainty principle. 

Here’s the essential piece of physics:  In a classically forbidden region, the wavefunction decays exponentially with distance (mathematically equivalent to the wave having an imaginary wavelength), but it can’t change abruptly.  That means that if you solve the problem of a quantum particle incident on a finite (in energy and spatial size) barrier from one side, there is always some probability that the particle will be found on the far side of the classically forbidden region.  

This means that it’s technically possible for the car to “tunnel” through the hillside and end up on the downslope.  I would not recommend this as a transportation strategy, though, because that’s incredibly unlikely.  The more massive the particle, and the more forbidden the region (that is, the more negative the classical kinetic energy of the particle would have to be in the barrier), the faster the exponential decay of the probability of getting through.  For a 1000 kg car trying to tunnel through a 10 cm high speed bump 1 m long, the probability is around exp(-2.7e20).  That kind of number is why quantum tunneling is not an obvious part of your daily existence.  For something much less massive, like an electron, the tunneling probability from, say, a metal tip to a metal surface decays by around a factor of \(e^2\) for every 0.1 nm of tip-surface distance separation.  It’s that exponential sensitivity to geometry that makes scanning tunneling microscopy possible.

However, quantum tunneling is very much a part of your life.  Protons can tunnel through the repulsion of their positive charges to bind to each other – that’s what powers the sun.  Electrons routinely tunnel in zillions of chemical reactions going on in your body right now, as well as in the photosynthesis process that drives most plant life. 

On a more technological note, tunneling is a key ingredient in the physics of flash memory.  Flash is based on field-effect transistors, and as I described the other day, transistors are switched on or off depending on the voltage applied to a gate electrode.  Flash storage uses transistors with a “floating gate”, a conductive island surrounded by insulating material, some kind of glassy oxide.  Charge can be parked on that gate or removed from it, and depending on the amount of charge there, the underlying transistor channel is either conductive or not.   How does charge get on or off the island?  By a flavor of tunneling called field emission.  The insulator around the floating gate functions as a potential energy barrier for electrons.  If a big electric field is applied via some other electrodes, the barrier’s shape is distorted, allowing electrons to tunnel through it efficiently.  This is a tricky aspect of flash design.  The barrier has to be high/thick enough that charge stuck on the floating gate can stay there a very long time - you wouldn’t want the bits in your SSD or your flash drive losing their status on the timescale of months, right? - but ideally tunable enough that the data can be rewritten quickly, with low error rates, at low voltages.

Physics around you: the field-effect transistor

While dark matter and quantum gravity routinely get enormous play in the media, you are surrounded every day by physics that enables near miraculous technology.  Paramount among these is the field-effect transistor (FET).   That wikipedia link is actually pretty good, btw.  While I've written before about specific issues regarding FETs (here, here, here), I hadn't said much about the general device.

The idea of the FET is to use a third electrode, a gate, to control the flow of current through a channel between two other electrodes, the source and drain.  The electric field from the gate controls the mobile charge in the channel - this is the field effect.   You can imagine doing this in vacuum, with a hot filament to be a source of electrons, a second electrode (at a positive voltage relative to the source) to collect the electrons, and an intervening grid as the gate.  Implementing this in the solid state was proposed more than once (Lilienfeld,  Heil) before it was done successfully. 

Where is the physics?  There is a ton of physics involved in how these systems actually work.  For example, it's all well and good to talk about "free" electrons moving around in solids in analogy to electrons flying in space in a vacuum tube, but it's far from obvious that you should be able to do this.   Solids are built out of atoms and are inherently quantum mechanical, with particular allowed energies and electronic states picked out by quantum mechanics and symmetries.  The fact that allowed electronic states in periodic solids ("Bloch waves") resemble "free" electron states (plane waves, in the quantum context) is very deep and comes from the underlying symmetry of the material.  [Note that you can have transistors even when the charge carriers should be treated as hopping from site to site - that's how many organic FETs work.]  It's the Pauli principle that allows us to worry only about the highest energy electronic states and not have to worry about, e.g., the electrons deep down in the ion cores of the atoms in the material.  Still, you do have to make sure there aren't a bunch of electronic states at energies where you don't want them - these the are traps and surface states that made FETs hard to get working.  The combo of the Pauli principle and electrostatic screening is why we can largely ignore the electron-electron repulsion in the materials, but still use the gate electrode's electric field to affect the channel.  FETs have also been great tools for learning new physics, as in the quantum Hall effect. 

What's the big deal?  When you have a switch that is either open or closed, it's easy to realize that you can do binary-based computing with a bunch of them.  The integrated manufacturing of the FET has changed the world.  It's one of the few examples of a truly disruptive technology in the last 100 years.  The device you're using to read this probably contains several billion (!) transistors, and they pretty much all work, for years at a time.  FETs are the underlying technology for both regular and flash memory.  FETs are what drive the pixels in the flat panel display you're viewing.  Truly, they are so ubiquitous that they've become invisible.

"Active learning" or "research-based teaching" in upper level courses

This past spring Carl Wieman came to Rice's Center for Teaching Excellence, to give us this talk, about improving science pedadogy.  (This video shows a very similar talk given at UC Riverside.) He is very passionate about this, and argues strongly that making teaching more of an active, inquiry-based or research-question-based experience is generally a big improvement over traditional lecture.  I've written previously that I think this is a complicated issue. 

Does anyone in my readership have experience applying this approach to upper-level courses?  For a specific question relevant to my own teaching, have any of you taught or taken a statistical physics course presented in this mode?  I gather that PHYS 403 at UBC and PHYS 170 at Stanford have been done this way.  I'd be interested in learning about how that was implemented and how it worked - please feel free to post in comments or email me.

(Now that the semester is over and some of my reviewing responsibilities are more under control, the frequency of posting should go back up.)

Short items

A couple of points of interest:

• Bill Gates apparently turned down an offer from the Trump administration to be presidential science advisor.  It's unclear if this was a serious offer or an off-hand remark.   Either way it underscores what a trivialized and minimal role OSTP appears to be playing in the present administration.  It's a fact of modern existence that there are many intersections between public policy and the need for technical understanding of scientific issues (in the broad sense that includes engineering).   While an engaged and highly functional OSTP doesn't guarantee good policy (because science is only one of many factors that drive decision-making), the US is doing itself a disservice by running a skeleton crew in that office.  
• Phil Anderson has posted a document (not a paper submitted for publication anywhere, but more of an essay) on the arxiv with the sombre title, "Four last conjectures".  These concern: (1) the true ground state of solids made of atoms that are hard-core bosons, suggesting that at sufficiently low temperatures one could have "non-classical rotational inertia" - not exactly a supersolid, but similar in spirit; (2) a discussion of a liquid phase of (magnetic) vortices in superconductors in the context of heat transport; (3) an exposition of his take on high temperature superconductivity (the "hidden Fermi liquid"), where one can have non-Fermi-liquid scattering rates for longitudinal resistivity, yet Fermi liquid-like scattering rates for scattering in the Hall effect; and (4) a speculation about an alternative explanation (that, in my view, seems ill-conceived) for the accelerating expansion of the universe.   The document is vintage Anderson, and there's a melancholy subtext given that he's 94 years old and is clearly conscious that he likely won't be with us much longer.
• On a lighter note, a paper (link goes to publicly accessible version) came out a couple of weeks ago explaining how yarn works - that is, how the frictional interactions between a zillion constituent short fibers lead to thread acting like a mechanically robust object.  Here is a nice write-up.