Sunday, February 25, 2024

2024 version: Advice on choosing a graduate school

It's been four years since I posted the previous version of this, so it feels like the time is right for an update.

This is written on the assumption that you have already decided, after careful consideration, that you want to get an advanced degree (in physics, though much of this applies to any other science or engineering discipline).  This might mean that you are thinking about going into academia, or it might mean that you realize such a degree will help prepare you for a higher paying technical job outside academia.  Either way,  I'm not trying to argue the merits of a graduate degree - let's take it as given that this is what you want to do.

  • It's ok at the applicant stage not to know exactly what research area you want to be your focus.  While some prospective grad students are completely sure of their interests, that's more the exception than the rule.  I do think it's good to have narrowed things down a bit, though.  If a school asks for your area of interest from among some palette of choices, try to pick one (rather than going with "undecided").  We all know that this represents a best estimate, not a rigid commitment.
  • If you get the opportunity to visit a school, you should go.  A visit gives you a chance to see a place, get a subconscious sense of the environment (a "gut" reaction), and most importantly, an opportunity to talk to current graduate students.  Always talk to current graduate students if you get the chance - they're the ones who really know the score.  A professor should always be able to make their work sound interesting, but grad students can tell you what a place is really like.
  • International students may have a very challenging time being able to visit schools in the US, between the expense (many schools can help defray costs a little but cannot afford to pay for airfare for trans-oceanic travel) and visa challenges.  Trying to arrange zoom discussions with people at the school is a possibility, but that can also be challenging.  I understand that this constraint tends to push international students toward making decisions based heavily on reputation rather than up-close information.  
  • Picking an advisor and thesis area are major decisions, but it's important to realize that those decisions do not define you for the whole rest of your career.  I would guess (and if someone had real numbers on this, please post a comment) that the very large majority of science and engineering PhDs end up spending most of their careers working on topics and problems distinct from their theses.  Your eventual employer is most likely going to be paying for your ability to think critically, structure big problems into manageable smaller ones, and knowing how to do research, rather than the particular detailed technical knowledge from your doctoral thesis.  A personal anecdote:  I did my graduate work on the ultralow temperature properties of amorphous insulators.  I no longer work at ultralow temperatures, and I don't study glasses either; nonetheless, I learned a huge amount in grad school about the process of research that I apply all the time.
  • Always go someplace where there is more than one faculty member with whom you might want to work.  Even if you are 100% certain that you want to work with Prof. Smith, and that the feeling is mutual, you never know what could happen, in terms of money, circumstances, etc.  Moreover, in grad school you will learn a lot from your fellow students and other faculty.  An institution with many interesting things happening will be a more stimulating intellectual environment, and that's not a small issue.
  • You should not go to grad school because you're not sure what else to do with yourself.  You should not go into research if you will only be satisfied by a Nobel Prize.  In both of those cases, you are likely to be unhappy during grad school.  
  • I know grad student stipends are low, believe me.  However, it's a bad idea to make a grad school decision based purely on a financial difference of a few hundred or a thousand dollars a year.  Different places have vastly different costs of living - look into this.  Stanford's stipends are profoundly affected by the cost of housing near Palo Alto and are not an expression of generosity.  Pick a place for the right reasons.
  • Likewise, while everyone wants a pleasant environment, picking a grad school largely based on the weather is silly.  
  • Pursue external fellowships if given the opportunity.  It's always nice to have your own money and not be tied strongly to the funding constraints of the faculty, if possible.  (It's been brought to my attention that at some public institutions the kind of health insurance you get can be complicated by such fellowships.  In general, I still think fellowships are very good if you can get them.)
  • Be mindful of how departments and programs are run.  Is the program well organized?  What is a reasonable timetable for progress?  How are advisors selected, and when does that happen?  Who sets the stipends?  What are TA duties and expectations like?  Are there qualifying exams?  Where have graduates of that department gone after the degree?  Are external internships possible/unusual/routine? Know what you're getting into!  Very often, information like this is available now in downloadable graduate program handbooks linked from program webpages.   
  • When talking with a potential advisor, it's good to find out where their previous students have gone and how long a degree typically takes in their group.  What is their work style and expectations?   How is the group structured, in terms of balancing between team work to accomplish goals vs. students having individual projects over which they can have some ownership? 
  • Some advice on what faculty look for in grad students:  Be organized and on-time with things.  Be someone who completes projects (as opposed to getting most of the way there and wanting to move on).  Doctoral research should be a collaboration.  If your advisor suggests trying something and it doesn't work (shocking how that happens sometimes), rather than just coming to group meeting and saying "It didn't work", it's much better all around to be able to say "It didn't work, but I think we should try this instead", or "It didn't work, but I think I might know why", even if you're not sure. 
  • It's fine to try to communicate with professors at all stages of the process.  We'd much rather have you ask questions than the alternative.  If you don't get a quick response to an email, it's almost certainly due to busy-ness, and not a deeply meaningful decision by the faculty member.  For a sense of perspective: I get 50+ emails per day of various kinds not counting all the obvious spam that gets filtered.  

There is no question that far more information is now available to would-be graduate students than at any time in the past.  Use it.  Look at departmental web pages, look at individual faculty member web pages.  Make an informed decision.  Good luck!

Tuesday, February 13, 2024

Continuing Studies course, take 2

A year and a half ago, I mentioned that I was going to teach a course through Rice's Glasscock School of Continuing Studies, trying to give a general audience introduction to some central ideas in condensed matter physics.  Starting in mid-March, I'm doing this again.  Here is a link to the course registration for this synchronous online class.  This course is also intended as a potential continuing education/professional development offering for high school teachers, community college instructors, and other educators, and thanks to the generous support of the NSF, the Glasscock School is able to offer a limited number of full scholarships for educators - apply here by February 27 for consideration.   

(I am aware that the cost of the course is not trivial; at some point in the future I will make the course materials available broadly, and I will be sure to call attention to that at the time.)

Wednesday, February 07, 2024

A couple of links + a thought experiment about spin

A couple of interesting things to read:

  • As someone interested in lost ancient literature and also science, I really liked this news article from Nature about progress in reading scrolls excavated from Herculaneum.  The area around the Bay of Naples was a quite the spot for posh Roman families, and when Vesuvius erupted in 79 CE, whole villas, complete with their libraries of books on papyrus scrolls, were buried and flash-cooked under pyroclastic flows.  Those scrolls now look like lump charcoal, but with modern x-ray techniques (CT scanning using the beam from a synchrotron) plus machine learning, it is now possible to virtually unroll the scrolls and decipher the writing, because the ink has enough x-ray contrast with the carbonized papyrus to be detected.  There is reason to believe that there are more scrolls out there still buried, and there are lots of other books and scrolls out there that are too delicate or damaged to be handled and read the normal way.  It's great to see this approach starting to succeed.
  • I've written about metalenses before - using nanostructured surfaces for precise control of optical wavefronts to make ultrathin optical elements with special properties.  This extended news item from Harvard about this paper is a nice piece of writing.  With techniques now developed to make dielectric metalenses over considerably larger areas (100 mm silica wafers), these funky lenses can now start to be applied to astronomy.  Nifty.
And now the gedanken experiment that I've been noodling on for a bit.  I know what the correct answer must be, but I think this has done a good job at reminding me how what constitutes a measurement is a very subtle issue in quantum mechanics.

Suppose I have a single electron roughly localized at the origin.  It has spin-1/2, meaning that, if there are no other constraints, if I choose to make a measurement of the electron spin along some particular axis, I will find that with 50/50 probability the component of the angular momentum of the electron is \(\pm \hbar/2\) along that axis.  Suppose that I pick a \(z\) axis and do the measurement, finding that the electron is "spin-up" along \(z\).  Because the electron has a magnetic dipole moment, that means that the magnetic field at some distance \(r\) away from the origin should be the field from a magnetic dipole along \(z\).  

Now suppose I make another measurement of the spin, this time along the \(x\) axis.  I have a 50/50 chance of finding the electron spin up/down along \(x\).  After that measurement, the magnetic field at the same location \(r\) away from the origin should be the field from a magnetic dipole along \(x\).  It makes physical sense that the magnetic field at location \(r\) can only "know" that a measurement was done at the origin on a timescale \(r/c\).  (Note:  A truly correct treatment of this situation would seem to require QED, because the spin is entangled with the electromagnetic field via its magnetic moment; likewise one would really need to discuss in detail what it means to measure the spin state at the origin and what it means to measure the magnetic field locally.  Proper descriptions of detectors and measurements are really necessary.)

To highlight how subtle the situation is, suppose the spin at the origin is initially half of an EPR pair, so that it's in a spin singlet with a second spin near Alpha Centauri, so that the total spin of the two is zero.  Now a measurement of \(s_{z}\) at the origin determines the state of \(s_{z}\) at Alpha Centauri, and the magnetic field near that dipole at Alpha Centauri should be consistent with that.  Thinking about all of the subtleties here has been a good exercise for me in remembering how the seemingly simple statements we make when we teach this stuff can be implicitly very complicated.

Saturday, February 03, 2024

Large magnetic fields as a scientific tool

When I was at Berkeley at the beginning of the week to give a seminar, I was fortunate enough to overlap with their departmental physics colloquium by Greg Boebinger, an accomplished scientist who is also an extremely engaging and funny speaker.  Since 2004 he has been the director of the National High Magnetic Field Lab in Tallahassee, Florida, the premier user facility for access to large magnetic fields for scientific research.  He gave a great talk that discussed both the challenges in creating very large magnetic fields and a sampling of the cool science that can be done using these capabilities.

Leaving aside spin for a moment, magnetic fields* in some reference frame are generated by currents of moving charges and changing electric fields, as in Ampère's law, \(\nabla \times \mathbf{B} = \mu_{0}\mathbf{J} + \epsilon_{0}\mu_{0}\partial_{t}\mathbf{E}\), where \(\mathbf{J}\) is the current density.  Because materials have collective responses to magnetic fields, generating within themselves some magnetization (magnetic dipole moment per volume \(\mathbf{M}\)), we can think of the magnetic field as a thermodynamic variable, like pressure.  Just as all kinds of interesting physics can be found by using pressure to tune materials between competing phases (because pressure tunes interatomic spacing, and thus things like the ability of electrons to move from atom to atom, and hence the magnitude of magnetic exchange), a magnetic field can tune materials across phase transitions.  

It's worth remembering some physically relevant scales.  The earth's magnetic field at the surface is around 30-50 microTesla.  The magnetic field at the surface of a rare earth magnet is around 1 Tesla.  The field in a typical MRI machine used for medical imaging is 1.5 or 3 T.  The energy levels for the spin of an electron in a magnetic field are set by the Zeeman effect and shift by an amount around \(\mu_{\mathrm{B}}B\), where \(\mu_{\mathrm{B}}\) is the Bohr magneton, \(9.27 \times 10^{-24}\) J/T.  A 10 T magnetic field, about what you can typically get in an ordinary lab, leads to a Zeeman energy comparable to the thermal energy scale at about 6.7 K, or compared to an electron moving through a voltage of 0.6 mV.   In other words, magnetic fields are weak in that it generally takes a lot of current to generate a big field, and the associated energies are small compared to room temperature (\(k_{\mathrm{B}}T\) at 300 K is equivalent to 26 mV) and the eV scales relevant to chemistry.  Still, consequences can be quite profound, and even weak fields can be very useful with the right techniques. (The magnetic field at the surface of a neutron star can be \(10^{11}\) T, a staggering number in terms of energy density.)

Generating large magnetic fields is a persistent technological challenge.  Superconductors can be great for driving large currents without huge dissipation, but they have their own issues of critical currents and critical fields, and the mechanical forces on the conductors can be very large (see here for a recent review).  The largest steady-state magnetic field that has been achieved with a (high-Tc) superconducting coil combined with a resistive magnet is around 45.5 T (see here as well).  At the Los Alamos outpost of the Magnet Lab, they've achieved non-destructive pulsed fields as large as 101 T (see this video).  A huge limiting factor is the challenge of making joints between superconducting wires, so that the joint itself remains superconducting at the very large currents and fields needed. 

The science that can be done with large fields extends well beyond condensed matter physics.  One example from the talk that I liked:  Remarkable resolution is possible in ion cyclotron resonance mass spectroscopy, so that with a single drop of oil, it is possible to identify the contribution of the many thousands of hydrocarbon molecules in there and "fingerprint" where it came from.  

Fun stuff, and a great example of an investment in technology that would very likely never have been made by private industry alone.

* I know that \(\mathbf{B}\) is technically the magnetic induction or magnetic flux density in SI units, but colloquially everyone calls it the magnetic field, so I'll do the same here.