Papers and news items

First, some science, clearing out a number of papers and articles that I've been collecting for some time in my far-too-numerous browser tabs:

• I've written before (here) about dimensional analysis and similarity, techniques commonly used in the engineering world that can seem quasi-miraculous at times.  This paper gets into why this approach works, and different categories of physical similarity.  I'd mentioned it when the book came out, but this kind of thinking is also a key component of Anthony Zee's Fly by Night Physics.
• This review article is about fundamental limits in photonics and electromagnetics.  This is a very handy review that I'm going to point my students toward.
• On a lighter note, a colleague pointed me to this collection of (AI-generated) songs related to thermodynamics.    
• Speaking of thermodynamics, here is a recent paper about the thermodynamic description of wealth inequality (treating the flow of money in a physics formalism - see here for a prior discussion.).  Edging closer....  
• There was a nice post on substack about Wojciech Zurek's approach to decoherence in quantum mechanics (quantum darwinism).   Cleanly written.  
• Along these lines, this paper is a survey/guide to issues in quantum foundations and interpretations of quantum mechanics.
• Lastly, Jim Freericks has a new quantum mechanics textbook out (for free!), with the challenging idea of making the subject accessible without calculus or differential equations.  (I'm jealous.  My textbook's UK publisher would not let me use Steve Martin's quote for a chapter epigraph, but Prof. Freericks was able to do it - well played.)

And more news/policy-related items:

• The presidential science advisor and head of OSTP, Michael Kratsios, appeared before the House science committee this week, timed to be coincident with the release of OSTP's new report, "Science: A New Golden Age".  A lot has already been written by many people about this report, which contains a number of actual proposals, some good and others of varying degrees of vagueness/underwear gnomes-level magical thinking.  Two pretty good (in my view) takes on this are this article in ars technica and this policy piece by Cole Donovan (former OSTPer).  It's important to remember:  This is a policy document, not something that has automatic impact, no matter how the Wall Street Journal frames its reporting on this.  (Hint:  This document alone does not somehow grant the president the authority or ability to redirect $200B in research funding.  Maybe their reporting on this would be better if they hadn't laid off all their science reporters.)  It's important to pay attention to what is said here, without giving it more oxygen than it deserves.  It's also unclear whether anything OSTP is saying and doing is aligned with what OMB is doing.  Declaring a new golden age of science while simultaneously proposing large cuts in all the science agencies is not exactly a sign of coherence.  Derek Lowe at Science has it right, essentially.  Nature reports that the mid-year budget clawbacks from NSF are apparently going toward some OSTP grand challenge initiative, something about which Kratsios denied all knowledge when talking to the House committee.  
• Holden Thorpe also raises a key point, that universities need to get their collective act together, have a plan about the future of research, and act on it, rather than scrambling for remaining scraps while trying hard not to be seen.  The AAU is important, but hoping that the AAU will accomplish difficult tasks without individual institutions having to take a public stand is unlikely to be successful as strategy.  Organizations like SUFS, UCS, and FAS are pushing the agenda; universities need to decide how they want to play this.
• The first round of DOE Genesis Mission awards were announced this week in DC as well.  
• SpaceX had a pretty successful test flight of their huge rocket, culminating with unexpectedly soft-landing the second stage ("Starship") in the Indian Ocean.  If they really can get this working at the level of reliability and reusability they've done with the Falcon 9, it truly would be game-changing for large-scale payload to orbit.  (Data centers in space still make no sense btw.)
• This week was also a big one in the world of mathematics, with an AI tool (Claude Fable) being used to find a counterexample to the previously outstanding Jacobian Conjecture.  Here is a write-up by Fields medalist Terence Tao, and here is a discussion among other mathematicians.  That wasn't alone.  Here (link to x) is a counterexample being found to a conjecture in graph theory, and it approaches "proof by intimidation" - the human basically harasses and bullies the AI tool into the solution without contributing any intellectual argument.  It seems like it's only a matter of time before some major theoretical physics result gets generated by these tools, though it's important to note that many physics problems are NP-hard/just not integrable.  AI tools are impressive, especially since they're trained on the entire corpus of technical literature, but they are not miraculous:  Claude can't somehow factor large numbers efficiently, or exactly solve the many-electron interacting Hamiltonian for the Hubbard model, because those are truly difficult problems.  Update:  Here are Terence Tao’s slides about AI and the future of mathematics.  As usual, these are excellent.

A brief serious note about mental health and well-being

I've been blogging for 21 years now (!!), and over that time I've had a wide variety of comments on here, but there have been a couple of anonymous ones in the last few weeks that really worried me.  It's the internet, so you can't readily tell when someone is trolling, but these made me concerned for the safety and emotional state of the commenter.   Just remember, there is always someone to talk to who is ready to listen, and we're all better with you than without you.  The 988 hotline (https://988lifeline.org/) is available 24/7/365, free and confidential.  Please take care.

A few optics/metamaterials highlights from META 2026

This past week I attended META 2026, the 16th International Conference on Metamaterials, Photonic Crystals and Plasmonics, at Trinity College, Dublin.  This was the first time I've ever gone to this conference, which has grown from somewhat blurry beginnings to a ~ 900+ person annual event.  Here are a few scientific highlights:

• Metasurfaces, built up from spatial arrays of dielectric (or sometimes semiconductor or plasmonic) resonators called "meta-atoms", have matured into very impressive, versatile tools.  In her plenary talk, Ruwen Peng from Nanjing showcased different approaches, combining angularly rotated meta-atoms ("Pencharatnam-Berry") and size-modulated meta-atoms.  The result can produce polarization-entangled photon beams, entangle photon spin and orbital angular momentum for quantum key distribution, and do full entanglement distribution over many channels.  Similarly, Federico Capasso gave a very impressive talk about the progress in the field, from visible wavelength flat optics ten years ago to compact platforms for sophisticated quantum tomography.
• Nikolay Zheludev gave a great overview about combining measurements + machine learning estimators (e.g., here) to achieve effective optical resolution far better than conventional limits.  This can be used to make optics-base estimates of nanowire lateral displacements down to the 100 pm level, for example.  Rather than looking at the flow of energy in an optical imaging system, one can look at the flow of Fisher information regarding the object being imaged.
• There were a series of talks throughout the meeting about chirality of optical scattering, what this means, and what it can lead to (including enantiomer-selective imaging and chemistry).  Note that it's important to distinguish between intrinsic chirality (e.g., the object scattering the light has a real structural handedness), extrinsic chirality (the object scattering the light is not chiral, but the experimental arrangement to do and measure the scattering introduces chirality into the measurement), and chirality in the fields themselves (think swirling Poynting vectors locally) that don't necessarily extend to the far field.  There are some neat probes of local effects, like this use of local polymerization.
• Roman Quidant gave a talk about metalenses that are also optomechanical structures (e.g., use a pump beam to excite mechanical deformation of the metalens to steer the focus of a probe beam).  This lets you do some pretty neat things, like control the sign of optical forces by dynamically tuning the relative importance of momentum transfer (pushing objects with light by direct momentum kick from photons) and polarization forces (the classical optical tweezer situation where polarizable objects "seek" regions of high intensity).  This can enable feedback control to do optical cooling of trapped, levitated particles, potentially down to the quantum level.
• Alessandra Boltasseva presented a variety of recent advances, including a look at how plasmonic ceramics like TiN and HfN have properties that can be dramatically tuned as their thickness gets down to the few-unit-cell level, a regime she and collaborators term "transdimensional" (to distinguish from atomically thin 2D van der Waals materials).  The possibility of Wigner crystallization in such systems is exciting, though disorder is a likely complication.  

• 

  A 4-channel wavelength division multiplexer
  made from etched Si3N4, from this paper.

  Jeremy Baumberg talked about building metamaterials out of molecularly-spaced nanoparticles, and how this has opened up real opportunities for chemical sensing based on surface-enhanced Raman and infrared absorption, as in this example.  Neat stuff.
• There were multiple talks about metasurfaces for nonlinear optics, including one by Igal Brener on cool ways to use GaAs metasurfaces to produce entangled photon pairs via bound states in the continuum.  
• Likewise, there were a number of presentations about inverse design, where computational tools are used to produce very funky looking structures which can act as, e.g., multichannel routers of optical signals.  Jelena Vuckovic presented an overview of this, showing how it can be done at scale to produce a chip that acts as a 1 TB/s optical router.  Structures produced this way always seem to me like some kind of eldritch geometry out of HP Lovecraft (see figure), but they work.  
  

As always, apologies to those whose work I didn't mention above; my note-taking was pretty uneven.

(I am trying to strike a balance between talking and educating people about science, which is basically the point of this blog, and keeping people informed/voicing some of my personal opinions about the crisis in the US research ecosystem (arguably the most consequential challenge facing US researchers today, with long-term implications that will be felt for many years).  There is still very exciting work being done in nanoscience, the physics of materials, etc. - we are just facing a future where if current trends continue the major advances may increasingly happen outside the US.)

Bad to worse at NSF? (July 2026 edition)

When I wrote this post last month, I really did not want it to be first in a series.

The inciting incident to write that post was a news article in Science reporting that there have been draconian ~ 30% cuts in present fiscal year budgets within the NSF.  Program officers were instructed to keep this confidential and not talk about it with PIs.  The rumor was that this funding would go to support the TIP directorate and its activities, particularly the "X-Labs".  

Now Dan Garisto has broken this story in Nature. For some, this is behind a paywall, so let me hit the highlights.

• "NSF staff members — who asked to remain anonymous out of fear of retaliation — and an internal NSF ledger seen by Nature suggest that the NSF plans to claw back around US$500 million that has already been distributed to grant-making divisions. "
• "Several NSF staff members told Nature that at least some of the funds will be funnelled to another project, a brainchild of the White House OSTP."
• "Even though programme officers have less to spend than they had expected, those who spoke to Nature are unsure how many new grants will make it out the door. “They could make it through if the process is allowed to work without interference or interruption,” one staff member says. But most of “the process is now a black box and unpredictable”. "
• "NSF staff members estimate that if the withdrawals are finalized, hundreds more proposals that have been recommended for funding across the engineering, computer and information science and engineering, and maths and physical science directorates would need to be sent back to programme officers for revision. Some proposals would be held until a later date when funds are available. Others would have their budgets reduced, and some would simply be declined."
• "Staff members say that they are frustrated by the planned diversion of funds and the lack of communication about the agency’s spending. “We don’t know where the money’s going or what’s going on,” says one staff member. Programme officers are not allowed to pass on what they know to researchers. “We cannot communicate to the community at all. We’re forbidden.”"

Basically, this reporting confirms the unprecedented mid-fiscal-year cuts; confirms that there is zero transparency about this with the community and even within the agency; and reveals that the funds are apparently being diverted to some mysterious OSTP project.  

To get a sense of scale, consider a typical program within MPS, with an annual budget of around X dollars.  About 20% or more of those funds are "mortgaged", set aside for ongoing already-funded projects, leaving 0.8X dollars for new awards.  Now, however, there is a 30% cut in the middle of the fiscal year, so the resources now available for new awards are 0.7X-0.2X = 0.5X.  The number of new awards therefore has to be cut by 37.5% relative to last year.   

This is a huge deviation from what Congress appropriated, seemingly being steered at the direction of the White House.  Will Congress care, or will the majority just give this power to the executive branch?  Is anyone going to disclose what the mystery project is?  Is any major national media outlet going to report on this?

I will post more science soon, I promise, and I hope that I don't have more posts in this series.

OMB proposed rule changes - act now

For non-US folks, feel free to skip. 

For US folks:  The Office of Management and Budget, which for much of its history has been a comparatively uncontroversial element of the executive branch, has set rules and guidelines for how many executive-branch agencies conduct business and interact with, e.g., universities.  For the purposes of how the research ecosystem operates, the most relevant is OMB's "Uniform Guidance" about how grants and contracts work.  Periodically these rules are updated for various reasons, including the goals and policies of the presidential administration.  The standard way this works is that the proposed changes are published in the Federal Register; there is a public comment period; OMB makes revisions and then publishes the new rules.  In principle, Congress can act to override or prevent rule changes, but without the agreement of the President, this is an extremely challenging path.

OMB has proposed sweeping changes to the Uniform Guidance, summarized here.  These proposed rule changes are huge deviations from previous practice.  For example, they would have all final grant decisions made by political appointees or hires of the executive branch (rather than, e.g., agency subject matter experts); grants could be cancelled at any time for essentially any reason (completely undefined insufficient support of the president's priorities), with no appeal process; international collaborations would be severely curtailed. That's just three for starters.  Note that this would also go beyond just the public research enterprise - it would allow the executive branch to cancel funding for things like bridges, roads, schools, agriculture, etc. for undefined political reasons.  It would be a huge transfer of power from Congress to the presidency.  Here is another summary by the AAU.  Here is an editorial essay from ars technica.  

The public comment period on this runs until July 13.  Here is a link where you can make a comment.  Here is a guide for how to be effective at this from Stand Up for Science.  The APS has a tool for helping people to comment about specific aspects of the rule changes.  It is also a good idea to contact congressional delegations (representatives, senators).  

It's important to have a clear public record about the proposed changes.  They may try to implement these regardless, but if so, there will be a continued fight over this in Congress and through the courts.  

Some science/tech items - scrolls, nanostacks, and beyond

 Some brief science and technology items heading into the weekend:

• IBM has reported making prototype chips for the "0.7 nm node".   As always, one should not interpret that size scale literally, since the effective diameter of a single silicon atom is around 0.2 nm.  The basic building block of their architecture here is the nanostack, which is a limiting case, somewhat 3D-integrated version of their nanosheet "gate all around" field effect transistors.  The fact that these structures can be made at this scale, reliably and en masse, is just phenomenal.  
   

  

  
  
  
  
• I'd written previously about the Vesuvius Challenge, the attempt to use a combination of x-ray tomographic imaging and machine learning to read the carbonized ancient Roman scrolls found in a villa in Herculaneum, where they had been buried by the pyroclastic flow from the eruption in 79CE.  Well, they've managed to read a complete scroll - here's the preprint.  Very cool, and the hope is that among those scrolls might be books believed lost to history.
• At the beginning of the month, Microsoft unveiled the next iteration of their approach to implementing topological qubits based on superconductor/semiconductor hybrid devices, as described here.  The relevant preprint is this one.  Some reporting on this is here.  This week, Nature published a comment on the prior work as well as the reply.  
• There has been an explosion of research in recent years about trying to use electromagnetic cavities to tune the physical properties of condensed matter systems.  I'd discussed this here.  In the last couple of weeks, this preprint appeared, reporting that placing few-layer NbSe2 in an appropriate (THz) cavity can increase the superconducting transition temperature from 3.02 K to 3.41 K.  A 13% increase in \(T_{\mathrm{c}}\) is certainly interesting.
• The incoming president of the National Academy of Sciences has a nice statement in Science.  The key passage for me:  "By its charter, the Academy is nonpartisan and neither a progressive organization nor a conservative one. It is a scientific body that follows the evidence wherever it leads, even when the destination might be unwelcome. In heated and polarized discourse, it is the Academy’s obligation to be the most careful and trustworthy voice. But rigorous science that arrives too late, or speaks too quietly, serves no one."  

Bad to worse at NSF? (June 2026 edition)

This is a US research ecosystem post.  Feel free to skip if this isn't your cup of tea.

I'm showing my internet age in thinking that the right image to put at the top of this post is either the Drudge Report emergency light icon or an animated Star Trek "red alert" sign.

As you may be aware, NSF spending is incredibly low this year.  How low is "low"?  Check out this graph from grant-witness.  

This is a funding trajectory that has not been seen since the 1970s.  Now, because of budget uncertainties and disruptions last year, there was a big burst of activity late in FY25, and eventually the NSF did end up spending about what it was budgeted.  I spoke with one program officer at NSF last month who said that they fully intended to get there again this year, even if it meant he didn't have a vacation until September.  

A lot of people had looked at the trajectory above and worried that we are headed toward some kind of very bad outcome.  For example, if NSF is underspent by $3B by August, whether because of direct OMB opposition or because the award office at NSF is told by political leadership not to make awards, then it might be nearly impossible for NSF to spend its budget, at which point there could be a pocket rescission.  Basically, the executive branch has wanted to enact 50+% cuts to NSF; Congressional appropriators have said "no", but the executive branch may be trying to get their cuts anyway.  This would a terrible precedent.  If it happened you might expect Congress to be upset that their appropriations were being ignored.  There would likely be lawsuits.

Today, however, this story broke in Science.  Supposedly, there are going to be broad cuts to many parts of the NSF, at the level of 20-30% in the present fiscal year, despite the fact that the NSF budget is only down 3% from last year and there is statutory language in the appropriation bill saying that no directorate could be cut by more than 5%.  

The article basically says that it is likely that the funds are going to support the X-Labs effort run out of the TIP directorate.  What is an X-Lab?  I have some inkling because I attended the webinar about the present solicitation a couple of weeks ago.

The idea of X-Labs comes from proposals like this.  The basic premise is (1) The present system holds back innovation for some and we need to be more flexible and entrepreneurial.  (2) We could bring together teams of people who could be in a position to do something transformative, with definite technology applications, but whose work is at an early stage such that it's too low a technology readiness level to attract VC/angel investors who could support a startup, or is too far off from deployment to be partnered with industry as in the long running SBIR/STTR program.  Thus, this team of people would form an X-Lab, where the key investment (say $50M/yr for 3-5 years, in a milestone-driven contracting method) would come from NSF/TIP.   This is not a priori crazy - multiple other groups have looked at non-profit startups as a way to fund science.  The program was announced at a level of $150M/yr for ten years.  (The Science article implies that those in charge want a lot more money now than was in the TIPS appropriation plan for this year.  Here is a claim that this is not true, which would make the cuts even harder to understand.)

One big catch:  The way the X-Labs are being implemented seems pretty inflexible.  An X-Lab has to be its own entirely independent ("autonomous") entity (rather like a company or non-profit), not a subsidiary or an operating unit of a company or university.  Any senior personnel involved are required to be 100% full-time associated with the X-Lab.  That means that anyone doing this from a company or national lab would have to quit their previous job or go on a complete leave of some kind.  Anyone doing this from a university would have to resign their faculty position or go on a complete leave of some kind.  Issues like IP and benefits/health insurance seem nontrivial and not worked out.  Given the current uncertainties with everything associated with the NSF, this is quite a proposition for established researchers to undertake.  

So, here we are, with reporting that there will be large cuts across the NSF, regardless of what the appropriations said.  Anyone with first-hand knowledge who wants to chime in, please weigh in in the comments, or drop me a line (presumably from a non-NSF email address).  

As bad as this is, the part of the article that truly angered me was this:

Program managers would normally rush to inform potential and current grantees about such dramatic changes. But the memo tells program managers to keep their mouths shut. “This information is highly confidential,” it reads. “Please do not communicate anything to PIs [principal investigators].”

Really?

You know this is not supported by the actual program officers, because this "highly confidential" information was almost immediately sent to a reporter.  Daylight is a great disinfectant.  Public pressure and Congressional pushing forced NSF leadership to relent on the plan to destroy the Ocean Observatories Initiative.  Maybe making this budget cutting known can focus attention on this, rather than having drastically reduced NSF research funding be a fait accompli.

What is weak localization?

A few days ago I wrote about localization, where waves in a medium can become trapped due to interference by scattering off disorder.  This is an extremely general phenomenon that applies to light, sound, and electronic waves in solids.  

Now I want to write about a phenomenon that is specific to electrons (or at least wavepackets that carry electronic charge, if we want to be very general).  Rather than the completely general arguments about conductivity scaling, now we are going to consider particular sets of trajectories in the weak scattering limit.  

We can define "weak" scattering here in terms of the ratio of the mean free path \(\ell\), the typical distance a wavepacket of electrons travels between being redirected by elastic scattering off disorder (vacancies, impurities, surfaces, grain boundaries), and the Fermi wavelength of the electrons, \(\lambda_{\mathrm{F}}\).  If \(\ell/\lambda_{\mathrm{F}} \gg 1\), then the scattering is weak.  (If you have some measurement that allows you to calculate that ratio for a given system and you find instead that you get \(\ell/\lambda_{\mathrm{F}} \ll 1\), then the disorder is so strong that the model of propagating electronic waves really fails and you have to worry about conduction by something like thermally assisted hopping between localized states.)

Electron wavepackets scattering around
a loop trajectory clockwise (red) or 
counterclockwise (blue).  Gray circles
are scattering sites.  Magnetic field \(B\)
is shown pointing out of the page.

In weak localization, as initially explored here, we consider electronic wavepackets bopping through a disordered environment, as shown.  There are many possible trajectories for the electrons, and bouncing off disorder (symbolized here as gray circles) leads to a shift in the phase of the waves as well as a direction change, but it's all deterministic and reversible.  An electron can bounce around a particular loop trajectory from defect to defect in two ways, clockwise or counterclockwise.  The reversibility means that whatever phase the wavepacket racks up going clockwise, it would accumulate the same phase if it went counterclockwise.  This means that there is constructive interference from the loop trajectories for the electron to end up back where it started - that tends to localize the electrons.  Each particular loop trajectory has its own amount of accumulated phase, but all of them have this "constructive interference for back-scattering" issue.

How can we tell this is really going on?  We can turn on a magnetic field \(\mathbf{B} = \nabla \times \mathbf{A}\) that threads flux through the loops.  As I described here, the propagating electrons then pick up an additional phase \(\delta \varphi = (q/\hbar)\int \mathbf{A}\cdot d\mathbf{r}\) as they go along a trajectory.  This means that the clockwise and counterclockwise versions of the loop trajectories are now offset in phase by an amount proportional to the magnetic flux through the loop and in general no longer interfere constructively for back-scattering.   

How large of loops do we need to consider?  Because of inelastic interactions with other electrons, lattice vibrations, etc., the phase of the electronic waves gets scrambled on a characteristic coherence timescale \(\tau_{\phi}\), and a corresponding coherence length scale \(L_{\phi} = \sqrt{D \tau_{\phi}}\), where \(D\) is the diffusion constant for the electrons.  (See here.)

The result of all this is a positive magnetoconductance (equivalently a negative magnetoresistance), since applying the magnetic field suppresses the back-scattering.  The magnetic field scale over which the zero-field conductance dip gets suppressed is on the order of \(B_{c} \sim (h/e)/L_{\phi}^{2}\), though the detailed functional form of \(\delta \sigma (B)\) depends on the relative size of \(L_{\phi}\) and the sample dimensions.  (See here for a key reference if you want details.) Weak localization is one of the main techniques used to infer coherence properties of metals and semiconductors.  A classic review by Gerd Bergmann is here.  Note that this is also closely related to the physics of universal conductance fluctuations.

(One additional point for experts.  I hadn't mentioned spin or spin-orbit coupling.  It turns out that in the strong spin-orbit coupling limit (\(\tau_{\mathrm{so}} \ll \tau_{\phi}\)), the accumulated phases for the time-reversed loop trajectories are no longer of the same sign, but instead are of opposite signs.  The result is destructive interference for back-scattering, and therefore a negative magnetoconductance and "weak antilocalization" (WAL), where the analytic expressions for WAL differ from the WL forms by a factor of -1/2.)

What is localization?

Physicists love simplifying idealizations, and this is especially true in the physics of materials.  The simplest decent model for metals, for example, is the ideal Fermi gas, where we neglect the existence of atoms entirely and just model the electrons as noninteracting particles in some box.  One step up from there, the Sommerfeld model, assumes that the electrons are in a perfectly periodic crystal lattice.  In both cases, the standard semiclassical approach treats the electrons as waves but basically ignores quantum interference.  

Real conductors have defects that break the lattice periodicity, like vacancies, interstitials, impurities, grain boundaries, surfaces and interfaces, etc.  It's natural to wonder, are there major consequences to this "disorder"?  Common sense suggests that sufficiently minor or dilute disorder can't be too important.  Sure, once you break the lattice symmetry, the electronic wavefunctions can't be exactly Bloch waves anymore, but if only one atom out of 10 billion is out of place, how big a deal can it be?

In the late 1970s, a number of theorists were thinking about this problem, and they came up with some impressive insights about the role of disorder, leading to the concept of localization.  The key point to consider is whether the wavefunctions in the presence of disorder are delocalized (extending "to infinity", like plane waves or Bloch waves), or whether they are localized (decaying exponentially away from some origin region where their magnitude is large).  This idea can apply to wavefunctions for electrons, but it can also apply to other kinds of waves, including electromagnetic waves in inhomogeneous dielectric media (think light bouncing around in a cloud).  

Update:  As Andrew Millis pointed out to me, the genesis of this key idea came earlier, from Phil Anderson in this 1957 paper, "Absence of Diffusion in Certain Random Lattices".  Into the 1960s, Sir Nevill Mott introduced the idea of the "mobility edge" - that in a disordered system, the electronic states in the middle of a band are delocalized, but there is an energy threshold at the band edge beyond which the electronic states are localized.  

A major result that came out of the resurgence of this thinking in the 1970s was the scaling theory of localization.  That link points to some excellent lecture notes and a couple of youtube videos by Piet Brouwer for people interested in a more technical explanation.  Intuitively, if the electronic states are exponentially localized, then making a block of material bigger should lead to the conductance of that material dropping exponentially.  Alternately, if the electronic states are delocalized, making a hunk of material larger should generally increase its conductance.  (Think about a piece of copper wire.  Now double both the length and the diameter of the wire.  The conductance \(= \sigma (\pi d^2)/(4L)\) has doubled.)  

Let's call \(g(L) = G(L)/(e^2/h)\) the (dimensionless) conductance of some hunk of material of size \(L\).  The question is, if you increase \(L\), what happens to \(g\)?  There is a scaling function \(\beta(g) \equiv d \ln g/d \ln L\) that describes this.  If \(\beta(g)\) is positive, then the system is metallic.  If \(\beta(g)\) is negative, then the system is insulating in the large size limit, a situation called strong localization.  The technical bit is figuring out what \(\beta(g)\) looks like.   (This scaling idea had many contributors, including most famously people like Anderson and Thouless)  

Remarkably, in this famous paper, the conclusion is that in 2D and 1D, any disorder at all makes \(\beta(g)\) negative.  Thus the surprising conclusion is that, for this model (with no interactions), in principle there are no 2D or 1D metals.  (The distance scale over which the conductance decays with increasing size is the "localization length", \(\xi\), and it could be very long.  That's why seeing metal-like conduction in cm-scale gated graphene or 2D electron gas samples isn't surprising or necessarily inconsistent with this.  There are many subtleties here.)  In 3D, the situation depends on the actual magnitude of \(g\), where if \(g\) starts too small, the system runs away toward localization as system size is increased.

This idea, that interference of scattered waves from disorder can lead to exponentially confined waves, is called Anderson Localization.  This is generic to waves in disordered media, as in this famous paper where it was demonstrated for light.  By the way, you can think of localization of light as an effective cavity that confines the radiation via disorder scattering, an idea which in turn led to the random laser.  Just earlier this year, people successfully demonstrated 3D Anderson localization of ultrasound.

I used google gemini to code up a toy model of Anderson localization (of light) in HTML5, where the disorder is in the form of a spatially varying index of refraction. (I used periodic boundary conditions.) If the disorder is weak (5 in toy units), all the energy dumped into the middle of the space spreads out roughly equally to fill the whole region.  However, if the disorder is strong (50 in toy units), the energy of the waves is localized near the origin for long simulation times.  Here is the model.  (No deep claims of strict accuracy here; this was quick and dirty.  To really see localization in this small play area, we'd need to \(\xi\) to be small compared to the size of the region because of the periodic boundary conditions.)

The ideas here have had a very long reach, and I'll likely write more about related physics soon.

Thermometry at the mK scale, revisited

It's been almost a decade since I last wrote about this topic, and a preprint on the arXiv this week is a good jumping off point for more discussion.

Thermometers are devices that allow us to take some physical observable and infer temperature.  I wrote about the nature of temperature 17 years ago (!!!) in a way that did not completely satisfy me or most of my readers, so maybe I should take another crack at it.  Temperature is a statistically emergent quantity (it doesn't make sense to talk about the temperature of a single particle in isolation) that tells us whether there will be a net flow of energy when a system we care about is brought into contact (able to exchange energy via microscopic degrees of freedom that we aren't tracking, like jiggling of atoms bumping into each other or emission/absorption of radiated photons) with some other system.  Temperature is closely related to the energy stored in the microscopic degrees of freedom of a system.  Our definition of \(T\) is such that there will be a spontaneous, net, averaged flow of energy from hot (a high \(T\) system) to cold (a low \(T\) system).  Two systems in contact at the same \(T\) will still exchange energy microscopically, but on average there will be no net flow, and in the absence of other complications, these systems are said to be in thermal equilibrium.

Measuring temperature is serious business with a fascinating history.  The kelvin is, as of 2019 (see, told you it was time to revisit this), defined by using the fundamental definitions of the kilogram, the meter, and the second, and by declaring that Boltzmann's constant \(k_{\mathrm{B}}\) is exactly 1.380 649 ×10⁻²³ J/K or equivalently kg m²/s²K.   In practice, there are fixed, measurable reference points that help make sure temperatures are calibrated.  For example, the triple point of water is a standard reference point at 273.16 K.  In total, there are two internationally agreed temperature scales, ITS-90 (pdf) and PLTS-2000 (pdf), that include a total of 21 reference points spanning from 0.9 mK to 1357.77 K.  

It's extremely helpful to have primary thermometers, where the physics involved in some measurable quantity are so well known that it is possible to analyze a measurement and directly pull out \(T\) based only on the data and known fundamental and numerical constants.  The preprint linked at the top of this post does an extremely careful comparison of two nanostructure-based approaches.  

Adapted from Fig. 1 from here.

A Coulomb blockade thermometer consists of a series of tiny metal/insulator/metal junctions.  The energy required to move a single electron across one such junction is proportional to \(e^2/C\), where \(C\) is the capacitance of the junction structure.  When the temperature is low, that charging energy scale can exceed the thermal energy scale, \(k_{\mathrm{B}}T\), so that the conductance \(dI/dV\) of the junction near zero applied voltage is suppressed compared to its high voltage and high temperature value.   If temperature is very low, conductance is suppressed all the way to zero, and that is Coulomb blockade.  If instead you have an array of identical junctions in series, and the temperature isn't too low, there is a perturbative suppression of conductance at zero bias. Remarkably, in this regime the shape of \(dI/dV\) as a function of \(V\) is universal, independent of details, and for an array of \(N\) junctions in series, its width is \(5.44 N k_{\mathrm{B}}T/e\). (top panel of figure) 

In a single tunnel junction, it is possible to measure Johnson-Nyquist noise, the current (voltage) fluctuations that take place across the device due to thermally driven motion of the electrons in equilibrium, and the charge shot noise, the fluctuations due to the statistical variations in the arrival times of the electrons.  The theoretical expression for the noise as a function of bias voltage is known (Eq. (2) in the paper).  (bottom panel of figure).

The authors find that the two thermometric approaches are quantitatively consistent to better than 2.5% between 20 mK and 235 mK, and the biggest uncertainty comes from knowing the effective bandwidth of the noise measurement.  This is a characteristically careful, clean work from this Finnish group, who are world experts in the field.  

NAS "State of Science" 2026 address

I watched the webcast of the NAS State of Science address by outgoing NAS president Dr. Marcia McNutt.  (I did not watch the panel discussion afterward, so sorry if I missed critical pieces.)  A few thoughts on this:

• The intro music was a very classy baroque string quartet.  Hard not to think of this scene from Titanic.
• 
  The main theme was about ways to revitalize US science, and there were six main points that she wanted to emphasize, each with examples of relevant projects underway, ways to measure success, and the consequences of failure.  That's fine, and I'll relay them below with some comments, but first an overall impression:  This was largely an exercise in avoiding talking about the elephant in the room, the overt hostility toward and the attempted wanton dismantling of much of the publicly funded US research ecosystem by the executive branch.  I'm unfortunately not surprised that this was largely brushed over, given the position of the Academies (see here).  As the saying goes, I'm not mad, I'm just disappointed.  The realization that the National Academies leadership do not feel empowered to have a frank discussion about this publicly has been depressing.
• Dr. McNutt mentioned that in her previous address, she had pointed out the US vulnerability in STEM by being so reliant on international talent, and that now that other countries are heavily investing in research, the US STEM research world needs to do a better job getting US citizens in the workforce.  That's all true, but leaving out how the government leadership is explicitly trying to curtain international scholars and international collaboration seems like quite an omission.
• She mentioned in passing that industrial research in the US in the 1950s was tiny, nothing compared to the fraction of R&D it is today.  Is that actually correct?  I mean, that was the heyday of Bell Labs, IBM, GE, Westinghouse, and big research labs at companies like Ford and GM.  Much has been written about this.  
• The first big point was the need for improved relationships between universities and industry, and some examples of ways to encourage this, including relatively simple policy changes like making it easier for faculty and others to take leaves in industry.  Certainly it would be broadly good for the US research ecosystem to have more diverse forms of support, and as I've written before, major industrial sectors with lots of capital rely in the long term on trained people. 
• The second point was the need to realign the academic reward system, so that industrial/entrepreneurial/coalition-building activities are incentivized, rather than rewarding on lone-wolf PIs. That's fine, and honestly I think it's already happening to some large degree at major research universities. 
• The third point was meeting the needs of the STEM workforce, though increased interactions with industry (including, e.g., prospective industrial employers helping to define dissertation topics), co-op efforts, some training in businessy aspects (note:  the Sloan Foundation was pushing this 25 years ago.).  This is all laudable to try, but I don't see how any of this actually addresses the issue of fewer STEM workforce participation from US citizens, which is quite complicated.
• The fourth point was the need to reduce regulatory burden.  Sure, we all want to reduce bureaucratic BS.  I have to say, though, that it was genuinely baffling to me that the most Dr. McNutt had to say about the threatened OMB rule changes (apart from a passing mention early on) is that they would increase bureaucracy.  That isn't even in the top 15 problems raised by those changes.  Remember, the default position of those pushing those rules is that academics are fundamentally untrustworthy and poor stewards of public resources.  
• Fifth was the need for automated/self-driving labs.  I agree completely that advanced degree training should not be driven by the need for cheap labor to do tedious lab tasks (e.g. a zillion cell cultures or chemical syntheses).  Overall this was pretty innocuous.
• Sixth, Dr. McNutt emphasized the need to take on big challenges - researchers need to be bold and not play it safe, and peer review can be inherently biased toward incrementalism.  She gave examples of large privately endowed institutes as enabling such work (MBARI, the Allen Institute).  Apparently STAC will be proposing new multi-agency science and technology "breakthrough funds".  The argument in favor of public investment in science in this section sounded rote rather than heartfelt.  If anything, I thought knocking peer review right now at a time when OMB wants to ignore it at their pleasure was a weird position to take.

To be clear:  I don't think any of the ideas highlighted in the speech are actually bad (necessarily).  It just avoided emphasizing that publicly funded research has been incredibly beneficial, and that irreversible harm is being done.  The statement that science agencies "have seen a loss of key personnel" is the worst kind of passive voice garbage.  A hundred thousand technical personnel leaving agencies is not something that just "happened" like the weather.  Being quiet, avoiding confrontation, and only trying to work behind the scenes is not the leadership that is needed now.  (See, I can do passive voice, too.)

I will try to get back to more science posting....

Info gathering: Excellent intro undergrad lab courses and facilities?

Introductory undergraduate labs are a recurring challenge at nearly every university.  Is the purpose to teach students something about how experimental science works (formulating hypotheses, defining measurement needs, setting up equipment, acquiring and analyzing data)?  Is the purpose to emphasize and reinforce specific scientific points from the curriculum?  How structured should they be?  Where are there opportunities for interdisciplinary labs rather than traditional physics/chemistry/biology/earth sciences stovepipes?  

I'm interested in learning about US examples of outstanding introductory physics labs - both in their content/execution, and in the intro lab facilities that my readers consider to be particularly well done.  Please respond in the comments or via email.   I'd really appreciate your thoughts on this, even knowing that my blog readership is a highly biased sample.

(I tried launching a survey about undergrad physics lab instruction five years ago.  I got zero responses.  Hopefully this will be a little more successful.)

The Manhattan Project and public communication

The Manhattan Project was the largest government sponsored research and development project of its time.  Some things worth noting, in light of the present US government attitude toward science:

• It's hard to overstate the role played by immigrant scientists in this story.  Szilard, Einstein, Fermi, Wigner, Teller, von Neumann, and many more.  
• I was trying to remember when the Manhattan Project became publicly known in any detail.  It turns out, within three days of the US bombing of Nagasaki, the US released a tidily written report headlined by Henry DeWolf Smyth on all the essentials, including the administrative story of how the project came to be and was managed.  That report is available in many forms, including this cute version on the internet archive and simple pdf files at DOE and Princeton.  It's an outstanding piece of clear, spare writing.  It almost boggles the mind: Here was a technical topic that the national leadership considered important for the public to understand (!), so a highly readable report was prepared and released basically immediately following public knowledge of the bombs. (!!)
• The National Academies played a pivotal role in this story.  On page 51:  "In the spring of 1941, Briggs, feeling that an impartial review of the problem was desirable, requested [presidential science adviser Vannevar] Bush to appoint a reviewing committee. Bush then formally requested F. B. Jewett, president of the National Academy of Sciences, to appoint such a committee. Jewett complied, appointing A. H. Compton, chairman; W. D. Coolidge, E. O. Lawrence, J. C. Slater, J. H. Van Vleck, and B. Gherardi."  Once upon a time, the national leadership respected the National Academies and trusted them to provide impartial, accurate scientific advice to inform policy.  Somehow I doubt that Frank Baldwin Jewett, president of the NAS at the time, was worried that the government would cut off funding to the Academy if they didn't toe the line.  (As far as I know, no one from the Roosevelt administration was taking “donations” for lucrative government contracts on the bomb, and no one from the cabinet or the Department of War were personally betting for profit on whether it would work, either, but I digress.)

Just some food for thought.

Brief items - news roundup, AI, international issues, good reading

Several items worth reading about as we head into a long weekend in the US.  Starting with news related to funding and other aspects of US government policy:

• US government taking equity stakes in some quantum information sciences companies while investing around $2B (seemingly from the Department of Commerce and the CHIPs Act resources.  (Non-paywall news story here).  This raises a number of thorny issues. 
• Some US funding agencies (NIH, NASA) are enacting restrictions (Science article here, Inside Higher Ed article here) on publishing scientific papers with non-US coauthors.  It's understandable that US funding agencies are concerned about the possibility US funds directly or effectively supporting researchers in foreign countries.  This is not that, though.  Some people making policy seem to be moving toward wanting to ban any co-authorship, but even the agencies seem confused about what they want.
• In a move that will stress out many non-US-citizens in the country, the administration is floating making people leave the US to apply for green cards (PBS article here).  This just was sort of announced yesterday, so I don't know anything about this other than on its face it sounds to me like a terrible idea for multiple reasons.  
• The AAAS is pushing for a Senate hearing on the nominee for NSF director, on the theory that this issue and the nominee at least need to be discussed in a public forum rather than coasting along without a NSB and no end in sight to interim leadership.
• It would seem that some Republican congresspeople are pushing the idea of de-funding the National Academies.  This is directly related to the issues mentioned here.  I think the National Academies should be endowed and thus not so reliant on federal funding; this would be a way to make sure that they always feel secure in delivering reports even if the customer is a part of the government and the conclusions might be something the customer doesn't want to hear.

There was a lot of AI-related news this week:

• 
  There were three papers published in Nature about using AI agents to do science (here, here, and here, with a news and views).  The first two papers are both about drug discovery research, and the third is about using AI to help write scientific software models (also medically related).  It'll be interesting to see how this progresses.  
• One of OpenAI's tools solved an Erdos problem (that's the OpenAI release) by finding a counterexample to a conjecture long thought to be true.  Here is the accompanying paper, which includes commentary by several esteemed mathematicians.  The commentary parts of the paper are very much for non-mathematicians and fascinating to read.  It seems like the AI tools are genuinely good at pulling together complex arguments, and that so far a key advantage they have is an exhaustive familiarity with the full breadth of the literature.
• Unsurprisingly, university graduates are not fans of AI.  This cartoon from this week's New Yorker is topical.  
  

 Additional suggestions that look cool but I haven't had time to actually read:

• Jeremy Levy at Pitt has posted his draft graduate quantum mechanics textbook to the arXiv - looks like an interesting take on the pedagogy of the subject for sure. 
• Dimitrii Makarov at UT Austin has posted a list of critical papers in chemical physics.  
• Samuel Braunstein at York has put up this preprint regarding the Clay Millennium Prize problem about the Navier-Stokes equations.  His main points seem at a quick read to be (1) at finite temperature, fluctuation-dissipation requires some additional noise term be present in the N-S equations; and (2) the N-S equations assume a continuum fluid, so that infinitely-short wavelength excitations are permitted, while for all real fluids wavelengths get cut off at the molecule size.  Basically the issues w/ the N-S equations come from unphysical aspects of the formulation.

What are heavy fermions?

I'm surprised that I haven't written about heavy fermions as a separate post before, so here we go. (It's a break from thinking about science and politics, anyway.)

I've written before about "effective mass" for electronic excitations in solids (wiki page here).  From classical physics, we are used to the idea that inertial mass \(m\) is the ratio between an external force \(\mathbf{F}\) and the acceleration \(\mathbf{a}\) of some object, \(\mathbf{F} = m\mathbf{a}\), which is also the rate of change of momentum, \(d\mathbf{p}/dt\).  Kinetic energy (for a nonrelativistic particle) is \(p^{2}/2m\).  Electrons in crystalline solids "feel" the lattice, so in general their kinetic energy \(\epsilon\) can be a more complicated function of their (crystal) momentum, and we can try do define an effective mass as \(1/m* \equiv d^{2}\epsilon/dp^{2}\).  So, if the kinetic energy is very weakly dependent on \(p\), this corresponds to having a very large effective mass.  TL/DR:  the periodic lattice can strongly alter how an electronic excitation accelerates in the presence of a force from, e.g., an electric field, compared to a free particle.  This isn't too surprising.  

Interestingly, in most semiconductors and metals, \(m*\) for electrons in the conduction band (or holes in the valence band) is not thaaaaat different than the free electron mass \(m_{0}\).  The lightest effective mass I know (leaving aside graphene and other Dirac systems when \(\epsilon\) is approximately linear in \(p\)) is electrons in InSb, about \(0.014 m_{0}\).  Holes tend to be a bit heavier.  Also, \(m*\) in molecular organic semiconductors like pentacene tends to be a bit larger, since hopping from molecule to molecule is comparatively weak.  There are ways to measure effective mass, including cyclotron resonance, electronic transport including Shubnikov-de Haas oscillations, magnetic susceptibility and de Haas/van Alphen oscillations, and specific heat measurements.  The electronic specific heat contribution for a metal is linear in the temperature at low \(T\), and the constant of proportionality includes the density of electronic states at the Fermi energy, which can be written in terms of \(m*\).  I've left out a lot of the complications of real anisotropic materials with complicated band structures, but generally the different measurements give consistent results. 

Therefore, it was a big surprise in 1975 when investigators found a material, CeAl3, in which the heat capacity implied an effective mass tens to hundreds of times larger than \(m_{0}\).  They knew right away that this had something to do with the very localized \(4f\) electrons of the Ce atoms.  Because those electrons are very localized, their energy is almost independent of \(p\), implying a large effective mass.  (Some heavy fermion materials also superconduct at temperatures surprisingly high given their effective masses.)

Heavy fermions, adapted from here.  (a) At high temperatures, the 

conduction  electrons are not well coupled to the unpaired local 4f 

moments.  (b) At low enough temperatures, Kondo scattering

hybridizes the f electrons with the conduction  electrons, boosting 

the carrier density.  (c) The hybridized energy-momentum relation 

is much flatter near the Fermi energy leading to a large effective mass.  

So what's the physics?  I wrote about the Kondo effect here, where "ordinary" conduction electrons scatter in a nontrivial way from local magnetic moments (such as partially filled \(4f\) states), and well below a characteristic temperature \(T_{\mathrm{K}}\), the conduction electrons hybridize with the impurities, screening out the unpaired spin.  In the heavy fermion compounds, instead of impurities, there is a whole crystal lattice of local magnetic moments. At sufficiently low temperatures, thanks to that Kondo scattering process, those otherwise localized electrons hybridize with the conduction electrons, boosting the effective density of charge carriers (see figure) and greatly increasing the effective mass.  See this figure, adapted from excellent lecture notes by Piers Coleman.  

So, two key ingredients for heavy fermions are itinerant conduction electrons and a periodic array of comparatively localized, unpaired electrons that have magnetic moments. It turns out that this combination can also be achieved in moiré lattice materials.  There are no \(f\) electrons here, but the moiré lattice can localize spins.  Apologies for not linking to all the relevant papers, but a couple of key theory results are here, here, and here, and a key experimental result is here.  The tunability of the 2D material-based systems is an excellent feature for digging down into the detailed physics.

Update:  Now some added insight from Prof. Andrew Millis:

Hi Doug:

An addendum to your very nice post on heavy fermions, to draw attention to what I think were important experimental results: Frank Steglich’s 1979  Phys. Rev. Lett. 43, 1892–1896 reporting superconductivity in CeCu2Si2 and Louis Taillefer and Gil Lonzarich’s 1988 determination of the quasiparticle mass and fermi surface in UPt3.

Prior to Steglich’s paper we knew that some rare earth/actinide intermetallics (e.g. CeAl3) had a very enhanced specific heat coefficient at low temperatures and that the entropy implied by  this specific heat was  derived from the magnetic moments of the rare earth ions. But  while it was plausible, there was no direct evidence that this enhanced specific heat was associated with heavy-mass fermions, so the physical relevance of the Kondo lattice concept remained uncertain.

Steglich observed that in CeCu2Si2 the specific heat jump at the superconducting transition (which in BCS theory is basically the same size as the electronic specific heat at Tc) was about as big as the normal state specific heat coefficient, thus showing that the spin entropy had been transmuted into something that could go superconducting. Then (I think in subsequent experiments) Steglich observed that the rest of the superconducting thermodynamics in Cecu2Si2 was also consistent with pairing of heavy mass entities. This, I believe, is what convinced everyone that the spin entropy from the rare earth moments had been converted into heavy mass electrons—in other words, that the lattice Kondo effect was real. 

A few years after this, Louis Taillefer and Gil Lonzarich’s quantum oscillation study of UPt3 (Phys. Rev. Lett. 60, 1570 ) showed indeed that the U-f electrons (which appear as local moments at higher temperatures) were included in the Fermi surface at low T and had heavy masses, providing direct experimental confirmation of the Kondo lattice concept.

Cheers

Andy Millis

NSF, National Science Board, and the politics of staying quiet

As I mentioned previously, the National Science Board was summarily fired on April 25.  The NSB nominally advises the National Science Foundation.  There have been a number of pieces written about this:

• Going back in time to 2022, this essay is interesting to read, about the history of the NSF and the NSB, and the compromises put in place with the administrative structure.  Short version: Initially there was a real tension between the Director (reporting to the President) and the NSB.  Over time, the NSB was made subordinate to the director (1968).  Senatorial confirmation of board members was waived by the Senate in 2011.  
• Many professional organizations issued statements expressing grave concern about this wholesale dismissal of the board.  This AIP news article has a summary.  The CEO of the APS wrote this, the ACS leadership wrote this, the AAS wrote this, etc.
• The presidents of the National Academy of Sciences, National Academy of Engineering, and National Academy of Medicine issued this joint statement.  That has to set some kind of record for blandness, as it somehow does not even mention that the NSB was fired.  I fully understand that the Academies have a number of federal contracts, as one of their key responsibilities is leveraging their membership to do authoritative studies, with federal agencies usually being the customers.  I have no inside knowledge, but it sure looks like they are trying to walk a line of not raising the administration's ire.  (Surely this raises the question:  If it's never acceptable to say anything that might upset the administration, then how can the objectivity of their reports relating to policy ever be trusted?)
• In contrast to the leadership, a lot of Academy membership has signed an open letter to Congress demanding the reinstatement of the board.
• Scientific American has very good reporting on this, including a no-holding-back statement by my colleague Neal Lane.
• Update:  Here is Dan Garisto's reporting in Science about letters sent by House Democrats and by Senate Democrats demanding action on this.  That article includes a statement by the fired head of the NSB, basically saying they were dismissed for defending the NSF budget from OMB.  I'm glad these letters were sent, but without the R majority signing on, I'm not holding my breath.

Meanwhile, the pace of NSF awards continues to be glacial, even compared to last year.  See this plot from Grant Witness. 

We are 7 months into the fiscal year, and obligated dollars are less than half at this time last year, and more like 27% of those at this time in "normal" year.  It's hard to look at that and not wonder whether someone is aiming for a pocket rescission, regardless of what Congress appropriated.  NSF looks like an outlier here, by the way.  As badly hit as NIH has been, their award curves look much closer to last year.

Other related things worth reading:  

• This is a sobering and interesting article about what the author describes as the anti-science movement.
• When is staying quiet effectively giving tacit support to administration policies?  There is an article in The Nation (not readable without a free signup) talking about what they term "Vichy Science".
• Update:  Essay by Holden Thorp, EIC of Science, including a link to a half-hour interview with Tim Snyder, author of "On Tyranny", about how resistance can work.  

Back to science in my next post.