What are parastatistics?

While I could certainly write more about what is going on in the US these days (ahh, trying to dismantle organizations you don't understand), instead I want to briefly highlight a very exciting result from my colleagues, published in Nature last month.  (I almost titled this post "Lies, Damn Lies, and (para)Statistics", but that sounds like I don't like the paper.)

When we teach students about the properties of quantum objects (and about thermodynamics), we often talk about the "statistics" obeyed by indistinguishable particles.  I've written about aspects of this before.  "Statistics" in this sense means, what happens mathematically to the multiparticle quantum state \(|\Psi\rangle\) when two particles are swapped.  If we use the label \(\mathbf{1}\) to mean the set of quantum numbers associated with particle 1, etc., then the question is, how are \(|\Psi(\mathbf{1},\mathbf{2})\rangle\) and \(|\Psi(\mathbf{2},\mathbf{1})\rangle\) related to each other.  We know that probabilities have to be conserved, so \(\langle \Psi(\mathbf{1},\mathbf{2}) | \Psi(\mathbf{1},\mathbf{2})\rangle = \langle \Psi(\mathbf{2},\mathbf{1}) | \Psi(\mathbf{2},\mathbf{1})\rangle\).   

The usual situation is to assume \(|\Psi(\mathbf{2},\mathbf{1})\rangle\ = c |\Psi(\mathbf{1},\mathbf{2})\rangle\), where \(c\) is a complex number of magnitude 1.  If \(c = 1\), which is sort of the "common sense" expectation from classical physics, the particles are bosons, obeying Bose-Einstein stastistics.   If \(c = -1\), the particles are fermions and obey Fermi-Dirac statistics.  In principle, one could have \(c = \exp(i\alpha)\), where \(\alpha\) is some phase angle.  Particles in that general case are called anyons, and I wrote about them here.  Low energy excitations of electrons (fermions) confined in 2D in the presence of a magnetic field can act like anyons, but it seems there can't be anyons in higher dimensions.

 Being imprecise, when particles are "dilute" -- "far" from each other in terms of position and momentum -- we typically don't really need to worry much about what kind of quantum statistics govern the particles.  The distribution function - the average occupancy of a typical single-particle quantum state (labeled by a coordinate \(\mathbf{r}\), a wavevector \(\mathbf{k}\), and a spin \(\mathbf{\sigma}\) as one possibility) - is much less than 1.  When particles are much more dense, though, the quantum statistics matter enormously.  At low temperatures, bosons can all pile into the (single-particle, in the absence of interactions) ground state - that's Bose-Einstein condensation.   In contrast, fermions have to stack up into higher energy states, since FD statistics imply that no two indistinguishable fermions can be in the same state - this is the Pauli Exclusion Principle, and it's basically why solids are solid.  If a gas of particles is at a temperature \(T\) and a chemical potential \(\mu\), then the distribution function and a function of energy \(\epsilon\) for bosons or fermions is given by \(f(\epsilon,\mu,T) = 1/ (\exp((\epsilon-\mu)/k_{\mathrm{B}}T) \pm 1 )\), where the \(+\) sign is the fermion case and the \(-\) sign is the boson case.  

In the paper at hand, the authors take on parastatistics, the question of what happens if, besides spin, there are other "internal degrees of freedom" that are attached to particles described by additional indices that obey different algebras.  As they point out, this is not a new idea, but what they have done here is show that it is possible to have mathematically consistent versions of this that do not trivially reduce to fermions and bosons and can survive in, say, 3 spatial dimensions.  They argue that low energy excitations (quasiparticles) of some quantum spin systems can have these properties.  That's cool but not necessarily surprising - there are quasiparticles in condensed matter systems that are argued to obey a variety of exotic relations originally proposed in the world of high energy theory (Weyl fermions, Majorana fermions, massless Dirac fermions).  They also put forward the possibility that elementary particles could obey these statistics as well.  (Ideas transferring over from condensed matter or AMO physics to high energy is also not a new thing; see the Anderson-Higgs mechanism, and the concept of unparticles, which has connections to condensed matter systems where electronic quasiparticles may not be well defined.)

Fig. 1 from this paper, showing distribution functions for fermions, bosons, 
and more exotic systems studied in the paper.

Interestingly, the authors work out what the distribution function can look like for these exotic particles, as shown here (fig 1 from the paper).  The left panel shows how many particles can be in a single-particle spatial state for fermions (zero or one), bosons (up to \(\infty\)), and funky parastatistics-obeying particles of different types.  The right panel shows the distribution functions for these cases.  I think this is very cool.  When I've taught statistical physics to undergrads, I've told the students that no one has written down a general distribution function for systems like this.  Guess I'll have to revise my statements on this!

Indirect costs + potential unintended consequences

It's been another exciting week where I feel compelled to write about the practice of university-based research in the US.  I've written about "indirect costs" before, but it's been a while.  I will try to get readers caught up on the basics of the university research ecosystem in the US, what indirect costs are, the latest (ahh, the classic Friday evening news dump) from NIH, and what might happen.  (A note up front:  there are federal laws regulating indirect costs, so the move by NIH will very likely face immediate legal challenges.  Update:  And here come the lawsuits.  Update 2:  Here is a useful explanatory video.)  Update 3:  This post is now closed (7:53pm CST 13 Feb).  When we get to the "bulldozer going to pile you lot onto the trash" level of discourse, there is no more useful discussion happening.

How does university-based sponsored technical research work in the US?  Since WWII, but particularly since the 1960s, many US universities conduct a lot of science and engineering research sponsored by US government agencies, foundations, and industry.  By "sponsored", I mean there is a grant or contract between a sponsor and the university that sends funds to the university in exchange for research to be conducted by one or more faculty principal investigators, doctoral students, postdocs, undergrads, staff scientists, etc.  When a PI writes a proposal to a sponsor, a budget is almost always required that spells out how much funding is being requested and how it will be spent.  For example, a proposal could say, we are going to study superconductivity in 2D materials, and the budget (which comes with a budget justification) says, to do this, I need $37000 per year to pay a graduate research assistant for 12 months, plus $12000 per year for graduate student tuition, plus $8000 in for the first year for a special amplifier, plus $10000 to cover materials, supplies, and equipment usage fees.  Those are called direct costs.  

In addition, the budget asks for funds to cover indirect costs.  Indirect costs are meant to cover the facilities and administrative costs that the university will incur doing the research - that includes things like, maintaining the lab building, electricity, air conditioning, IT infrastructure, research accountants to keep track of the expenses and generate financial reports, etc.  Indirect costs are computed as some percentage of some subset of the direct costs (e.g.,  there are no indirect costs charged on grad tuition or pieces of equipment more expensive than $5K).  Indirect cost rates have varied over the years but historically have been negotiated between universities and the federal government.  As I wrote eight years ago, "the magic (ahem) is all hidden away in OMB Circular A21 (wiki about it, pdf of the actual doc).  Universities periodically go through an elaborate negotiation process with the federal government (see here for a description of this regarding MIT), and determine an indirect cost rate for that university."  Rice's indirect cost rate is 56.5% for on-campus fed or industrial sponsored projects.  Off-campus rates are lower (if you're really doing the research at CERN, then logically your university doesn't need as much indirect).  Foundations historically try to negotiate lower indirect cost rates, often arguing that their resources are limited and paying for administration is not what their charters endorse.  The true effective indirect rate for universities is always lower than the stated number because of such negotiations.

PIs are required to submit technical progress reports, and universities are required to submit detailed financial reports, to track these grants.  

This basic framework has been in place for decades, and it has resulted in the growth of research universities, with enormous economic and societal benefit.  Especially as industrial long term research has waned in the US (another screed I have written before), the university research ecosystem has been hugely important in contributing to modern technological society.  We would not have the internet now, for example, if not for federally sponsored research.

Is it ideal?  No.  Are there inefficiencies?  Sure.  Should the whole thing be burned down?  Not in my opinion, no.

"All universities lose money doing research."  This is a quote from my colleague who was provost when I arrived at Rice, and was said to me tongue-in-cheek, but also with more than a grain of truth.  If you look at how much it really takes to run the research apparatus, the funds brought in via indirect costs do not cover those costs.  I have always said that this is a bit like Hollywood accounting - if research was a true financial disaster, universities wouldn't do it.  The fact is that research universities have been willing to subsidize the additional real indirect costs because having thriving research programs brings benefits that are not simple to quantify financially - reputation, star faculty, opportunities for their undergrads that would not exist in the absence of research, potential patent income and startup companies, etc.

Reasonable people can disagree on what is the optimal percentage number for indirect costs.   It's worth noting that the indirect cost rate at Bell Labs back when I was there was something close to 100%.  Think about that.  In a globally elite industrial research environment, with business-level financial pressure to be frugal, the indirect rate was 100%.  

The fact is, if indirect cost rates are set too low, universities really will be faced with existential choices about whether to continue to support sponsored research.  The overall benefits of having research programs will not outweigh the large financial costs of supporting this business.

Congress has made these true indirect costs steadily higher.  Over the last decades, both because it is responsible stewardship and because it's good politics, Congress has passed laws requiring more and more oversight of research expenditures and security.  Compliance with these rules has meant that universities have had to hire more administrators - on financial accounting and reporting, research security, tech transfer and intellectual property, supervisory folks for animal- and human-based research, etc.  Agencies can impose their own requirements as well.  Some large center-type grants from NIH/HHS and DOD require preparation and submission of monthly financial reports. 

What did NIH do yesterday?  NIH put out new guidance (linked above) setting their indirect cost rate to 15% effective this coming Monday.  This applies not just to new grants, but also to awards already underway.  There is also a not very veiled threat in there that says, we have chosen for now not to retroactively go back to the start of current awards and ask for funds (already spent) to be returned to us, but we think we would be justified in doing so.   The NIH twitter feed proudly says that this change will produce an immediate savings to US taxpayers of $4B. 

What does this mean?  What are the intended and possible unintended consequences?  It seems very likely that other agencies will come under immense pressure to make similar changes.  If all agencies do so, and nothing else changes, this will mean tens of millions fewer dollars flowing to typical research universities every year.   If a university has $300M annually in federally sponsored research, then that would be generating under the old rules (assume 55% indirect rate) $194M of direct and $106M of indirect costs.  If the rate is dropped to 15% and the direct costs stay the same at $194M, then that would generate $29M of indirect costs, a net cut to the university of $77M per year.

There will be legal challenges to all of this, I suspect. 

The intended consequences are supposedly to save taxpayer dollars and force universities to streamline their administrative processes.  However, given that Congress and the agencies are unlikely to lessen their reporting and oversight requirements, it's very hard for me to see how there can be some radical reduction in accounting and compliance staffs.  There seems to be a sentiment that this will really teach those wealthy elite universities a lesson, that with their big endowments they should pick up more of the costs.

One unintended consequence:  If this broadly goes through and sticks, universities will want to start making new direct costs.  For a grant like the one I described above, you could imagine asking for $1200 per year for electricity, $1000/yr for IT support, $3000/yr for lab space maintenance, etc.  This will create a ton of work for lawyers, as there will be a fight over what is or is not an allowable direct cost.  This will also create the need for even more accounting types to track all of this.  This is the exact opposite of "streamlined" administrative processes.

A second unintended consequence:  Universities for whom doing research is financially a lot more of a marginal proposition would likely get out of those activities,  if they truly can't recover the costs of operating their offices of research.  This is the opposite of improving the situation and student opportunities at the less elite universities.

From a purely real politik perspective that often appeals to legislators:  Everything that harms the US research enterprise effectively helps adversaries.  The US benefitted enormously after WWII by building a global premier research environment.  Risking that should not be done lightly.

Don't panic.  There is nothing gained by freaking out.  Whatever happens, it will likely be a drawn out process.  It's best to be aware of what's happening, educated about what it means, and deliberate in formulating strategies that will preserve research excellence and capabilities.

(So help me, I really want my next post to be about condensed matter physics or nanoscale science!)

NSF targeted with mass layoffs, acc to Politico; huge cuts in president’s budget request

According to this article at politico, there was an all-hands meeting at NSF today (at least for the engineering directorate) where they were told that there will be staff layoffs of 25-50% over the next two months.

This is an absolute catastrophe if it is accurately reported and comes to pass.  NSF is already understaffed.  This goes far beyond anything involving DEI, and is essentially a declaration that the US is planning to abrogate the federal role in supporting science and engineering research.  

Moreover, I strongly suspect that if this conversation is being had at NSF, it is likely being had at DOE and NIH.

I don't even know how to react to this, beyond encouraging my fellow US citizens to call their representatives and senators and make it clear that this would be an unmitigated disaster.

Update: looks like the presidential budget request will be for a 2/3 cut to the NSF.  Congress often goes against such recommendations, but this is certainly an indicator of what the executive branch seems to want.  

An update, + a paper as a fun distraction

My post last week clearly stimulated some discussion.  I know people don't come here for political news, but as a professional scientist it's hard to ignore the chaotic present situation, so here are some things to read, before I talk about a fun paper:

• Science reports on what is happening with NSF.  The short version: As of Friday afternoon, panels are delayed and funds (salary) are still not accessible for NSF postdoctoral fellows.  Here is NPR's take.
• As of Friday afternoon, there is a new court order that specifically names the agency heads (including the NSF director), saying to disburse already approved funds according to statute.  
• Update: The NSF is now allowing postdocs and GRF recipients to get paid; they are obeying the new court order.  See here and the FAQ specifically.

Looks like on this and a variety of other issues, we will see whether court orders actually compel actions anymore.

Now to distract ourselves with dreams of the future, this paper was published in Nature Photonics, measuring radiation pressure exerted by a laser on a 50 nm thick silicon nitride membrane.  The motivation is a grand one:  using laser-powered light sails to propel interstellar probes up to a decent fraction (say 10% or more) of the velocity of light.  It's easy to sketch out the basic idea on a napkin, and it has been considered seriously for decades (see this 1984 paper).  Imagine a reflective sail say 10 m\(^{2}\) and 100 nm thick.  When photons at normal incidence bounce from a reflective surface, they transfer momentum \(2\hbar \omega/c) normal to the surface.  If the reflective surface is very thin and low mass, and you can bounce enough photons off it, you can get decent accelerations.  Part of the appeal is, this is a spacecraft where you effectively keep the engine (the whopping laser) here at home and don't have to carry it with you.  There are braking schemes so that you could try to slow the craft down when it reaches your favorite target system.

A laser-powered lightsail (image from CalTech)

Of course, actually doing this on a scale where it would be useful faces enormous engineering challenges (beyond building whopping lasers and operating them for years at a time with outstanding collimation and positioning).  Reflection won't be perfect, so there will be heating.  Ideally, you'd want a light sail that passively stabilizes itself in the center of the beam.  In this paper, the investigators implement a clever scheme to measure radiation forces, and they test ideas involving dielectric gratings etched into the sail to generate self-stabilization.   Definitely more fun to think about such futuristic ideas than to read the news.

(An old favorite science fiction story of mine is "The Fourth Profession", by Larry Niven.  The imminent arrival of an alien ship at earth is heralded by the appearance of a bright point in the sky, whose emission turns out to be the highly blue-shifted, reflected spectrum of the sun, bouncing off an incoming alien light sail.  The aliens really need humanity to build them a launching laser to get to their next destination.)

Turbulent times

While I've been absolutely buried under deadlines, it's been a crazy week for US science, and things are unlikely to calm down anytime soon.  As I've written before, I largely try to keep my political views off here, since that's not what people want to read from me, and I want to keep the focus on the amazing physics of materials and nanoscale systems.  (Come on, this is just cool - using light to dynamically change the chirality of crystals?  That's really nifty.)   

Still, it's hard to be silent, even just limiting the discussion to science-related issues.  Changes of presidential administrations always carry a certain amount of perturbation, as the heads of many federal agencies are executive branch appointees who serve at the pleasure of the president.  That said, the past week was exceptional for multiple reasons, including pulling the US out of the WHO as everyone frets about H5N1 bird flu; a highly disruptive freeze of activity within HHS (lots of negative consequences even if it wraps up quickly); and immediate purging of various agency websites of any programs or language related to DEI, with threatened punishment for employees who don't report their colleagues for insufficient reporting of any continued DEI-related activities.

Treating other people with respect, trying to make science (and engineering) welcoming to all, and trying to engage and educate the widest possible population in expanding human knowledge should not be controversial positions.  Saying that we should try to broaden the technical workforce, or that medical trials should involve women and multiple races should not be controversial positions.

What I wrote eight years ago is still true.  It is easier to break things than to build things.  Rash steps very often have lingering unintended consequences.  

Panic is not helpful.  Doomscrolling is not helpful.  Getting through challenging times requires determination, focus, and commitment to not losing one's principles.  

Ok, enough out of me.  Next week (deadlines permitting) I'll be back with some science, because that's what I do.

This week in the arXiv: quantum geometry, fluid momentum "tunneling", and pasta sauce

Three papers caught my eye the other day on the arXiv at the start of the new year:

arXiv:2501.00098 - J. Yu et al., "Quantum geometry in quantum materials" - I hope to write up something about quantum geometry soon, but I wanted to point out this nice review even if I haven't done my legwork yet.  The ultrabrief point:  The single-particle electronic states in crystalline solids may be written as Bloch waves, of the form \(u_{n \mathbf{k}}(\mathbf{r}) \exp(i \mathbf{k} \cdot \mathbf{r})\), where the (crystal) momentum is given by \(\hbar \mathbf{k}\) and \(u_{n \mathbf{k}}\) is a function with the real-space periodicity of the crystal lattice and contains an implicit \(\mathbf{k}\) dependence.  You can get very far in understanding solid-state physics without worrying about this, but it turns out that there are a number of very important phenomena that originate from the oft-neglected \(\mathbf{k}\) dependence of \(u_{n \mathbf{k}}\).  These include the anomalous Hall effect, the (intrinsic) spin Hall effect, the orbital Hall effect, etc.  Basically the \(\mathbf{k}\) dependence of \(u_{n \mathbf{k}}\) in the form of derivatives defines an internal "quantum" geometry of the electronic structure.  This review is a look at the consequences of quantum geometry on things like superconductivity, magnetic excitations, excitons, Chern insulators, etc. in quantum materials.

Fig. 1 from arXiv:2501.01253

arXiv:2501.01253 - B. Coquinot et al., "Momentum tunnelling between nanoscale liquid flows" - In electronic materials there is a phenomenon known as Coulomb drag, in which a current driven through one electronic system (often a 2D electron gas) leads, through Coulomb interactions, to a current in adjacent but otherwise electrically isolated electronic system (say another 2D electron gas separated from the first by a few-nm insulating layer).  This paper argues that there should be a similar-in-spirit phenomenon when a polar liquid (like water) flows on one side of a thin membrane (like one or few-layer graphene, which can support electronic excitations like plasmons) - that this could drive flow of a polar fluid on the other side of the membrane (see figure).  They cast this in the language of momentum tunneling across the membrane, but the point is that it's some inelastic scattering process mediated by excitations in the membrane.  Neat idea.

arXiv:2501.00536 - G. Bartolucci et al., "Phase behavior of Cacio and Pepe sauce" - Cacio e pepe is a wonderful Italian pasta dish with a sauce made from pecorino cheese, pepper, and hot pasta cooking water that contains dissolved starch.  When prepared well, it's incredibly creamy, smooth, and satisfying.  The authors here perform a systematic study of the sauce properties as a function of temperature and starch concentration relative to cheese content, finding the part of parameter space to avoid if you don't want the sauce to "break" (condensing out clumps of cheese-rich material and ruining the sauce texture).  That's cool, but what is impressive is that they are actually able to model the phase stability mathematically and come up with a scientifically justified version of the recipe.  Very fun.