What is a glass?

I want to write about a recently published paper, but to do so on an accessible level, I should really lay some ground work first.

At the primary school level, typically people are taught that there are three states of matter: solid, liquid, and gas.  (Plasma may be introduced as a fourth state sometimes.)  These three states are readily distinguished because they have vastly different mechanical properties.  We now know that there are many more states of matter than just those few, because we have developed ways to look at materials that can see differences that are much more subtle than bulk mechanical response.  As I discussed a little bit here, something is a "solid" if it resists being compressed and sheared; the constituent atoms/molecules are right up against each other, and through their interactions (chemical bonds, "hard-core repulsion"), the material develops internal stresses when it's deformed that oppose the deformation.   

Broadly speaking, there are two kinds of solids, crystals and glasses.  In crystals, which physicists love to study because the math is very pretty, the constituent atoms or molecules are spontaneously arranged in a regular, repeating pattern in space.  This spatial periodicity tends to minimize the interaction energy between the building blocks, so a crystalline structure is typically the lowest energy configuration of the collective bunch of building blocks.  The spatial periodicity is readily detectable because that repeating motif leads to constructive interference for scattering of, e.g., x-rays in particular directions - diffraction spots.  (Most crystalline solids are really polycrystalline, an aggregation of a bunch of distinctly oriented crystal grains with boundaries.)

The problem is, just because a crystalline arrangement is the most energetically favored situation, that doesn't mean that the building blocks can easily get into that arrangement if one starts from a liquid and cools down.   In a glass, there are many, many configurations of building blocks that are local minima in the potential energy of the system, and the energy required to change from one such configuration to another is large compared to what is available thermally.  A paper on this is here.  In ordinary silica glass, the local chemistry between silicon and oxygen is the same as in crystalline quartz, but the silicon and oxygen atoms have gotten hung up somehow, kinetically unable to get to the crystalline configuration.  The glass is mechanically rigid (on typical timescales of interest - glass does not meaningfully flow).  Try to do x-ray diffraction from a glass, and instead of seeing the discrete spots that you would with a crystal, instead you will get a mushy ring indicating an average interparticle distance, like in a liquid (when the building blocks are also right up against each other).  

Figure (credit: Chiara Cammarota, from here): A schematic rugged
energy landscape with a multitude of energy minima,
maxima, and saddles. Arrows denote some of the possible
relaxation pathways. 

A hallmark of glasses is that they have a very broad distribution of relaxation times for structural motions, stretching out to extremely long timescales.  This is a signature of the "energy landscape" for the different configurations, where there are many local minima with a huge distribution of "barrier heights".  This is illustrated in the figure at right (sourced from the Simons Collaboration on Cracking the Glass Problem).  Glasses have been a fascinating physics problem for decades.  They highlight challenges in how to think about thermodynamic equilibrium, while having universality in many of their properties.  Window glass, molecular glasses, many polymers that we encounter - all of these disparate systems are glasses.

Anyons, simulation, and "real" systems

 Quanta magazine this week published an article about two very recent papers, in which different groups performed quantum simulations of anyons, objects that do not follow Bose-Einstein or Fermi-Dirac statistics when they are exchanged.  For so-called Abelian anyons (which I wrote about in the link above), the wavefunction picks up a phase factor \(\exp(i\alpha)\), where \(\alpha\) is not \(\pi\) (as is the case for Fermi-Dirac statistics), nor is it 0 or an integer multiple of \(2\pi\) (which is the case for Bose-Einstein statistics).  Moreover, in both of the new papers (here and here), the scientists used quantum simulators (based on trapped ions in the former, and superconducting qubits in the latter) to create objects that act like nonAbelian anyons.  For nonAbelian anyons, you shouldn't even think in terms of phase factors under exchange - the actual quantum state of the system is changed by the exchange process in a nontrivial way.  That means that the system has a memory of particle exchanges, a property that has led to a lot of interest in trying to encode and manipulate information that way, called braiding, because swapping objects that "remember" their past locations is a bit like braiding yarn - the braided lengths of the yarn strands keep a record of how the yarn ends have been twisted around each other.

Hat tip to Pierre-Luc Dallaire-Demers for the meme.

I haven't read these papers in depth, but the technical achievements seem pretty neat.  The discussion of these papers has also been interesting - see the meme to the right.  Condensed matter physicists have been trying for a long time to look at nonAbelian objects, specifically quasiparticle excitations in certain 2D systems, including particular fractional quantum Hall states, to demonstrate conclusively that these objects exist in nature.  (Full disclosure, my former postdoctoral mentor has done very impressive work on this.)  So, the question arises, does the quantum simulation of nonAbelian anyons "count"?  This issue, the role of quantum simulation, is something that I wrote about last year in the media tizzy about wormholes.  The related issue, are quasiparticles "real", I also wrote about last year. The meme pokes fun at peoples' reactions (and is so narrow in its appeal that the general public truly won't get it).  

Analog simulation goes back a long way.  It is possible to build electronic circuits using op-amps and basic components so that the output voltage obeys desired differential equations, effectively solving some desired problem.  In some sense, the present situation is a bit like this.  Using (somewhat noise, intermediate-scale) quantum computing hardware, the investigators have set up a system that obeys the math of nonAbelian anyons, and they report that they have demonstrated braiding.  Assuming that the technical side holds up, this is impressive and shows that it is possible to implement some version of the math behind this idea of topologically encoding information.  That is not the same, however, as showing that some many-body system's spontaneously occurring excitations obey that math, which is the key scientific question of interest to CM physicists.

(Obligatory nerdy joke:  What is purple and commutes?  An Abelian grape.)  

Michio Kaku and science popularization in the Age of Shamelessness

In some ways, we live in a golden age of science popularization.  There are fantastic publications like Quanta doing tremendous work; platforms like YouTube and podcasts have made it possible for both practicing scientists and science communicators to reach enormous audiences; and it seems that prior generations' efforts (Cosmos, A Brief History of Time, etc.) inspired whole new cohorts of people to both take up science and venture into explaining it to a general audience.  

Science popularization is important - not at the same level as human rights, freedom, food, clothing, and shelter, of course, but important.  I assert that we all benefit when the populace is educated, able to make informed decisions, and understands science and scientific thinking.  Speaking pragmatically, modern civilization relies on a complex, interacting web of technologies, not magic.  The only way to keep that going is for enough people to appreciate that and continue to develop and support the infrastructure and its science and engineering underpinnings.  More philosophically, the scientific understanding of the world is one of humanity's greatest intellectual achievements.  There is amazing, intricate, beautiful science behind everything around us, from the stars in the skies to the weirdness of magnets to the machinery of life, and appreciating even a little of that is good for the soul.

Michio Kaku, once a string theorist (albeit one who has not published a scientific paper in over 20 years), has achieved great fame as a science popularizer.  He has written numerous popular books, increasingly with content far beyond his own actual area of expertise.  He has a weekly radio show and the media love to put him on TV.  For years I've been annoyed that he clearly values attention far beyond accuracy, and he speaks about the most speculative, far-out, unsupported conjectures as if they are established scientific findings.  Kaku has a public platform for which many science communication folks would give an arm an a leg.  He has an audience of millions.  

This is why the his recent appearance on Joe Rogan's podcast is just anger-inducing.   He has the privilege of a large audience and uses it by spewing completely not-even-wrong views about quantum computing (the topic of his latest book), a subject that already has a serious hype problem.  An hour of real research would show him that he is wrong about nearly everything he says in that interview.  Given that he's written a book about the topic, surely he has done at least a little digging around.  All I can conclude is, he doesn't care about being wrong, and is choosing to do so to get exposure and sell books.  I'm not naive, and I know that people do things like that, but I would hope that science popularizers would be better than this.  This feels like the scientific equivalent of the kind of change in discourse highlighted in this comic.  

Update:  Scott Aaronson has a review of Kaku's book up.  This youtube video is an appropriate analogy for his views about the book.