Saturday, November 30, 2019

What is a liquid?

I wrote recently about phases of matter (and longer ago here).  The phase that tends to get short shrift in the physics curriculum is the liquid, and this is actually a symptom indicating that liquids are not simple things. 

We talk a lot about gases, and they tend to be simple in large part because they are low density systems - the constituents spend the overwhelming majority of their time far apart (compared to the size of the constituents), and therefore tend to interact with each other only very weakly.  We can even look in the ideal limit of infinitesimal particle size and zero interactions, so that the only energy in the problem is the kinetic energy of the particles, and derive the Ideal Gas Law.  

There is no such thing as an Ideal Liquid Law.  That tells you something about the complexity of these systems right there.

A classical liquid is a phase of matter in which the constituent particles have a typical interparticle distance comparable to the particle size, and therefore interact strongly, with both a "hard core repulsion" so that the particles are basically impenetrable, and usually through some kind of short-ranged attraction, either from van der Waals forces and/or longer-ranged/stronger interactions.  The kinetic energy of the particles is sufficiently large that they don't bond rigidly to each other and therefore move past and around each other continuously.  However, the density is so high that you can't even do very well by only worrying about pairs of interacting particles - you have to keep track of three-body, four-body, etc. interactions somehow.    

The very complexity of these strongly interacting collections of particles leads to the emergence of some simplicity at larger scales.  Because the particles are cheek-by-jowl and impenetrable, liquids are about as incompressible as solids.  The lack of tight bonding and enough kinetic energy to keep everyone moving means that, on average and on scales large compared to the particle size, liquids are homogeneous (uniform properties in space) and isotropic (uniform properties in all directions).  When pushed up against solid walls by gravity or other forces, liquids take on the shapes of their containers.  (If the typical kinetic energy per particle can't overcome the steric interactions with the local environment, then particles can get jammed.  Jammed systems act like "rigid" solids.)

Because of the constant interparticle collisions, energy and momentum get passed along readily within liquids, leading to good thermal conduction (the transport of kinetic energy of the particles via microscopic, untraceable amounts we call heat) and viscosity (the transfer of transverse momentum between adjacent rough layers of particles just due to collisions - the fluid analog of friction).  The lack of rigid bonding interactions means that liquids can't resist shear; layers of particles slide past each other.  This means that liquids, like gases, don't have transverse sound waves.   The flow of particles is best described by hydrodynamics, a continuum approach that makes sense on scales much bigger than the particles.   

Quantum liquids are those for which the quantum statistics of the constituents are important to the macroscopic properties.  Liquid helium is one such example.  Physicists have also adopted the term "liquid" to mean any strongly interacting, comparatively incompressible, flow-able system, such as the electrons in a metal ("Fermi liquid").  

Liquids are another example emergence that is deep, profound, and so ubiquitous that people tend to look right past it.  "Liquidity" is a set of properties so well-defined that a small child can tell you whether something is a liquid by looking at a video of it; those properties emerge largely independent of the microscopic details of the constituents and their interactions (water molecules with hydrogen bonds; octane molecules with van der Waals attraction; very hot silica molecules in flowing lava); and none of those properties are obvious if one starts with, say, the Standard Model of particle physics.  


Jacques Distlere said...

"...and none of those properties are obvious if one starts with, say, the Standard Model of particle physics."

Except that the most astonishing liquid to have been discovered in recent decades is the (grossly misnamed) "quark-gluon plasma," an incredibly strongly-interacting quantum liquid which, among its other exotic properties, exhibits the lowest η/s (shear viscosity to entropy density) ratio of any known substance.

Its properties are entirely determined by QCD.

Douglas Natelson said...

Jacques, I think you're making my point for me. Are the properties of the QGP an obvious consequence of the QCD lagrangian? I'm no expert, but I think the answer is "no". The collective properties of the strongly interacting quantum fluid are remarkable and non-obvious, as emergent, collective effects tend to be.

Jacques Distler said...

Nothing is obvious in QCD. Not the masses of hadrons (or even the existence of hadrons) nor the properties of the QGP.

QCD is an inherently strongly-coupled theory, so staring at the QCD Lagrangian gives you very little clue about just about anything in QCD. (Well, to be fair, QCD is asymptotically-free, which means that the high-energy scattering of individual quarks and gluons is well-described by perturbation theory using the QCD Lagrangian. But that's it.)

By that standard, the proton is every bit as mysterious as the quark-gluon plasma.

If we relax our standard from "obvious consequence of the QCD lagrangian" to "calculable in Lattice QCD," then yes, static properties of hadrons are (with various caveats) understandable in way that the transport properties of the QGP are not.

But I think that's more ascribable as a defect of Lattice QCD. AdS/CFT gives a qualitative understanding of transport properties in the QGP, even though it's pretty useless for understanding static properties of hadrons.

Jacques Distler said...

I guess that my point is that this distinction between "obvious from the Lagrangian" few-body interactions and "emergent" many-body physics — a distinction that is second-nature to anyone in condensed matter physics — is absent in theories, like QCD, which are strongly-coupled from the get-go.

I probably wouldn't have complained, if you had used the phrase "Quantum Electrodynamics" (where I think the distinction is justified) instead "the Standard Model" (where I think it's not).

Anonymous said...


Douglas Natelson said...

Fixed, thanks.

Anonymous said...

Hi Doug, anything exciting happening these days in condensed matter physics?

Douglas Natelson said...

Anon, there's lots of stuff going on. Twisted 2D material structures are a hot-bed of activity, as are ultrathin magnetic materials. Both of these fall within an overarching heightened level of action about correlations and topology. Topologically nontrivial materials (including photonic, magnonic, and phononic as well as electronic) are all the rage, both for fundamental interest and the prospect of devices for information processing. There is a clear ramp-up of funding support for all things connected to quantum information science - platforms for quantum information processing, communications, and sensing. There continues to be a lot of interest in spin-orbit effects, spin transport, and other aspects of magnetism. Superconductivity is always active (more recent results on cuprates, pnictides, and other nontrivial systems like ruthenates, UTe2, low density systems like SrTiO3). Nonequilibrium and driven systems are very busy as well ("time crystals", nonequilibrium correlated transitions), and recent interest in "neuromorphic" computing has led to a ramp up of action in resistive switching/metal-insulator transition systems.

Pizza Perusing Physicist said...

Personally I'd be very interested in hearing a post on that last one (neuromorphic computing and the rise of metal-insulator transition / resistive switching).