Active matter — why does it matter- ▸ -KITP Blackboard Talk by Cristina Marchetti

Metadata

• URL: https://www.youtube.com/watch?v=ZOlVu5TMT1I
• Publisher: Kavli Institute for Theoretical Physics
• Published Date: 2020-05-19

Notes

Summary

Active matter is the study of systems of many active particles, which themselves are particles which (I think) individually break time reversal symmetry via for instance chemical reactions which produce propulsion.
Marchetti discusses some examples of models of active matter, from which you get some interesting behavior.

1. The first model is in 2D Euclidean space, where the active matter is modeled by a navier stokes like differential equation, but with an added sort of "propulsion minus friction" term. This makes it so that the equilibrium states here are the ones where the flow all points in a single direction, with magnitude of velocity dictated by the damping term. This seems like an instance of spontaneous symmetry breaking. And I guess also global time reversal symmetry breaking.
   1. The interesting behavior Marchetti points out here is that, despite the damping, you can get long range "sound wave" like density waves. This is because changing the direction of the whole field doesn't require any energy, and so you can get these waves caused by rotation in direction.
   2. Seems like a non-instance of gapped hamiltonian
2. The second model is the same thing, but on a 2D sphere. In this case, you get a Coriolis type force so that pressure is concentrated near the equator. And apparently it's like a quantum hall effect type state, where you can still get waves, but these fluctuations are now concentrated on the equator and "topologically protected". I didn't fully get this part, but I think it has something to do with the fact that the set of ground states isn't connected by continuous transformations. E.g. I can't go from waves going right, to waves going to the left without energy?

She then goes on to talk about some interesting open questions/directions:

My thoughts

I don't yet have the physics background to really appreciate what's going on in the examples she discusses. But I am starting to put together some pieces maybe. In that I keep seeing all of these same words popping up:

• topologically protected: is this related at all to symmetry protected topological phase?
• quantum hall effect: this seems to refer to when you get some sort of emergent, particle like behavior

Things I'm curious about:

• I just listened to this really interesting podcast FE2.7 - Kelp Worlds- Trophic Cascadia (Part 1), on the ecology of the Aleutian islands; in particular, the interplay between sea otters, sea urchins, and kelp (as well as orcas, whales, and others), and the kinds of phenomena that can occur when you disturb the ecosystem, especially near the top of the food chain.
  • One particularly interesting tidbit was about the stable state phenomenon that occurs: where when either sea urchins dominate (called an urchin barren) or kelp dominate, these are stable states in the sense that, even as you, say, reintroduce urchins and/or reduce the otter population (urchin preadotrs) in the case of kelp domination, it takes a lot of force (like an activation energy, reaching a critical threshold) before the kelp domination might be broken.
  • I guess this also sounds like a breaking of time reversal symmetry, in that you get a smooth transition to the kelp domination, but then a sharp transition on the way back.
  • I wonder if one might be able to come up with some nice active matter models to study these ecological systems?
• Related to resilience more generally: a vague curiosity about how maybe this topologically protected notion might be behind other instances of biological resilience (like resilience in the brain, the immune system, etc...)
• Can one model brains as active matter?
• how do hamiltonians describing emergent phenomena arise:
  • Have people studied instances where, in addition to the local dynamics, you get global terms as well? For instance, things like, preventing total flow in a given direction from exceeding a certain magnitude.

Other related things

• self induced phase transition

Highlights

program called symmetry, thermodynamic and topology in active matter.

breaks trs, time reversal symmetry locally, and it does in a way that is sustained and therefore is very different from a system where you apply an external field. So you have charged particles, and you apply an external field. These particles, of course, also an external field, an electric field, say, also based on reversal symmetry, but it does so globally, the same for all the particles. So it's different from these active systems, which are made of components that are driven individually.

focus of this our program has been especially on what we call emerging behavior, that is, the collective behavior of disadvantaged systems.

Phil W. Anderson, more is different article back in 1972

a peculiar type of phase transition, not just non equilibrium ones, but ones that are not tuned by an external parameter, such as temperature or similar, but often are tuned internally by the system itself.

if you have an xy model in two dimensions, there can be no order in equilibrium, meaning you cannot have a state where the spins, on average, all point in the same direction, and the system has nonzero magnetization.

universal scaling characteristics that are the same across all these different systems. Bacteria epithelial cells and so on. And if you want to learn more about this, I refer to a couple of talks we had early on in the program by Francois Joanni and Luca John.

And this is something very closely behaved, very closely related to what in quantum hall systems, to the behavior of electrons in quantum hall systems, and to what gives rise to the quantum hall effect.

And therefore, it turns out to be what's called a topologically protected mode. In fact, you think about the integer quantum hall effect there. What you have is that the conductance of electrons is quantized, is an integer, and cannot be changed by a small perturbation because of this quantization. Similarly, what happens here is that these sound moles actually have a conserved charge, we could call it, which is called the churn number, and cannot be changed, therefore, by continuous deformation, and therefore are protected from coupling and scattering into the bulk.

So these systems, just like charged quantum particle in a magnetic field field, this time, reverse broken fluids, have topologically protected state.

interesting question is, can we actually have emergent chirality from a collection of interacting I chiral objects? So how does chirality emerge as a collective property?

understanding living tissue collection of cells as materials and trying to understand whether we can describe them as liquids, or whether, or when I should say, describe them as liquid or solids

if you have an xy model in two dimensions, there can be no order in equilibrium, meaning you cannot have a state where the spins, on average, all point in the same direction, and the system has nonzero magnetization.Phil W. Anderson, more is different article back in 1972a peculiar type of phase transition, not just non equilibrium ones, but ones that are not tuned by an external parameter, such as temperature or similar, but often are tuned internally by the system itself.
Note: huh???