## Saturday, January 10, 2009

### What are quasiparticles?

The word quasiparticle is a term of art that condensed matter physics types throw around quite a bit. What does is it really mean? I'll describe one analogy that may be useful, and then give a more rigorous definition. Suppose you had a bin filled up to some height with rubber balls of uniform size. The lowest energy ("ground") state of this would be the one with the balls pretty much forming a close-packed structure, all stacked up. If you took one ball from somewhere and set it on top of the others, that would cost a little bit of energy, because the ball has some mass acted on by gravity and it takes work to lift it up. This one ball popped up above the rest is not exactly a quasiparticle. Notice that it's not really the same as an isolated ball. It's a bit deformed from interactions with the balls underneath it, since it has weight and the balls are all a little squishy. Similarly, if you took a step back and looked really carefully, you'd see that the balls right under that one have all had to rearrange themselves a little. The whole package (popped-up ball + deformations + rearrangement of the positions of the neighboring balls) is analogous to a quasiparticle, since you can't really have some parts without the others. In condensed matter physics, a fancier scientific definition would be: "a low energy excitation of a system, possessing a set of quantum numbers and/or well-defined expectation values of certain operators (position, charge, momentum, angular momentum, energy) often associated with isolated particles."

More postings soon, but looming deadlines may mean a slow-down.

Massimo (formerly known as Okham) said...

So, I take it that you don't like the analogy proposed by R. Mattuck in his masterpiece "A guide to Feynman diagrams in the many-body problem" (aka "Feynman diagrams for idiots" :-) in which he compared a particle to a horse and a quasi-particle to a horse surrounded by a dust cloud (he calls it "quasi-horse"). That book is hilarious... er, if you are into this kind of humor, that is...

Doug Natelson said...

I really like Mattuck. It's very good, fun, and moreover, cheap. That one and Goodstein's States of Matter are fantastic Dover books for people who do what we do.

To be honest, I'd forgotten Mattuck's analogy. Now that you bring it up, I actually do have a minor quibble. In his version, the dust cloud that "dresses" the particle is made of, well, dust, which is very different than a horse. In the real system, bare electrons are dressed, at least in part, by other electrons. Hmm. Maybe there's some other livestock-based analogy lurking in there, where one steer affects and is affected by the surrounding herd....

Massimo (formerly known as Okham) said...

I may be wrong but, I don't think that the definition requires that the "dust" consist of the same particles -- or, at least, the terminology "quasi-particle" is utilized in other contexts where the dust is represented by something else.
The first example that comes to my mind is dilute helium mixtures -- in the limit of low he-3 concentration, the he-3 system is a normal Fermi liquid of tunable degeneracy (you simply change its concentration), and in this case quasi-particles (as people in this are call them) are he-3 atoms "dressed" by a he-4 cloud.

Doug Natelson said...

Sorry - imprecise wording on my part. The "dressing" doesn't have to be from the same particles, and your 3He in 4He case is a perfect example of this. Likewise, the Holstein model of polarons, where an electron gets dressed by a lattice distortion to form a composite object, is another.

However, the case that I was thinking about was that of an electron dressed by other electrons, as in Landau Fermi liquid theory, where the Fermi liquid parameters come mostly from e-e effects.

tg said...

A rather canonical example along the line of Massimo would be just the lowest order [in e^2/(hc)] correction to photon's self-energy in QED. At the first order electrons could be thought of as 'dust' and photon as the 'horse'.

If someone insists on giving a condensed matter example one can replace photons by phonons.

Peter Armitage said...

One of the nicest pedagogical introductions to the general idea of quasi-particles is by Sachdev in this Science mag perspective. I use this in my Intro to Cond Matter class.

http://www.sciencemag.org/cgi/content/full/sci;288/5465/475

As explained nicely by Sachdev... The "Landau prescription", when confronted by a many-body state is

1.) Identify the ordering principle of that state. i.e. periodic tranlational symmetry for crystals, a discontinuity in the occupation of single particle states for metals, etc.

2.) Identify a perturbation that disturbs that order. i.e. vibrational motion for a crystal, particle hole excitations for a metal, etc.

Actually Sachdev writes it better than I do....

>let us review the essence of
>Landau's strategy. His starting
>point is the proper identification
>of the quantum "coherence" or
>order in the ground state of the
>system. In the theory of metals,
>the order is that implied by the
>distribution in the occupation
>number of plane wave states of
>electrons--the plane waves with
>small wavevectors are fully
>occupied, but there is an abrupt
>decrease in the average occupation
>number above a certain "Fermi
>wavevector"; in the superfluid
>state of 4He, the order in the
>ground state is the presence of
>the Bose-Einstein condensate--the
>macroscopic occupation of 4He
>atoms in the ground state. Landau
>then proceeds to describe the
>low-energy excited states, and
>hence the finite temperature
>properties, by identifying
>elementary excitations that
>perturb the order of the ground
>state in a fundamental way. These
>excitations can be thought of as
>new, emergent particles (or
>"quasiparticles") that transport
>spin, charge, momentum, and
>energy, and whose mutual
>collisions are described by a
>Boltzmann-like transport equation.
>In metals, the quasiparticles are
>electrons and holes in the
>vicinity of the Fermi wavevector,
>whereas in 4He they are phonon and
>roton excitations.

Ralph said...

It seems to me we might someday regard the entities we now call "elementary particles" as the quasi-particles of some newly-discovered underlying structure. Potentially the only difference between our elementary particles and our quasi-particles is that we can currently see the background situation for one but not for the other.

I understand that there is a large web of evidence and physical constants that tells us today's elementary particles are quite different from quasi-particles. I'm just not convinced we can ever get to the bottom of all this, or that there even is a bottom.

ZT said...

I see you guys are talking about quasi particles and this is great because I am a physics student and I am doing a paper about normal fermi liquids...Landau liquid. Now, I am a bit confused about a concept of a quasi particle and this confusion is not letting me move on. So, if you have an interacting system of particles, it can be in its ground state, right? And there are no qparticles there? But since you say, just as this book I am reading says, that quasiparticle is a particle dressed in a distortion brought about by interaction, then quasiparticle exists even in a ground state? Why do we have to talk about excitations?

Douglas Natelson said...

ZT - I don't know when you asked your question, and it's been five years (!) since the original post, but here's an attempt at an answer. An interacting system of particles of course can have a ground state, in which there are no excitations. The point is, an excitation of that interacting system should look like an excitation of the non-interacting system, dressed by additional perturbations of the non-interacting system. Think of it like the non-interacting system and its excitations are a basis that you can use to describe the interacting system. An elementary excitation of the interacting system has strong overlap with one excitation of the non-interacting system, but it also has some projected component "along" other excitations.