Is a phonon a quasiparticle or a collective excitation?

[emmaphysicshelp229]

TL;DR Summary

Hello, I am trying to self-study non-linear optics for an upcoming internship and am studying quasiparticles.

I read through this blog post talking about quasiparticles that defined the phonon as a quasiparticle but this article on Wikipedia defines phonons as collective excitations.

I gathered quasiparticles are dressed particles - particle at its core whose behaviour is affected by the environment and that collective excitations don't have a particle at its "core" and a reaction.

Thanks!

The Blog Post
The Wikipedia Article

 

[emmaphysicshelp229]

Also if my understanding of quasiparticles and collective excitations is wrong please let me know, I would appreciate any help.

 

[malawi_glenn]

There is no contradiction here. A quasiparticle is just a disturbance of a system that has an energy-momentum relation like that of an "ordinary" particle. A photon for instance, more examples are plasmons and magnons

 

[hutchphd]

I gathered quasiparticles are dressed particles - particle at its core whose behaviour is affected by the environment and that collective excitations don't have a particle at its "core" and a reaction.

Thanks!

The Blog Post
The Wikipedia Article

I don't like this part of your characterization. Ordinary phonons, for instance, are not "dressed" versions of some other particle. They are the eigensolutions to the vibrational Hamiltonian for a crystal lattice (masses on a goemetrical array of springs). Being eigensolutions they have a certain permanence and often provide a useful description of the internal dynamics of solids They resemble photons but differ because they are quantized sound waves and they live in a world with periodicity. Hence they have definite energy but the momentum is trickier.
Just don't put too much credence in the analogy

 

[Hornbein]

I thought quasiparticles and collective excitations were the same thing. But I'm hardly an expert.

 

[hutchphd]

I thought quasiparticles and collective excitations were the same thing.

To my surprise I see all kinds of definitions in the popular literature, some of them contradictory. I guess my working definition is to call the classical objects collective oscillations and the Quantum versions something-ons. There are all kinds of interactions in solids and often the treatment is semiclassical so this distinction is sometimes ambiguous. The quasiparticle may refer to a point object and some collective response. I did not realize this was a can of worms! Again floundering in the semantic sea.

 

[Hornbein]

To my surprise I see all kinds of definitions in the popular literature, some of them contradictory. I guess my working definition is to call the classical objects collective oscillations and the Quantum versions something-ons. There are all kinds of interactions in solids and often the treatment is semiclassical so this distinction is sometimes ambiguous. The quasiparticle may refer to a point object and some collective response. I did not realize this was a can of worms! Again floundering in the semantic sea.

I thought a quasi particle was a localized collective excitation that behaves much like a particle that has momentum. I guess that distinguishes it from a wave, which is also a collective excitation but not as localized. Be warned though that I'm talking over my head. I don't really know this.

 

[hutchphd]

I think there is not a one size fits all definition. The good news is that the maths are definitive uynto themselves.

 

[Vanadium 50]

thought quasiparticles and collective excitations were the same thing. But I'm hardly an expert.

They are.

I thought a quasi particle was a localized collective excitation that behaves much like a particle that has momentum.

"Localized" is not a requirement. It can even get in the way of undertsanding.

Consider the phonon. I can discuss an atom's displacement, or I can discuss a series of displacements with constant momentum. Same phenomena, different description. The latter is the phonon.

 

[vanhees71]

To my surprise I see all kinds of definitions in the popular literature, some of them contradictory. I guess my working definition is to call the classical objects collective oscillations and the Quantum versions something-ons. There are all kinds of interactions in solids and often the treatment is semiclassical so this distinction is sometimes ambiguous. The quasiparticle may refer to a point object and some collective response. I did not realize this was a can of worms! Again floundering in the semantic sea.

Quasiparticles are never interpreted as "point objects" (in the sense of some possibility to "localize" them). Neither are photons, but that's another story.

In a modern way quasiparticles occur as approximate treatments of the Kadanoff-Baym equations, describing fully interacting two-point Green's functions, when the spectral representation of these Green's functions shows very narrow peaks. Then you can approximate the dynamics of the system in terms of quasi-particles in the sense that the Green's functions then are well approximated in terms of modes with a definite energy-momentum (dispersion) relation and thus with creation and annihilation operators similar to "particles". That's why they are named quasiparticles. They are however describing indeed "collective excitations", not something that has localizable states like (massive) particles in the vacuum. Of course this also works for non-relativistic many-body quantum field theory, as applied in solid-state physics.

Phonons are an example, where you can indeed make this more intuitive by starting with a classical description of a crystal as the lattice of point masses bound together by harmonic-oscillator interactions. Classically you get a set of eigenmodes, which you can then quantize simply as a set of non-interacting harmonic oscillators, and this is of course pretty much the same mathematics as a set of particles in vacuum described by the eigenmodes of the fields. Nevertheless from the classical picture it's clear that the modes rather describe a collective vibration of the lattice as a whole.

 

[Demystifier]

The notion of "quasiparticle" is not unique. There are two different meanings of that word in the literature.

Mattuck in the book "A Guide to Feynman Diagrams in the Many-Body Problem"
distinguishes quasiparticles from collective excitations. In his terminology, quasiparticle is an original individual particle together with a cloud of disturbed neighbors. For the sake of intuition, he compares it with a quasihorse, which is a running horse surrounded by the dust (see the picture below). On the other hand, a collective excitation (e.g. phonon) is not centered around an individual particle, so it's not a quasiparticle according to Mattuck.

In a large part of other literature, collective excitations (such as phonons) are considered as a kind of quasiparticles. Even though they are not localized in space, they are particle-like in the sense that they are described by the same mathematical formalism as "ordinary" quantum particles.

See also my http://thphys.irb.hr/wiki/main/images/6/6f/Quasiparticles.pdf

 

[vanhees71]

The latter meaning is more frequent, at least in my scientific community (relativistic heavy-ion theory). It's just an approximation in many-body QFT, where the width of the spectral function, i.e., $A(X,p)=-2 \text{Im} G_{\text{ret}}(X,p)$, where $G_{\text{ret}}(X,p)$ is the Wigner transform of the retarded real-time Green's function in the Schwinger-Keldysh real-time contour formalism is small. Then one can approximate this spectral function by a Dirac-$\delta$ function ("on-shell condition") with the effective mass determined self-consistently via the real part of the corresponding self-energy. This defines the "quasi-particle excitations" of the system.

 

[Demystifier]

The latter meaning is more frequent, at least in my scientific community (relativistic heavy-ion theory).

It's more frequent even in condensed-matter community.