Understanding Quasi-Particles: Visualizing a Difficult Concept

[Rage]

What is "quasi particles"? Any ways to visualize this concept? I have so many troubles with this :yuck:. Need your help, guys. :blush:

 

[ZapperZ]

What is "quasi particles"? Any ways to visualize this concept? I have so many troubles with this :yuck:. Need your help, guys. :blush:

I'm assuming that you read the postings on the "Electron transmission through a condutor" thread. Not to go back TOO far, let's first of all make it clear where the concept of quasiparticles came from. It came from Landau's treatment of weakly-interacting electrons (or charge carriers) in a conductor. This treatement is the celebrated formulation known as the Fermi Liquid theory, which along with BCS theory, is one of the most successful theory in condensed matter physics. It describes everything from conventional metals, semiconductors, band insulators, and conventional superconductors.

In an electron gas, the Drude model assumes that the electrons within this gas are non-interacting with each other. So it is very much like a classical gas obeying the Kinetic Theory. While this approximation can describe a number of observations such as Ohm's Law in metals, it fails to describe many others. Other than the fact that the electrons experiences a Bloch potential (so they are not entirely free), they also interact with each other via the Coulombic potential. When you have a gazillion electrons interacting with each other, our ability to solve such a system exactly becomes nonexistent.

This is where the Fermi Liquid theory comes in. Landau shows that if the interaction between the electrons are "weak", then we can renormalize all of the interaction that a single electron experience into its "self-energy" (within the QFT formulation). We literally lump all of the interactions into the electron's mass and then treat this new particle as "free". So we end up with a free electron but with a new "effective mass". This new particle is called a quasiparticle. It is a particle that is a result of the renormalized self-interaction incorporated into it. What the Fermi Liquid theory did was to reduce one many-body problem into many one-body problem. We can't solve a many-body problem, but we know how to solve one-body problem.

You didn't say at what level you are at, or if this question is part of your study. If it is, I HIGHLY recommend you get Richard Mattuck's book "A guide to Feynman diagrams in the many-body problem". It is a Dover book, so it doesn't cost an arm and a leg. You'll like his explanation of what a quasiparticle is via his "quasi horse" analogy.

Zz.

 

[Rage]

Thank ZapperZ.

I am reading the book of Mattuck :), I like his "quasi horse" but how about the "life time"?
How can I visualize the life time of a quasi horse?

 

[ZapperZ]

Thank ZapperZ.

I am reading the book of Mattuck :), I like his "quasi horse" but how about the "life time"?
How can I visualize the life time of a quasi horse?

You need to keep in mind that quasiparticles are the renormalized single-particle EXCITATION. These are states above the "vacuum state" or Fermi energy in a fermionic system. When there is no interactions between the electrons, the single-particle states at the Fermi level have infinite lifetime, as in no scattering with other electrons to take them out of that state, or that state is continuously occupied. Turning on the interactions causes excitation into those states above the Fermi energy. Weak scattering causes a finite lifetime, strong scattering, or higher scattering rate will reduce the lifetime, of the quasiparticles.

In the single-particle Green's function, the lifetime is reflected by the imaginary part of the self-energy. Without any scattering (infinite lifetime), the Green's function has a peak in the form of a pole at the quasiparticle energy. So Delta(E) approaches zero and equivalently, Delta(t) approaches infinity. As soon as you have a self-energy term, the peak broadens and the lifetime starts to diminish. The "sharpness" of this peak in the Green's function indicates how well-defined the quasiparticle is.

Moral of the story: the lifetime of a quasiparticle is inversely related to the scattering rate. Larger scattering rate, smaller the lifetime. The lifetime measures how long a quasiparticle can hold it's identity as defined within the Fermi Liquid picture.

Zz.

 

[Gonzolo]

At the risk of stating what you may have known for years, I'll add that "quasi-particle" literally and exactly means "almost a particle" in modern French.

 

[Rage]

Nice inputs guys. Thanks a lot.