Re: Fermi Liquid?

[Bowman_David/tiger_mpc@tiger.gtc.georgetown.ky.us]

Daniel Finkenthal wrote:
> Can someone please explain to me what a Fermi Liquid is? I was asked this
> question last night at a dinner party by a colleage who is a history prof.
> Needless to say I was befudled, and left asking myself if I really actually
> did get a PhD!

A Fermi liquid is a macroscopic sample of *interacting* spin-1/2 particles
obeying Fermi statistics.  Examples of Fermi liquids are electrons in metals,
liquid ^3He, and nuclear matter (the stuff of neutron stars and heavy nuclei).
The model (first worked out by Landau I believe) of Fermi liquid theory treats
such a system at sufficiently low temperatures that its elementary excitations
can be modeled as single particle-hole pair-type exitations (with Fermi
statistics) whose energies are close to the Fermi surface of a nearly filled
Fermi sea.  These particle-like excitations, called quasi-particles, are taken
to be sufficiently weakly interacting that they act much like a non-
interacting or weakly interacting system of bare particles.  The major effects
of the actual interactions between the actual fermions present are pushed into
such things as a modified exitation spectrum, and effective mass for the
quasi-particles (and holes).  The remaining higher order effects of the
interactions between bare particles are taken, in the model, to be treated
perturbatively as "weak" interactions between the quasi-particles (and the
quasi-holes).  This model allows a treatment of an interacting system of
fermions in terms of a handful of effective parameters--called Fermi liquid
parameters which characterize the quasi-particles (their excitation spectrum,
chemical potential, effective mass, etc.) and their "weak" interactions.
Fermi liquid theory works best when the system's temperature (kT) is "low",
i.e. much less than the Fermi energy for the system.

To learn more about Fermi liquids just consult any good advanced graduate-
level textbook on condensed matter physics.

David Bowman
dbowman@gtc.goergetown.ky.us

P.S.  BTW, how on earth did a history professor learn enough about Fermi
liquids for him/her to know that such a thing exists?