Download Thursday afternoon

Physics 541
A quantum approach to condensed
matter physics
Syracuse students - please put homework from all of you
in one envelope and mail to me no later than Thursday
afternoon.
If you are not ready by that time, then mail your homework
separately.
Mail it to: Prof Philip Taylor
Dept of Physics
CWRU
Cleveland OH 44106-7079
CWRU students - please put your individual homework
in my mail box no later than Thursday afternoon.
Recapitulation of Class 4
Hartree-Fock approximation gives an answer that is worse than
if we just ignored interactions!
Recapitulation of Class 5
To second order in V
Look for approach that could give plasmons
Problem: What operator creates plasma oscillations?
Quasiparticle excitations vs collective excitations
Equation-of-motion approach
Can we find an operator like this for the Coulomb gas?
Can we find an operator like Try
this for the Coulomb gas?
After lots of work:
So this operator is good if q is big, but not if it is small.
Can we find an operator like
this for the Coulomb gas?
doesn’t work
Try the density fluctuation operator
We know that
so we just sum this over all p
Interaction terms cancel, so
still
no
good!
Remember that plasmon energy squared is linear in the coupling
Could it be that
Let’s miss out a few steps and go to the result --
becomes
is really special!
For small q
is really special!
What is happening? Screening!
Small q -- screening possible. Plasmons are relevant excitations
Large q -- screening impossible. Quasiparticles are
relevant excitations
Can this be related to the concept of a dielectric constant?
Terms linear in U can be written as
with
Look at a sample term in Ueff