Lecture 1: Linear Response Theory
Last semester in 8.511, we discussed linear response theory in the context of charge screening and
the freefermion polarization function. This theory can be extended to a much wider range of
areas, however, and is a very
Lecture 4
3.1
Thomas-Reiche-Kuhn or f-sum rule
Motivation :- One can derive following equation for one partice energy levels
2m(n 0 )|n|x|0|2 = 1
(3.1)
n
Proof :
1 = i0|[x, p]|0
1=
0|x|nn|p|0 0|p|nn|x|0
n
p = im[H, x]
n|p|0 = im(n 0 )0|x|n
1 =
2m(n 0 )|n
1
Lectures 11: Eect of Disorder on Superconductors
We discuss the eect of disorder on the electromagnetic response of a superconductor
and show that the Meissner eect survives in the presence of disorder. The method we
use is called the exact eigenstate m
Lecture Notes: Theory of Solids I I
Patrick Lee
Massachusetts Institute of Technology
Cambridge, MA
March 2, 2004
Contents
Contents
1 Lecture 2: Scattering and the Correlation Function
1.1 Scattering
1.2 Application: Electron Energy Loss Spectroscopy (EEL
L ecture 3: P roperties of t h e Response Function
In this lecture we will discuss some general properties of the response functions X, and some
uselul relations that they satisfy.
3.1
General Properties of ~ ( q ' , w )
Recall that
wit11 n(F, i) E
I and
Lecture 10: Superconductors With Disorder
Up to now, all of our discussions have centered around superconductivity in an idealized, per
fectly isotropic environment. Because such perfect order is never realized in the real world, it
is important to extend
1
Lectures 11: Eect of Disorder on Superconductors
We discuss the eect of disorder on the electromagnetic response of a superconductor
and show that the Meissner eect survives in the presence of disorder. The method we
use is called the exact eigenstate m
1
Lecture 8: Motts Variable Range Hopping
Mott variable range hopping theory describes the low temperature behavior of the resis
tivity in strongly disordered systems where states are localized. Consider two states located
a distance R apart. The state on
Lecture 7: The Scaling Theory of Conductance
Part I I
Last time, we studied localization and conductance in one dimension using arguments about
the scaling behavior of systems with random potentials. In this lecture, we will extend those
arguments to hig
Lecture 9: Superconductor Diamagnetism
In this lecture, we will apply linear response theory to the diamagnetism of a clean BCS super
conductor.
9.1
Clean BCS Superconductor Diamagnetism at T = 0
9.1.1
General Considerations
Based on symmetry arguments, i
LECTURE V
Continued discussion on Kubo formula:
Sanity Check with a random potential :
V (r)V (r ) = V02 (r r )
1
(q, ) =
11
=
dteit eiq.(rr ) < 0|[jp (r, t), jp (r , t)]|0 >
d(rr
dr
dteit eiq.(rr ) < 0|[jp (r, t), jp (r , t)]|0 >
dr
Where the bar in the