Problem 1
What are Shubnikov-de Haas oscillations? Why do they occur? What other quantities exhibit oscillations as the magnetic field is varied? How can the oscillations be used to experimentally determine the Fermi surface of a metal?

Problem 2
(a) How is an impulse response function related to the generalized susceptibility?

(b) Explain how you can calculate the dielectric function of some material theoretically, how you could measure it experimentally, and how you could check it with the Kramers-Kronig relations.

(c) Draw the dielectric function for a metal.

Problem 3
A metal-insulator transition can be induced by electron-electron interactions.

(a) Explain why electron-electron interactions are difficult to describe.

(b) A simple model for electron-electron interactions is electron screening. Explain what screening is and how it can be used to explain a Mott transition.

(c) Single electron effects are another simple way to include electron-electron interactions. Explain the single-electron charging effect.

Problem 4
The pyroelectric coefficient describes how the polarization of a crystal changes as the temperature changes.

(a) Assume Landau's theory of a second order phase transition can be used to describe polarization of the crystal. Sketch the pyroelectric coefficient as a function of temperature.

(b) If you measured the pryoelectric coefficient as a function of temperature and the electric susceptibilty as a function of temperature you would be able to predict the specific heat as a function of temperature. Explain how this is possible.