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) What is the differential equation that describes the motion of an electron in a diffusive metal? (Newton's law)

(b) What is the impulse response function that solves this differential equation? Sketch the impulse response function.

(c) How can you calculate the reflectivity of a diffusive metal from the impulse response function? Plot the reflectivity as a function of the frequency.

Problem 3
The piezo-thermal conductivity describes how stress induces changes in the thermal conductivity. The stress changes the arrangement of the atoms in the crystal.

(a) The thermal conductivity has two contributions that are typically calculated separately. What are these two contributions?

(b) How can the stress lead to a change in the thermal conductivity? How could this be calculated?

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.