Week 1

Lecture 15, 18 March, 10.00-12.00, FL51

Electrodynamics of conductors. Skin effect.
Plasma oscillations.
Screening of the Coulomb interaction.

Reading

A&M: Chapter 1, 16, 17 (p. 337-342).

Review questions

1. What is the condition for propagation of electromagnetic waves in conductors. Give estimate for the plasma frequency for typical metals.
2. What is the skin effect? Derive formula for the skin depth in low- and high-frequency limits.
3. What is the plasma oscillation?
4. Discuss static screening of electron-electron Coulomb interaction. Derive formula for the electron dielectric function in Thomas-Fermi approximation. What is the form of the screened Coulomb potential? What is the screening radius?

Home task

1. A&M: problem 17.3(a,b).

Lecture 16, 21 March, 13.15-15.00, FL51

More about screening of the Coulomb interaction: exchange energy.
Dynamics of ions. Phonon-induced attraction among electrons.
Fermi liquid theory.

Reading

A&M: Chapter 17 (p. 330-337, 345-351), 26 (p. 512-519),

Review questions

1. Describe the Hartry-Fock approximation. What is the exchange energy?
2. Discuss dynamics of bare ions. Derive formula for the dielectric function of bare ions and discuss the plasma oscillations. What is the ion plasma frequency? Compare it with the electron plasma frequency.
3. Discuss dynamics of ions and electrons within the Jellium model. What is the dispersion law of the collective mode? What is this mode, why is it different from the plasma oscillation? Derive formula for the sound velocity.
4. Discuss total dielectric function of the electrons and ions. Focus on the sign of the screened Coulomb potential, explain the mechanism of electron-electron attraction.
5. What is Fermi liquid? Explain the concept of quasiparticle, what is the role of the Fermi statistics? Estimate a quasiparticle lifetime near the Fermi surface.

Home task